Podcast
Questions and Answers
What is the value of $N$ in the equation $\frac{35}{N} + \frac{35}{N} = \frac{53}{22} + \frac{53}{22}$?
What is the value of $N$ in the equation $\frac{35}{N} + \frac{35}{N} = \frac{53}{22} + \frac{53}{22}$?
- 22 (correct)
- 70
- 35
- 53
Given the equation $\frac{_5}{10} + \frac{_9}{22} = R$, what is the value of $R$?
Given the equation $\frac{_5}{10} + \frac{_9}{22} = R$, what is the value of $R$?
- $\frac{14}{220}$
- $\frac{14}{32}$
- $\frac{5}{22}$
- $\frac{7}{11}$ (correct)
If $\frac{36}{36} - \frac{_6}{20} = \frac{30}{60}$ what number is represented by the blank space?
If $\frac{36}{36} - \frac{_6}{20} = \frac{30}{60}$ what number is represented by the blank space?
- 30 (correct)
- 6
- 5
- 20
What is the value of $FO$ if $\frac{_7}{13} - \frac{_4}{13} = FO$?
What is the value of $FO$ if $\frac{_7}{13} - \frac{_4}{13} = FO$?
Given the equation $\frac{15}{40} - \frac{_}{40} = \frac{_9}{19} - \frac{_5}{19}$, what is the missing number?
Given the equation $\frac{15}{40} - \frac{_}{40} = \frac{_9}{19} - \frac{_5}{19}$, what is the missing number?
A farmer planted half of their farm with maize. What fraction of the farm was not planted with maize?
A farmer planted half of their farm with maize. What fraction of the farm was not planted with maize?
Zawadi walked $\frac{4}{5}$ of her journey. What fraction of her journey remained?
Zawadi walked $\frac{4}{5}$ of her journey. What fraction of her journey remained?
What is the result of the following calculation? $6\frac{3}{4} \times 3$
What is the result of the following calculation? $6\frac{3}{4} \times 3$
What is the result of the following calculation? $2\frac{1}{7} \times \frac{2}{9}$
What is the result of the following calculation? $2\frac{1}{7} \times \frac{2}{9}$
In the rectangle method of multiplying fractions, what does the number of twice-shaded small rectangles represent?
In the rectangle method of multiplying fractions, what does the number of twice-shaded small rectangles represent?
When using the rectangle method to visualize $\frac{1}{3} \times \frac{1}{4}$, into how many total small rectangles is the rectangle divided?
When using the rectangle method to visualize $\frac{1}{3} \times \frac{1}{4}$, into how many total small rectangles is the rectangle divided?
With reference to multiplying fractions, what does subdividing a rectangle into horizontal and vertical rectangles represent?
With reference to multiplying fractions, what does subdividing a rectangle into horizontal and vertical rectangles represent?
In the rectangle method, if a rectangle is subdivided into 5 horizontal and 6 vertical sections, what multiplication problem is being visually represented?
In the rectangle method, if a rectangle is subdivided into 5 horizontal and 6 vertical sections, what multiplication problem is being visually represented?
What does the total number of small rectangles represent in rectangle method?
What does the total number of small rectangles represent in rectangle method?
How do you represent $\frac{2}{3}$ using the rectangle method?
How do you represent $\frac{2}{3}$ using the rectangle method?
If you shade the first vertical and horizontal rectangle, what does that represent?
If you shade the first vertical and horizontal rectangle, what does that represent?
What is the first step of visualizing fractions multiplication using the rectangle method?
What is the first step of visualizing fractions multiplication using the rectangle method?
What value does the following expression result in using the rectangle method: $\frac{2}{5} \times \frac{1}{4}$?
What value does the following expression result in using the rectangle method: $\frac{2}{5} \times \frac{1}{4}$?
$\frac{4}{8} \times \frac{2}{2}$ is equal to what value?
$\frac{4}{8} \times \frac{2}{2}$ is equal to what value?
Which of the following steps is crucial when adding fractions with different denominators?
Which of the following steps is crucial when adding fractions with different denominators?
Suppose you want to add $\frac{1}{3}$ and $\frac{1}{6}$. What would be a suitable common denominator?
Suppose you want to add $\frac{1}{3}$ and $\frac{1}{6}$. What would be a suitable common denominator?
Which of the following fractions is the largest?
Which of the following fractions is the largest?
What is the result of $\frac{2}{5} + \frac{3}{10}$?
What is the result of $\frac{2}{5} + \frac{3}{10}$?
You have $\frac{1}{2}$ of a pizza and your friend has $\frac{2}{8}$ of a pizza. If you combine them, how much pizza do you have?
You have $\frac{1}{2}$ of a pizza and your friend has $\frac{2}{8}$ of a pizza. If you combine them, how much pizza do you have?
Arrange the following fractions in descending order: $\frac{1}{2}$, $\frac{3}{8}$, $\frac{1}{4}$.
Arrange the following fractions in descending order: $\frac{1}{2}$, $\frac{3}{8}$, $\frac{1}{4}$.
Which statement accurately describes the process of finding a common denominator?
Which statement accurately describes the process of finding a common denominator?
If you have $\frac{2}{3}$ of a chocolate bar and you give away $\frac{1}{6}$ of the whole bar, how much of the chocolate bar do you have left?
If you have $\frac{2}{3}$ of a chocolate bar and you give away $\frac{1}{6}$ of the whole bar, how much of the chocolate bar do you have left?
What is the first step in comparing fractions with different denominators?
What is the first step in comparing fractions with different denominators?
Which of the following expressions is correctly rewritten with a common denominator, ready for addition?
Which of the following expressions is correctly rewritten with a common denominator, ready for addition?
If you have two fractions, $\frac{3}{8}$ and $\frac{3}{5}$, and you need to determine which one is larger without using a visual aid, which method would be most efficient?
If you have two fractions, $\frac{3}{8}$ and $\frac{3}{5}$, and you need to determine which one is larger without using a visual aid, which method would be most efficient?
Consider two fractions, $\frac{a}{b}$ and $\frac{c}{d}$, where a, b, c, and d are positive integers. If $ad > bc$, what can be concluded about the relationship between the two fractions?
Consider two fractions, $\frac{a}{b}$ and $\frac{c}{d}$, where a, b, c, and d are positive integers. If $ad > bc$, what can be concluded about the relationship between the two fractions?
You are comparing $\frac{5}{12}$ and $\frac{7}{15}$. Which of the following statements accurately describes the process and the result of comparing these fractions?
You are comparing $\frac{5}{12}$ and $\frac{7}{15}$. Which of the following statements accurately describes the process and the result of comparing these fractions?
Which of the following pairs of fractions is ordered from least to greatest?
Which of the following pairs of fractions is ordered from least to greatest?
Consider the fractions $\frac{x}{7}$ and $\frac{5}{y}$. If $\frac{x}{7} > \frac{5}{y}$, which of the following relationships must be true?
Consider the fractions $\frac{x}{7}$ and $\frac{5}{y}$. If $\frac{x}{7} > \frac{5}{y}$, which of the following relationships must be true?
Without calculating the exact values, determine which fraction is greater: $\frac{101}{200}$ or $\frac{51}{100}$?
Without calculating the exact values, determine which fraction is greater: $\frac{101}{200}$ or $\frac{51}{100}$?
You need to compare two fractions, $\frac{a}{a+1}$ and $\frac{a+1}{a+2}$, where 'a' is a positive integer. Which fraction is always smaller?
You need to compare two fractions, $\frac{a}{a+1}$ and $\frac{a+1}{a+2}$, where 'a' is a positive integer. Which fraction is always smaller?
Which scenario requires comparing fractions with different denominators to solve the problem?
Which scenario requires comparing fractions with different denominators to solve the problem?
If $\frac{p}{q} < \frac{r}{s}$, and both fractions are positive, what can you definitively say about the relationship between $ps$ and $qr$?
