PE4MA 7 Fractions: Comparing, Multiplying, and Dividing

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Questions and Answers

What symbol is used to compare fractions indicating one is smaller than the other?

  • =
  • < (correct)
  • +
  • >

What is the value of any fraction where the numerator and denominator are the same?

  • 2
  • 0
  • It varies
  • 1 (correct)

Multiplying a fraction by what value does not change the fraction's value?

  • Itself
  • 0
  • 1 (correct)
  • 2

Which of the following shows $\frac{1}{2}$ written as an equivalent fraction?

<p>$\frac{2}{4}$ (C)</p> Signup and view all the answers

To find an equivalent fraction, what must you do to both the numerator and the denominator?

<p>Multiply by the same number (C)</p> Signup and view all the answers

When comparing $\frac{1}{4}$ and $\frac{1}{2}$ using a fraction chart, which fraction has a larger shaded area?

<p>$\frac{1}{2}$ (D