If $\frac{p}{q} < \frac{r}{s}$, and both fractions are positive, what can you definitively say about the relationship between $ps$ and $qr$?
A baker uses $\frac{2}{5}$ of a bag of flour for cakes and $\frac{1}{3}$ of the bag for cookies. What fraction of the bag of flour did the baker use in total?
A baker uses $\frac{2}{5}$ of a bag of flour for cakes and $\frac{1}{3}$ of the bag for cookies. What fraction of the bag of flour did the baker use in total?
Sarah spends $\frac{1}{4}$ of her weekend reading and $\frac{3}{8}$ of her weekend on chores. What fraction of her weekend is spent on reading and chores combined?
Sarah spends $\frac{1}{4}$ of her weekend reading and $\frac{3}{8}$ of her weekend on chores. What fraction of her weekend is spent on reading and chores combined?
A construction worker uses $\frac{2}{7}$ of a truckload of sand for one job and $\frac{3}{14}$ of the same truckload for another job. What fraction of the truckload of sand was used for both jobs?
A construction worker uses $\frac{2}{7}$ of a truckload of sand for one job and $\frac{3}{14}$ of the same truckload for another job. What fraction of the truckload of sand was used for both jobs?
A recipe calls for $\frac{1}{3}$ cup of sugar and $\frac{2}{5}$ cup of flour. If a baker wants to make the recipe, what is the total amount of sugar and flour needed?
A recipe calls for $\frac{1}{3}$ cup of sugar and $\frac{2}{5}$ cup of flour. If a baker wants to make the recipe, what is the total amount of sugar and flour needed?
A painter mixed $\frac{2}{5}$ of a gallon of blue paint with $\frac{1}{4}$ of a gallon of yellow paint. How many gallons of paint does the painter have in total?
A painter mixed $\frac{2}{5}$ of a gallon of blue paint with $\frac{1}{4}$ of a gallon of yellow paint. How many gallons of paint does the painter have in total?
In the example provided, what common denominator is chosen when adding $\frac{2}{3} + \frac{2}{3}$?
In the example provided, what common denominator is chosen when adding $\frac{2}{3} + \frac{2}{3}$?
Based on the examples, what is the result of adding $\frac{1}{4} + \frac{2}{4}$?
Based on the examples, what is the result of adding $\frac{1}{4} + \frac{2}{4}$?
If you are adding two fractions with the same denominator, which part of the fraction do you add together?
If you are adding two fractions with the same denominator, which part of the fraction do you add together?
If $\frac{a}{c} + \frac{b}{c} = \frac{d}{c}$, which of the following is true?
If $\frac{a}{c} + \frac{b}{c} = \frac{d}{c}$, which of the following is true?
What is the simplified result of $\frac{2}{4} + \frac{2}{4}$?
What is the simplified result of $\frac{2}{4} + \frac{2}{4}$?
Consider the operation: $\frac{5}{x} + \frac{5}{x}$. Which of the following expressions represents the result?
Consider the operation: $\frac{5}{x} + \frac{5}{x}$. Which of the following expressions represents the result?
What is the sum of $\frac{x}{y} + \frac{x}{y}$?
What is the sum of $\frac{x}{y} + \frac{x}{y}$?
If $\frac{a}{b} + \frac{c}{b} = \frac{5}{b}$, which of the following statements must be true?
If $\frac{a}{b} + \frac{c}{b} = \frac{5}{b}$, which of the following statements must be true?
If you have $\frac{1}{5}$ of a pizza and get another $\frac{3}{5}$, how much of the pizza do you have in total?
If you have $\frac{1}{5}$ of a pizza and get another $\frac{3}{5}$, how much of the pizza do you have in total?
Which of the following fractions is equivalent to $\frac{1}{7}$?
Which of the following fractions is equivalent to $\frac{1}{7}$?
Which of the following completes the sequence: $\frac{1}{4}, \frac{2}{8}, \underline{\hspace{1cm}}, \frac{4}{16}$?
Which of the following completes the sequence: $\frac{1}{4}, \frac{2}{8}, \underline{\hspace{1cm}}, \frac{4}{16}$?
What fraction is equivalent to $\frac{3}{5}$ and has a denominator of 15?
What fraction is equivalent to $\frac{3}{5}$ and has a denominator of 15?
Which of the following fractions is NOT equivalent to $\frac{9}{48}$?
Which of the following fractions is NOT equivalent to $\frac{9}{48}$?
What is the result of $6\frac{3}{4} \times 2$?
What is the result of $6\frac{3}{4} \times 2$?
Determine the value of the following expression: $\frac{2}{3} \times 9 = $
Determine the value of the following expression: $\frac{2}{3} \times 9 = $
What value completes the following sequence of equivalent fractions: $\frac{3}{16}, \frac{6}{32}, \frac{9}{48}, \frac{\underline{\hspace{1cm}}}{64}$?
What value completes the following sequence of equivalent fractions: $\frac{3}{16}, \frac{6}{32}, \frac{9}{48}, \frac{\underline{\hspace{1cm}}}{64}$?
Given the expression $\frac{5}{6} \times 30$, what is the resulting value?
Given the expression $\frac{5}{6} \times 30$, what is the resulting value?
If $\frac{A}{B} = \frac{5}{8}$, which of the following statements must be true?
If $\frac{A}{B} = \frac{5}{8}$, which of the following statements must be true?
What is the outcome of the expression $\frac{1}{8} \times 24$?
What is the outcome of the expression $\frac{1}{8} \times 24$?
Evaluate the expression $2\frac{1}{7} \times \frac{1}{9}$
Evaluate the expression $2\frac{1}{7} \times \frac{1}{9}$
Calculate: $1\frac{2}{5} \times \frac{2}{5}$
Calculate: $1\frac{2}{5} \times \frac{2}{5}$
Determine the result of the following expression: $1\frac{1}{2} \times \frac{2}{6}$
Determine the result of the following expression: $1\frac{1}{2} \times \frac{2}{6}$
What is the result when $\frac{5}{9}$ is multiplied by 18?
What is the result when $\frac{5}{9}$ is multiplied by 18?
What is the value of $2\frac{1}{2} \times \frac{1}{36}$?
What is the value of $2\frac{1}{2} \times \frac{1}{36}$?
What is the result of multiplying a fraction by its reciprocal?
What is the result of multiplying a fraction by its reciprocal?
If $x$ and $y$ are non-zero numbers, then $\frac{5}{x} \times \frac{x}{5}$ is equal to what?
If $x$ and $y$ are non-zero numbers, then $\frac{5}{x} \times \frac{x}{5}$ is equal to what?
What happens to the value of a fraction when you multiply both the numerator and the denominator by the same whole number greater than 1?
What happens to the value of a fraction when you multiply both the numerator and the denominator by the same whole number greater than 1?
Which of the following expressions is equivalent to tripling the fraction $\frac{a}{b}$?
Which of the following expressions is equivalent to tripling the fraction $\frac{a}{b}$?
If the product of two fractions is $\frac{1}{2}$ and one of the fractions is $\frac{2}{5}$, what is the other fraction?
If the product of two fractions is $\frac{1}{2}$ and one of the fractions is $\frac{2}{5}$, what is the other fraction?
Select the option that correctly expresses $\frac{7}{9}$ multiplied by $\frac{3}{3}$.
Select the option that correctly expresses $\frac{7}{9}$ multiplied by $\frac{3}{3}$.
What happens when you multiply a fraction by a fraction less than 1?
What happens when you multiply a fraction by a fraction less than 1?
Consider the expression $\frac{a}{b} \times \frac{c}{d}$. If $a$, $b$, $c$, and $d$ are all positive integers and $c > d$, what must be true of the product compared to $\frac{a}{b}$?
Consider the expression $\frac{a}{b} \times \frac{c}{d}$. If $a$, $b$, $c$, and $d$ are all positive integers and $c > d$, what must be true of the product compared to $\frac{a}{b}$?
If you want to find half of $\frac{5}{7}$, which calculation should you perform?
If you want to find half of $\frac{5}{7}$, which calculation should you perform?
You have a recipe that calls for $\frac{2}{3}$ cup of flour, but you only want to make half of the recipe. How much flour do you need?
You have a recipe that calls for $\frac{2}{3}$ cup of flour, but you only want to make half of the recipe. How much flour do you need?
In the given example, why is 45 chosen as the common denominator when adding $\frac{2}{5}$ and $\frac{3}{9}$?
In the given example, why is 45 chosen as the common denominator when adding $\frac{2}{5}$ and $\frac{3}{9}$?
What operation is performed to convert $\frac{2}{5}$ to $\frac{18}{45}$ in the example?
What operation is performed to convert $\frac{2}{5}$ to $\frac{18}{45}$ in the example?
What is the simplified form of the fraction $\frac{33}{45}$?
What is the simplified form of the fraction $\frac{33}{45}$?
Suppose you are adding $\frac{a}{b} + \frac{c}{d}$, and you find that $b \times d = k$. Which of the following adjustments must you make to the fractions to add them?
Suppose you are adding $\frac{a}{b} + \frac{c}{d}$, and you find that $b \times d = k$. Which of the following adjustments must you make to the fractions to add them?
In the example, what is the result of adding the adjusted numerators once the fractions have a common denominator?
In the example, what is the result of adding the adjusted numerators once the fractions have a common denominator?
If you were to add $\frac{1}{4} + \frac{2}{7}$ using a similar approach to the example, what would be the common denominator?
If you were to add $\frac{1}{4} + \frac{2}{7}$ using a similar approach to the example, what would be the common denominator?
Following the method in the example, what would be the next step after finding the common denominator when adding $\frac{1}{3}$ and $\frac{2}{5}$?
Following the method in the example, what would be the next step after finding the common denominator when adding $\frac{1}{3}$ and $\frac{2}{5}$?
A baker has $2 rac{1}{2}$ cups of sugar and uses $\frac{2}{5}$ of it for a recipe. How many cups of sugar did the baker use?
A baker has $2 rac{1}{2}$ cups of sugar and uses $\frac{2}{5}$ of it for a recipe. How many cups of sugar did the baker use?
If you multiply $1\frac{2}{5}$ by $\frac{2}{5}$, what is the resulting fraction expressed in its simplest form?
If you multiply $1\frac{2}{5}$ by $\frac{2}{5}$, what is the resulting fraction expressed in its simplest form?
What is the value of the expression: $\frac{5}{9} \times 18$?
What is the value of the expression: $\frac{5}{9} \times 18$?
You have $2\frac{1}{7}$ of a pizza and you want to give $\frac{1}{9}$ of the entire pizza to each of your friends. How much of the pizza do you give away in total?
You have $2\frac{1}{7}$ of a pizza and you want to give $\frac{1}{9}$ of the entire pizza to each of your friends. How much of the pizza do you give away in total?
You have a board that is $6\frac{3}{4}$ meters long. You need to cut it into 3 equal pieces. How long will each piece be?
You have a board that is $6\frac{3}{4}$ meters long. You need to cut it into 3 equal pieces. How long will each piece be?
What conceptual step is being demonstrated by the transition from $\frac{3}{4}$ to $\frac{1}{2} + \frac{1}{4}$ in the context of fraction subtraction?
What conceptual step is being demonstrated by the transition from $\frac{3}{4}$ to $\frac{1}{2} + \frac{1}{4}$ in the context of fraction subtraction?
In the given example, what arithmetic operation is directly used after converting the fractions to have a common denominator?
In the given example, what arithmetic operation is directly used after converting the fractions to have a common denominator?
Using the diagrammatic approach, how does visualizing fractions help in understanding subtraction?
Using the diagrammatic approach, how does visualizing fractions help in understanding subtraction?
If a student understands that $\frac{3}{4} = \frac{2}{4} + \frac{1}{4}$, and needs to subtract $\frac{2}{4}$ from $\frac{3}{4}$, what does the decomposition of $\frac{3}{4}$ allow them to do more easily?
If a student understands that $\frac{3}{4} = \frac{2}{4} + \frac{1}{4}$, and needs to subtract $\frac{2}{4}$ from $\frac{3}{4}$, what does the decomposition of $\frac{3}{4}$ allow them to do more easily?
In the context of fraction subtraction, what is the purpose of finding a 'common denominator'?
In the context of fraction subtraction, what is the purpose of finding a 'common denominator'?
If you are subtracting $\frac{a}{b} - \frac{c}{d}$ and $b \neq d$, what is the initial step to solve correctly?
If you are subtracting $\frac{a}{b} - \frac{c}{d}$ and $b \neq d$, what is the initial step to solve correctly?
Consider the equation $\frac{5}{8} - \frac{1}{4} = x$. Which of the following steps is necessary to find the value of $x$?
Consider the equation $\frac{5}{8} - \frac{1}{4} = x$. Which of the following steps is necessary to find the value of $x$?
Suppose a problem requires you to calculate $\frac{7}{10} - \frac{2}{5}$. What would be the resulting fraction after performing the subtraction?
Suppose a problem requires you to calculate $\frac{7}{10} - \frac{2}{5}$. What would be the resulting fraction after performing the subtraction?
What is the value of $x$ in the following subtraction problem: $\frac{9}{12} - \frac{1}{3} = x$?
What is the value of $x$ in the following subtraction problem: $\frac{9}{12} - \frac{1}{3} = x$?
In the rectangle method, what does shading a certain number of horizontal rectangles represent when multiplying fractions?
In the rectangle method, what does shading a certain number of horizontal rectangles represent when multiplying fractions?
When using the rectangle method to multiply $\frac{3}{4} \times \frac{2}{3}$, what does the number of horizontally shaded rectangles initially represent?
When using the rectangle method to multiply $\frac{3}{4} \times \frac{2}{3}$, what does the number of horizontally shaded rectangles initially represent?
In the rectangle method for multiplying fractions, after shading both horizontally and vertically, how do you determine the numerator of the product?
In the rectangle method for multiplying fractions, after shading both horizontally and vertically, how do you determine the numerator of the product?
Using the rectangle method to solve $\frac{5}{8} \times \frac{3}{4}$, what is the significance of the total number of small rectangles in the entire rectangle?
Using the rectangle method to solve $\frac{5}{8} \times \frac{3}{4}$, what is the significance of the total number of small rectangles in the entire rectangle?
Consider using the rectangle method to visualize $\frac{a}{b} \times \frac{c}{d}$. What do the values 'b' and 'd' determine in the initial setup of the rectangle?
Consider using the rectangle method to visualize $\frac{a}{b} \times \frac{c}{d}$. What do the values 'b' and 'd' determine in the initial setup of the rectangle?
When using the rectangle method to multiply fractions, what does the act of subdividing the rectangle into smaller rectangles represent mathematically?
When using the rectangle method to multiply fractions, what does the act of subdividing the rectangle into smaller rectangles represent mathematically?
You're using the rectangle method to multiply two fractions. If you divide the rectangle into 5 horizontal sections and 7 vertical sections, what are you visually representing?
You're using the rectangle method to multiply two fractions. If you divide the rectangle into 5 horizontal sections and 7 vertical sections, what are you visually representing?
After completing the rectangle method for multiplying $\frac{3}{4}$ and $\frac{2}{5}$, you count the number of twice-shaded rectangles and find it to be 6. What does this number represent in the context of the problem?
After completing the rectangle method for multiplying $\frac{3}{4}$ and $\frac{2}{5}$, you count the number of twice-shaded rectangles and find it to be 6. What does this number represent in the context of the problem?
In the rectangle method, if the final answer is $\frac{15}{32}$, what does the number 32 represent?
In the rectangle method, if the final answer is $\frac{15}{32}$, what does the number 32 represent?
Suppose you are using the rectangle method to multiply fractions. If you shade 2 out of 5 columns and 3 out of 4 rows, which multiplication problem are you solving?
Suppose you are using the rectangle method to multiply fractions. If you shade 2 out of 5 columns and 3 out of 4 rows, which multiplication problem are you solving?
In the rectangle method, what geometric shapes are created by subdividing the initial rectangle?
In the rectangle method, what geometric shapes are created by subdividing the initial rectangle?
When using the rectangle method to multiply fractions, what does the shading of a horizontal rectangle represent?
When using the rectangle method to multiply fractions, what does the shading of a horizontal rectangle represent?
If a rectangle is divided into 5 horizontal sections and 7 vertical sections for fraction multiplication, what are the values of the denominators of the fractions being multiplied?
If a rectangle is divided into 5 horizontal sections and 7 vertical sections for fraction multiplication, what are the values of the denominators of the fractions being multiplied?
In the rectangle method, which part of the visual representation corresponds to the numerator of the resulting fraction after multiplication?
In the rectangle method, which part of the visual representation corresponds to the numerator of the resulting fraction after multiplication?
What does the total number of small rectangles within the whole rectangle represent in the rectangle method of multiplying fractions?
What does the total number of small rectangles within the whole rectangle represent in the rectangle method of multiplying fractions?
Using the rectangle method, how would you visually represent the multiplication problem $\frac{2}{5} \times \frac{3}{4}$?
Using the rectangle method, how would you visually represent the multiplication problem $\frac{2}{5} \times \frac{3}{4}$?
If you shade the first two horizontal rectangles and the first vertical rectangle in the grid, what multiplication problem is being visually represented?
If you shade the first two horizontal rectangles and the first vertical rectangle in the grid, what multiplication problem is being visually represented?
Why is it helpful to visualize fraction multiplication using the rectangle method?
Why is it helpful to visualize fraction multiplication using the rectangle method?
A rectangle is divided into horizontal and vertical rectangles to represent $\frac{1}{4} \times \frac{2}{3}$. How many small rectangles will be shaded twice?
A rectangle is divided into horizontal and vertical rectangles to represent $\frac{1}{4} \times \frac{2}{3}$. How many small rectangles will be shaded twice?
In Standard Four, students learned about the multiplication of fractions with the same denominator.
In Standard Four, students learned about the multiplication of fractions with the same denominator.
This chapter will cover addition and subtraction of fractions with different denominators.
This chapter will cover addition and subtraction of fractions with different denominators.
Competence in fractions is only useful for solving mathematical problems in school.
Competence in fractions is only useful for solving mathematical problems in school.
Fractions are not useful in medical prescriptions.
Fractions are not useful in medical prescriptions.
The chapter includes a revision exercise.
The chapter includes a revision exercise.
The revision exercise includes addition of fractions.
The revision exercise includes addition of fractions.
Question 9 in the revision exercise uses the division of fractions.
Question 9 in the revision exercise uses the division of fractions.
To subtract two fractions, you always subtract the numerators and denominators separately.
To subtract two fractions, you always subtract the numerators and denominators separately.
The result of subtracting $\frac{7}{9}$ from $\frac{6}{6}$ equals $\frac{47}{63}$.
The result of subtracting $\frac{7}{9}$ from $\frac{6}{6}$ equals $\frac{47}{63}$.
To find out how many litres of milk the grandmother drinks in 6 days, you should divide $\frac{3}{4}$ by 6.
To find out how many litres of milk the grandmother drinks in 6 days, you should divide $\frac{3}{4}$ by 6.
$\frac{18}{4}$ is an improper fraction.
$\frac{18}{4}$ is an improper fraction.
$\frac{18}{4}$ is equivalent to $4\frac{1}{2}$.
$\frac{18}{4}$ is equivalent to $4\frac{1}{2}$.
$ rac{1}{2}$ is greater than $ rac{1}{4}$.
$ rac{1}{2}$ is greater than $ rac{1}{4}$.
$ rac{1}{3}$ is less than $ rac{1}{5}$.
$ rac{1}{3}$ is less than $ rac{1}{5}$.
$ rac{1}{2}$ represents a larger portion than $ rac{1}{3}$.
$ rac{1}{2}$ represents a larger portion than $ rac{1}{3}$.
$ rac{1}{11}$ represents a bigger portion than $ rac{1}{10}$.
$ rac{1}{11}$ represents a bigger portion than $ rac{1}{10}$.
$ rac{1}{4}$ is equivalent to $0.40$.
$ rac{1}{4}$ is equivalent to $0.40$.
Subtracting fractions always results in a larger fraction.
Subtracting fractions always results in a larger fraction.
To subtract fractions, they must have different denominators.
To subtract fractions, they must have different denominators.
The result of $\frac{3}{4} - \frac{1}{2}$ is $\frac{1}{4}$.
The result of $\frac{3}{4} - \frac{1}{2}$ is $\frac{1}{4}$.
$\frac{3}{4}$ is equivalent to $\frac{6}{8}$.
$\frac{3}{4}$ is equivalent to $\frac{6}{8}$.
A diagram can be used to visualize fraction subtraction.
A diagram can be used to visualize fraction subtraction.
When subtracting fractions with the same denominator, you only subtract the denominators.
When subtracting fractions with the same denominator, you only subtract the denominators.
The fraction $\frac{1}{4}$ is larger than $\frac{1}{2}$.
The fraction $\frac{1}{4}$ is larger than $\frac{1}{2}$.
The numerator is the bottom number in a fraction.
The numerator is the bottom number in a fraction.
Subtracting $\frac{1}{2}$ from $\frac{3}{4}$ is the same as subtracting $\frac{2}{4}$ from $\frac{3}{4}$.
Subtracting $\frac{1}{2}$ from $\frac{3}{4}$ is the same as subtracting $\frac{2}{4}$ from $\frac{3}{4}$.
It is possible to get a zero result when you subtract two fractions.
It is possible to get a zero result when you subtract two fractions.
The result of $\frac{5}{6} - \frac{4}{7}$ is equal to $\frac{11}{42}$.
The result of $\frac{5}{6} - \frac{4}{7}$ is equal to $\frac{11}{42}$.
The result of $\frac{8}{9} - \frac{2}{6}$ is equal to $\frac{4}{3}$.
The result of $\frac{8}{9} - \frac{2}{6}$ is equal to $\frac{4}{3}$.
The result of $\frac{4}{8} - \frac{2}{10}$ equals $\frac{1}{3}$.
The result of $\frac{4}{8} - \frac{2}{10}$ equals $\frac{1}{3}$.
$\frac{1}{2} - \frac{1}{3}$ is equal to $\frac{1}{6}$.
$\frac{1}{2} - \frac{1}{3}$ is equal to $\frac{1}{6}$.
The result of $\frac{15}{20} - \frac{14}{40}$ is equal to $\frac{11}{20}$.
The result of $\frac{15}{20} - \frac{14}{40}$ is equal to $\frac{11}{20}$.
The result of $\frac{25}{30} - \frac{13}{90}$ is equal to $\frac{2}{3}$.
The result of $\frac{25}{30} - \frac{13}{90}$ is equal to $\frac{2}{3}$.
$\frac{3}{7} - \frac{2}{14}$ is equal to $\frac{1}{7}$.
$\frac{3}{7} - \frac{2}{14}$ is equal to $\frac{1}{7}$.
$\frac{6}{8} - \frac{2}{5}$ is equal to $\frac{7}{20}$.
$\frac{6}{8} - \frac{2}{5}$ is equal to $\frac{7}{20}$.
$\frac{54}{60} - \frac{9}{20}$ is equal to $\frac{9}{20}$.
$\frac{54}{60} - \frac{9}{20}$ is equal to $\frac{9}{20}$.
The result of $\frac{5}{6} - \frac{2}{4}$ equates to $\frac{1}{3}$.
The result of $\frac{5}{6} - \frac{2}{4}$ equates to $\frac{1}{3}$.
A proper fraction has a numerator smaller than its denominator.
A proper fraction has a numerator smaller than its denominator.
A mixed fraction consists of a whole number and an improper fraction.
A mixed fraction consists of a whole number and an improper fraction.
$\frac{15}{16}$ is an example of an improper fraction.
$\frac{15}{16}$ is an example of an improper fraction.
$5\frac{2}{3}$ is an example of a mixed fraction
$5\frac{2}{3}$ is an example of a mixed fraction
$\frac{4}{9}$ is a proper fraction.
$\frac{4}{9}$ is a proper fraction.
A mixed number is obtained when an improper fraction is simplified.
A mixed number is obtained when an improper fraction is simplified.
The fraction $\frac{2}{3}$ is an improper fraction.
The fraction $\frac{2}{3}$ is an improper fraction.
The fraction $\frac{7}{2}$ is an example of a proper fraction.
The fraction $\frac{7}{2}$ is an example of a proper fraction.
The number 5$\frac{1}{2}$ is a mixed number.
The number 5$\frac{1}{2}$ is a mixed number.
An improper fraction can be simplified into a mixed number.
An improper fraction can be simplified into a mixed number.
1/7 is equivalent to 2/14.
1/7 is equivalent to 2/14.
Multiplying the denominator of a fraction by a number will always result in an equivalent fraction.
Multiplying the denominator of a fraction by a number will always result in an equivalent fraction.
3/33 is an equivalent fraction to 1/11.
3/33 is an equivalent fraction to 1/11.
The fraction 1/4 is equivalent to 4/4.
The fraction 1/4 is equivalent to 4/4.
To find an equivalent fraction, you can only multiply the numerator and denominator.
To find an equivalent fraction, you can only multiply the numerator and denominator.
The fraction 5/40 simplifies to 1/8.
The fraction 5/40 simplifies to 1/8.
Equivalent fractions represent the same portion of a whole.
Equivalent fractions represent the same portion of a whole.
If two fractions have the same denominator, they are always equivalent.
If two fractions have the same denominator, they are always equivalent.
Subtracting $\frac{1}{2}$ from $\frac{3}{4}$ results in $\frac{1}{4}$.
Subtracting $\frac{1}{2}$ from $\frac{3}{4}$ results in $\frac{1}{4}$.
The result of $\frac{3}{4} - \frac{1}{2}$ is equivalent to $\frac{2}{4}$.
The result of $\frac{3}{4} - \frac{1}{2}$ is equivalent to $\frac{2}{4}$.
$\frac{3}{4}$ minus $\frac{2}{4}$ equals $\frac{1}{4}$.
$\frac{3}{4}$ minus $\frac{2}{4}$ equals $\frac{1}{4}$.
To subtract $\frac{1}{2}$ from $\frac{3}{4}$, you must first make the denominators the same.
To subtract $\frac{1}{2}$ from $\frac{3}{4}$, you must first make the denominators the same.
When adding fractions with the different denominators, you can add the numerators before finding a common denominator.
When adding fractions with the different denominators, you can add the numerators before finding a common denominator.
The sum of $\frac{2}{3} + \frac{2}{3}$ is equal to $\frac{4}{3}$.
The sum of $\frac{2}{3} + \frac{2}{3}$ is equal to $\frac{4}{3}$.
To find a common denominator, you only need to multiply the two denominators together.
To find a common denominator, you only need to multiply the two denominators together.
$\frac{4}{4}$ is equal to 1.
$\frac{4}{4}$ is equal to 1.
$\frac{2}{4}$ is in its simplest form.
$\frac{2}{4}$ is in its simplest form.
When adding fractions, you should always simplify the result.
When adding fractions, you should always simplify the result.
$\frac{1}{3} + \frac{2}{3} = \frac{3}{6}$.
$\frac{1}{3} + \frac{2}{3} = \frac{3}{6}$.
$\frac{2}{5}$ is larger than $\frac{4}{5}$.
$\frac{2}{5}$ is larger than $\frac{4}{5}$.
If a fraction's numerator and denominator are the same, the fraction equals zero.
If a fraction's numerator and denominator are the same, the fraction equals zero.
The expression $7 \frac{3}{5} \times 1 \frac{1}{4}$ is equivalent to $9 \frac{1}{2}$
The expression $7 \frac{3}{5} \times 1 \frac{1}{4}$ is equivalent to $9 \frac{1}{2}$
The expression $2 \frac{0}{4} \times \frac{3}{1}$ is equivalent to $6 \frac{1}{3}$
The expression $2 \frac{0}{4} \times \frac{3}{1}$ is equivalent to $6 \frac{1}{3}$
The product of $\frac{3}{11}$ and $6 \frac{3}{7}$ is less than 2
The product of $\frac{3}{11}$ and $6 \frac{3}{7}$ is less than 2
The expression $1 \frac{3}{13} \times \frac{1}{3}$ is equal to $\frac{16}{39}$
The expression $1 \frac{3}{13} \times \frac{1}{3}$ is equal to $\frac{16}{39}$
The expression $4 \frac{0}{20} \times \frac{1}{1}$ is equivalent to $4.5$
The expression $4 \frac{0}{20} \times \frac{1}{1}$ is equivalent to $4.5$
The fraction $\frac{16}{9}$ is a proper fraction.
The fraction $\frac{16}{9}$ is a proper fraction.
Fractions with the same numerator and denominator are always equivalent to 1.
Fractions with the same numerator and denominator are always equivalent to 1.
Multiplying a fraction by $\frac{2}{2}$ will change its value.
Multiplying a fraction by $\frac{2}{2}$ will change its value.
To find an equivalent fraction for $\frac{1}{2}$, only the numerator should be multiplied by a certain number.
To find an equivalent fraction for $\frac{1}{2}$, only the numerator should be multiplied by a certain number.
The fraction $\frac{4}{4}$ is equivalent to the fraction $\frac{8}{16}$.
The fraction $\frac{4}{4}$ is equivalent to the fraction $\frac{8}{16}$.
If a fraction is multiplied by $\frac{0}{1}$, its value remains unchanged.
If a fraction is multiplied by $\frac{0}{1}$, its value remains unchanged.
The product of $\frac{5}{8}$ and $\frac{3}{4}$ is equal to $\frac{15}{32}$.
The product of $\frac{5}{8}$ and $\frac{3}{4}$ is equal to $\frac{15}{32}$.
The equation $\frac{2}{5} \times \frac{3}{7} = \frac{6}{35}$ is correctly calculated.
The equation $\frac{2}{5} \times \frac{3}{7} = \frac{6}{35}$ is correctly calculated.
The expression $\frac{2}{9} \times \frac{6}{7} = \frac{12}{63}$, which simplifies to $\frac{4}{21}$.
The expression $\frac{2}{9} \times \frac{6}{7} = \frac{12}{63}$, which simplifies to $\frac{4}{21}$.
$\frac{5}{8} \times \frac{5}{10}$ equals $\frac{1}{4}$.
$\frac{5}{8} \times \frac{5}{10}$ equals $\frac{1}{4}$.
The result of $\frac{13}{15} \times \frac{2}{4}$ is equal to $\frac{26}{15}$.
The result of $\frac{13}{15} \times \frac{2}{4}$ is equal to $\frac{26}{15}$.
$\frac{7}{12} \times \frac{1}{6} = \frac{7}{72}$ is a true statement.
$\frac{7}{12} \times \frac{1}{6} = \frac{7}{72}$ is a true statement.
$\frac{4}{8} \times \frac{6}{10}$ simplifies to $\frac{3}{10}$.
$\frac{4}{8} \times \frac{6}{10}$ simplifies to $\frac{3}{10}$.
The expression $\frac{1}{1} \times \frac{2}{2}$ equals $\frac{1}{4}$.
The expression $\frac{1}{1} \times \frac{2}{2}$ equals $\frac{1}{4}$.
The expression $\frac{2}{6} \times \frac{7}{9}$ is equal to $\frac{14}{54}$, which simplifies to $\frac{7}{27}$.
The expression $\frac{2}{6} \times \frac{7}{9}$ is equal to $\frac{14}{54}$, which simplifies to $\frac{7}{27}$.
For any non-zero number $x$, $x \times \frac{1}{x}$ always equals 1.
For any non-zero number $x$, $x \times \frac{1}{x}$ always equals 1.
The fractions $\frac{2}{14}$, $\frac{3}{21}$, and $\frac{4}{28}$ are all equivalent to $\frac{1}{7}$.
The fractions $\frac{2}{14}$, $\frac{3}{21}$, and $\frac{4}{28}$ are all equivalent to $\frac{1}{7}$.
The fractions $\frac{2}{22}$, $\frac{3}{33}$, and $\frac{5}{55}$ are equivalent to $\frac{1}{11}$, but $\frac{4}{45}$ is also equivalent.
The fractions $\frac{2}{22}$, $\frac{3}{33}$, and $\frac{5}{55}$ are equivalent to $\frac{1}{11}$, but $\frac{4}{45}$ is also equivalent.
The fraction $\frac{1}{9}$ is equivalent to $\frac{2}{18}$, $\frac{3}{27}$, and $\frac{4}{36}$.
The fraction $\frac{1}{9}$ is equivalent to $\frac{2}{18}$, $\frac{3}{27}$, and $\frac{4}{36}$.
The fraction $\frac{1}{15}$ can be expressed equivalently as $\frac{3}{45}$, $\frac{5}{75}$ and $\frac{8}{120}$.
The fraction $\frac{1}{15}$ can be expressed equivalently as $\frac{3}{45}$, $\frac{5}{75}$ and $\frac{8}{120}$.
The fraction $\frac{1}{4}$ is equivalent to $\frac{5}{20}$, $\frac{6}{24}$, and $\frac{9}{36}$.
The fraction $\frac{1}{4}$ is equivalent to $\frac{5}{20}$, $\frac{6}{24}$, and $\frac{9}{36}$.
To complete the sequence $\frac{1}{4}$, $\frac{2}{8}$, ___, $\frac{4}{16}$, the missing fraction is $\frac{3}{9}$.
To complete the sequence $\frac{1}{4}$, $\frac{2}{8}$, ___, $\frac{4}{16}$, the missing fraction is $\frac{3}{9}$.
Given the sequence $\frac{1}{8}$, $\frac{2}{16}$, ___, ___, $\frac{5}{40}$, the missing fractions are $\frac{3}{24}$ and $\frac{4}{32}$.
Given the sequence $\frac{1}{8}$, $\frac{2}{16}$, ___, ___, $\frac{5}{40}$, the missing fractions are $\frac{3}{24}$ and $\frac{4}{32}$.
In the sequence $\frac{3}{5}$, ___, $\frac{9}{15}$, ___, the missing fractions are $\frac{5}{10}$ and $\frac{14}{20}$.
In the sequence $\frac{3}{5}$, ___, $\frac{9}{15}$, ___, the missing fractions are $\frac{5}{10}$ and $\frac{14}{20}$.
In the sequence $\frac{3}{16}$, ___, $\frac{9}{48}$, the missing fraction is equivalent to $\frac{4}{24}$.
In the sequence $\frac{3}{16}$, ___, $\frac{9}{48}$, the missing fraction is equivalent to $\frac{4}{24}$.
When subtracting fractions, if the denominators are already the same, you only need to subtract the numerators.
When subtracting fractions, if the denominators are already the same, you only need to subtract the numerators.
To subtract fractions with different denominators, you must first convert them to equivalent fractions with the lowest common multiple as the new numerator.
To subtract fractions with different denominators, you must first convert them to equivalent fractions with the lowest common multiple as the new numerator.
The result of $\frac{9}{4} - \frac{15}{30}$ is positive.
The result of $\frac{9}{4} - \frac{15}{30}$ is positive.
The expression $\frac{20}{22} - \frac{8}{11}$ simplifies to a fraction with a denominator of 11 after finding a common denominator and simplifying.
The expression $\frac{20}{22} - \frac{8}{11}$ simplifies to a fraction with a denominator of 11 after finding a common denominator and simplifying.
When multiplying fractions, you should first find a common denominator.
When multiplying fractions, you should first find a common denominator.
Multiplying $\frac{1}{3}$ by $\frac{1}{4}$ results in $\frac{2}{7}$.
Multiplying $\frac{1}{3}$ by $\frac{1}{4}$ results in $\frac{2}{7}$.
Subtracting $\frac{3}{5}$ from $\frac{7}{8}$ gives a result less than $\frac{1}{2}$.
Subtracting $\frac{3}{5}$ from $\frac{7}{8}$ gives a result less than $\frac{1}{2}$.
$\frac{28}{30} - \frac{24}{60}$ is equivalent to $\frac{4}{30}$ after simplification.
$\frac{28}{30} - \frac{24}{60}$ is equivalent to $\frac{4}{30}$ after simplification.
The result of $\frac{46}{50} - \frac{40}{100}$ is less than $\frac{1}{2}$.
The result of $\frac{46}{50} - \frac{40}{100}$ is less than $\frac{1}{2}$.
$\frac{18}{7} - \frac{19}{10}$ will result in a value greater than 1.
$\frac{18}{7} - \frac{19}{10}$ will result in a value greater than 1.
Flashcards
Fraction Subtraction (Same Denominator)
Fraction Subtraction (Same Denominator)
Subtracting two fractions with the same denominator means subtracting the numerators and keeping the same denominator.
Finding a Missing Part
Finding a Missing Part
To find the missing part, subtract the known part from the whole.
Meaning of 'Half'
Meaning of 'Half'
When a half of something is planted, the other half is not.
Calculating Survival Fraction
Calculating Survival Fraction
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Remaining Fraction of Journey
Remaining Fraction of Journey
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Fractions as Parts of a Whole
Fractions as Parts of a Whole
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Subtracting Fractions
Subtracting Fractions
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Multiplying a fraction by a whole number
Multiplying a fraction by a whole number
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Multiplying mixed numbers by fractions
Multiplying mixed numbers by fractions
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Multiplying a fraction by a fraction
Multiplying a fraction by a fraction
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What is 6 x 3/4?
What is 6 x 3/4?
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What is 2 1/7 x 1/5 ?
What is 2 1/7 x 1/5 ?
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Comparing Fractions Visually
Comparing Fractions Visually
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What is 1/2?
What is 1/2?
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What is 1/4?
What is 1/4?
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Larger Denominator
Larger Denominator
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What is 2/6?
What is 2/6?
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What is 2/5?
What is 2/5?
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Same Numerator, Smaller Denominator
Same Numerator, Smaller Denominator
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Visual Fraction Comparison
Visual Fraction Comparison
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Shaded Area and Size
Shaded Area and Size
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Descending Order
Descending Order
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Different Denominators
Different Denominators
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Common Denominator
Common Denominator
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Equivalent Fraction
Equivalent Fraction
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Numerator
Numerator
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Denominator
Denominator
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Scaling Fractions
Scaling Fractions
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Equivalent Fractions
Equivalent Fractions
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Lowest Common Denominator
Lowest Common Denominator
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Adding Fractions
Adding Fractions
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Multiplying Fractions
Multiplying Fractions
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Rectangle Method
Rectangle Method
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Example: (1/3) × (1/4)
Example: (1/3) × (1/4)
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Numerator (Rectangle Method)
Numerator (Rectangle Method)
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Denominator (Rectangle Method)
Denominator (Rectangle Method)
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Subdividing a Rectangle
Subdividing a Rectangle
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Fraction
Fraction
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Fraction Line
Fraction Line
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Creating Equivalent Fractions
Creating Equivalent Fractions
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Proper Fraction:
Proper Fraction:
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Improper Fraction
Improper Fraction
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Mixed Number
Mixed Number
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Simplifying fractions
Simplifying fractions
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Fractions of equal value
Fractions of equal value
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Adding Fractions (Same Denominator)
Adding Fractions (Same Denominator)
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Example: 1/4 + 2/4
Example: 1/4 + 2/4
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Common Denominator definition
Common Denominator definition
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Finding Missing Parts
Finding Missing Parts
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The Concept of 'Whole'
The Concept of 'Whole'
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Same Denominators
Same Denominators
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Fraction Addition
Fraction Addition
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Adding Fractions with different denominators
Adding Fractions with different denominators
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What is the Sum?
What is the Sum?
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What is a Fraction?
What is a Fraction?
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Garden Fractions
Garden Fractions
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Fractions of Salary
Fractions of Salary
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Mixed to Improper
Mixed to Improper
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Fraction Multiplication
Fraction Multiplication
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Mixed Numbers Multiplication
Mixed Numbers Multiplication
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Simplest Form
Simplest Form
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Cross-Cancellation
Cross-Cancellation
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Whole x Mixed
Whole x Mixed
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What does numerator represent?
What does numerator represent?
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What does denominator represent?
What does denominator represent?
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What is 2/3 x 9?
What is 2/3 x 9?
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What is 5/6 x 30?
What is 5/6 x 30?
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What is 1/8 x 24?
What is 1/8 x 24?
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What is 2 1/7 x 2/9?
What is 2 1/7 x 2/9?
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What is 1 2/5 x 2/5?
What is 1 2/5 x 2/5?
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What is 1 1/2 x 2/6?
What is 1 1/2 x 2/6?
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What is 2/10 x 4?
What is 2/10 x 4?
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What is 5/9 x 18?
What is 5/9 x 18?
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What is 21 x 1/3?
What is 21 x 1/3?
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Adding Fractions (Different Denominators)
Adding Fractions (Different Denominators)
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What is a Common Denominator?
What is a Common Denominator?
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Scaling to a Common Denominator
Scaling to a Common Denominator
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Adding Numerators (Common Denominator)
Adding Numerators (Common Denominator)
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Sum of Fractions
Sum of Fractions
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Simplifying Fractions (After Addition)
Simplifying Fractions (After Addition)
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Fraction Subtraction Rule
Fraction Subtraction Rule
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Subtracting Unlike Fractions
Subtracting Unlike Fractions
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Fraction Subtraction
Fraction Subtraction
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Comparing Fraction Sizes
Comparing Fraction Sizes
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Fractions Represent?
Fractions Represent?
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Whole as '1'
Whole as '1'
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What happens when you subtract?
What happens when you subtract?
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Equivalent Forms
Equivalent Forms
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What represents 1/4?
What represents 1/4?
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What is 1/3 x 1/4?
What is 1/3 x 1/4?
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Rectangle Method of Fraction Multiplication
Rectangle Method of Fraction Multiplication
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Subdividing a Rectangle - Fractions
Subdividing a Rectangle - Fractions
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What is 3/4 x 2/3?
What is 3/4 x 2/3?
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Horizontal rectangles
Horizontal rectangles
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Vertical rectangles
Vertical rectangles
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Small rectangles
Small rectangles
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What is 5/8 x 3/4?
What is 5/8 x 3/4?
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Shading a Rectangle-Fractions
Shading a Rectangle-Fractions
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What are Fractions?
What are Fractions?
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What is the Numerator?
What is the Numerator?
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What is the Denominator?
What is the Denominator?
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What are Equivalent Fractions?
What are Equivalent Fractions?
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Adding Same Denominator Fractions
Adding Same Denominator Fractions
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Subtracting Same Denominator Fractions
Subtracting Same Denominator Fractions
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Subtracting Fractions: Same Denominator
Subtracting Fractions: Same Denominator
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Fraction Subtraction Process
Fraction Subtraction Process
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Multiplying Fraction by Whole Number
Multiplying Fraction by Whole Number
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Mixed to Improper Conversion
Mixed to Improper Conversion
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What is a denominator?
What is a denominator?
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What is a numerator?
What is a numerator?
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Table of Fractions
Table of Fractions
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What is Fraction Subtraction?
What is Fraction Subtraction?
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What are diagrams?
What are diagrams?
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Using a diagram to solve?
Using a diagram to solve?
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What is rewriting?
What is rewriting?
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What is subtraction?
What is subtraction?
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Same Denominator is...
Same Denominator is...
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What is 3/4 - 1/2?
What is 3/4 - 1/2?
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How to get same denominator?
How to get same denominator?
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What is the remaining part?
What is the remaining part?
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What is to Subtract?
What is to Subtract?
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Subtracting Fractions (Same Denominator)
Subtracting Fractions (Same Denominator)
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Subtracting Fractions (Different Denominators)
Subtracting Fractions (Different Denominators)
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Subtracting Mixed Numbers
Subtracting Mixed Numbers
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Finding the Missing Part
Finding the Missing Part
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Same Denominators (Subtraction)
Same Denominators (Subtraction)
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Equivalent Forms (Subtraction)
Equivalent Forms (Subtraction)
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Fractions Representation
Fractions Representation
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Fraction Diagram
Fraction Diagram
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Common Denominator Importance
Common Denominator Importance
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Finding a Common Denominator
Finding a Common Denominator
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Fraction Subtraction Result
Fraction Subtraction Result
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Mixed Fraction
Mixed Fraction
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Sold Portion
Sold Portion
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Ate Portion
Ate Portion
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Fraction Sum
Fraction Sum
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Proper Fractions (Example)
Proper Fractions (Example)
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Improper Fractions (Example)
Improper Fractions (Example)
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What makes a fraction 'proper'?
What makes a fraction 'proper'?
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What makes a fraction 'improper'?
What makes a fraction 'improper'?
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What creates a mixed number?
What creates a mixed number?
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How are 1/2 and 2/4 Related?
How are 1/2 and 2/4 Related?
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Adding Fractions (Common Denominator)
Adding Fractions (Common Denominator)
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Steps to Add Fractions
Steps to Add Fractions
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Adding Numerators (Same Denominator)
Adding Numerators (Same Denominator)
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Example (Fraction addition)
Example (Fraction addition)
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Adding Unit Fractions
Adding Unit Fractions
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Understanding Denominator
Understanding Denominator
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Understanding Numerator
Understanding Numerator
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Fraction Multiplication by a Whole
Fraction Multiplication by a Whole
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Multiplying Mixed Numbers with Fractions
Multiplying Mixed Numbers with Fractions
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Multiplying Fraction by Fraction
Multiplying Fraction by Fraction
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Word Problems and Fractions
Word Problems and Fractions
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Start with the Whole
Start with the Whole
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What is a proper fraction?
What is a proper fraction?
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What is an improper fraction?
What is an improper fraction?
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How to create Equivalent Fractions.
How to create Equivalent Fractions.
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Fraction equals 1
Fraction equals 1
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Multiplying a Fraction by 1
Multiplying a Fraction by 1
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How to find equivalent fractions?
How to find equivalent fractions?
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Finding Equivalent Fractions
Finding Equivalent Fractions
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Missing Fraction Parts
Missing Fraction Parts
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Fraction Sequence
Fraction Sequence
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Scaling Up Fractions
Scaling Up Fractions
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Equivalent Fractions Definition
Equivalent Fractions Definition
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Fraction Multiplication Outcome
Fraction Multiplication Outcome
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What is Product?
What is Product?
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Rectangle Method (Fractions)
Rectangle Method (Fractions)
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What is Shaded Area?
What is Shaded Area?
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Fraction Multiplication Rule
Fraction Multiplication Rule
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Finding the Product of Fractions
Finding the Product of Fractions
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Simplifying After Multiplication
Simplifying After Multiplication
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Multiplying Mixed Numbers
Multiplying Mixed Numbers
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Whole Number × Fraction
Whole Number × Fraction
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Parts of a Fraction
Parts of a Fraction
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Fraction Product
Fraction Product
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What is a Mixed Number?
What is a Mixed Number?
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Study Notes
- The chapter focuses on fractions, including types, comparison, addition, subtraction, and word problems.
- Competence in fractions is useful in budgeting, time measurement, medical prescriptions, and assessing progress.
Revision Exercise
- A series of fraction addition and subtraction problems are provided for revision
Farm Questions
- Half of a farm was planted with maize, and the question asks what wasn’t planted with maize.
- Seedling question involving subtracting fractions
- Journey question involving subtracting fractions
- Cotton cooperative question
- Bread question
Types of Fractions
- Fractions can be proper, improper, or mixed.
- Proper Fraction: Numerator is smaller than the denominator and examples given: 1/4, 2/4, 1/9, 3/8, 10/12, 15/40
- Improper Fraction: Numerator is bigger than the denominator and examples are 6/5, 9/4, 10/7, 11/9, 12/11.
- Mixed Fraction: Combines a whole number and a proper fraction; results from simplifying an improper fraction and examples given 3 1/4, 4 1/2, 5 1/4, 5 5/4, 15 1/3, 22 1/3
Identifying Fractions
- Determine which fractions are improper
- Determine which fractions are proper
- Explain the difference between proper and improper fractions
Equivalent Fractions
- Any fraction where the numerator and denominator are the same equals 1.
- Multiplying a fraction by 1 does not change its value.
Equivalent Fraction Examples
- 1/2 = 2/4 = 3/6 = 4/8 = 5/10 etc
- 3/4, find equivalents
Comparing Fractions
- Fractions with different values can be shown in a table.
- The length of a shaded part represents the size or value of a particular fraction.
Comparing Fraction Example
- Determine whether 1/2 or 1/4 is larger.
- 1/2 is larger than 1/4.
Comparing Fraction example 2
- Determine whether 2/6 or 2/5 is smaller
- 2/6 is smaller than 2/5
Fraction Question Examples
- Identify which fraction is greater in the following pairs: 2/3 and 5/6, 1/8 and 1/9, 4/5 and 2/10
- Identify which fraction is smaller in the following pairs: 5/11 and 2/3, 4/12 and 6/10, 6/7 and 3/9
- Write the fractions in ascending order: 1/3, 5/6, 1/2 , and 3/4, 7/12, 2/3, 7/5, 3/8, 6/4
- Write the fractions in descending order: 5/6, 3/4, 2/3 and 7/12, 5/8, 3//7 , 7/10, 1/2, 3/5
Adding Fractions with Different Denominators
Adding Fractions with Different Denominators example
- To add 1/2 + 1/4, rewrite 1/2 as 2/4 and resulting in 2/4 + 1/4 = 3/4.
- 2/3 + 2/3 = 4/3 = 1 1/3
Adding Fractions with Different Denominators example 2
- The solution provided for adding 2/5 + 3/9 involves multiplying each fraction to obtain a common denominator of 45.
- 2/5 x 45/45 + 3/9 x 45/45 leads to 18/45 + 15/45, which equals 33/45, simplified to 11/15.
Adding Fractions with Different Denominators example 3
- 4/15 + 3/5 + 1/30, use 30 as common denominator
- It follows that: 4/15 + 3/5 + 1/30 = 8/30 + 18/30 + 1/30 = 27/30 or 9/10
More Fraction Exercises
- Practice adding more fractions
Subtracting Fractions with Different Denominators
- To subtract fractions, you must find a common denominator.
- To subtract 3/4 - 1/2, rewrite so we have 3/4 - 2/4 which is 1/4
Subtracting Fractions with Different Denominators example 2
- To subtract 3/5 - 1/4, use 20 as the common denominator and resulting in (3 x 4) - (1 × 5) / 20 which is 12-5/29
- (12-5)/20= 7/20
Subtracting Fractions with Different Denominators example 3
- To subtract 5/6 - 4/7, with a common denominator of 42,
- (5×7) - (4 × 6)/42, resulting in 35-24/42 which equals 11/42.
More Subtraction Exercises
- Practice subtracting more fractions
Multiplying Fractions with Different Denominators
- The solution is a fraction; numerator is the product of the two numerators and denominator is the product of the two denominators.
- Ex: 1/3 x 1/4 = 1x1 / 3x4 which results in 1/12
- Multiplication can be visualized constructing a rectangle and dividing it into horizontal and vertical rectangles to represent fractions.
- Ex: (b) 3/4 x2/3 Subdivide rectangle into 4 horizontal and 3 vertical
- Shade 3 out of 4 for horizontal rectangles with represent 3/4 and 2 of the 3 vertical rectangles that represent 2/3.
- Count the number of small rectangles that have been shaded twice
- There are 6 such small rectangle and this is the numerator.
- The total of of small rectangle is 12 and this is the denominator.
Multiplication Examples
- What is 5/8 x 3/4?
- Solution is: Subdivide a rectangle into 4 horizontal rectangles and 8 vertical rectangles
- *Shade 5 of the 8 vertical rectangles which represent 5/8
- *Shade 3 of the 4 horizontal rectangles and this represents 3/4
- *Count the numbers of small rectangle that have been shaded twice both horizontally and vertically,
- *There are 15 such small rectangle and this is the number.
- The Total number of all the small rectangle is32 and this is the denominator.
- What is 5/8 x 3/4 = 15/32?
More multiplication exercises
- Practicing multiplying more fractions
Multiplying Fractions by Whole Numbers
- When multiplying a fraction by a whole number, write the whole number over one. Ex: 4 = 4/1
- 4 x 1/5 = 4/1 x 1/5 = 4/5
- There after, multiplying the numerator by numerator and denominator by denominator :
- Examples Given: what is 2/3 x 12?
- Since all whole numbers can be written in form x/1: 2/3 x 12 = 2/3 x 12/1 = 24/3 which equates to 8.
More Practice
Practicing multiplying more fractions by whole numbers
Word Problems Involving Fractions
A household and 1 bag of sugar. If Anna used 5/6 of sugar and Magoma used 1/8; what fraction of the sugar was both sugar and Magoma?
- Solution: Add the two fractions: 5/6+1/8 = 20+3/24 = 23/24, Therefore Anna and Magoma used 23/24 of the sugar.
- If Ali harvested 6/7 of onions in that farm, and Zaituni harvested 1/9 of onions from the same farm; what is the difference between what Ali and Zaituni’s Harvest were?
- Solution is: 6/7 - 1/9 = 6(9)-1(7)/63 which equals 47/63
- Example 3: Grandmother drinks 3/4 of a litre of milk per day. How many litres of milk will she drink in 6 days?
- Solution is: 3/4 * 6/1 = 18/4, divide to make the litres 4 ½ litres of milk in 6 days
More Word Problems
- Practice solving word problems using fractions
Summary
- 3 Main Points
- 1.In multiplying a fraction by another fraction, multiply numerator by numerator, and denominator by denominator.
- 2.In multiplying a whole number by a fraction, the whole number is expressed as a faction
- 3.When an improper fraction is simplified, it gives a mixed number.
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Description
This quiz revises fractions, including proper, improper, and mixed types. It covers addition, subtraction, and word problems involving fractions. Competence in fractions is useful in budgeting, time measurement, medical prescriptions, and assessing progress.
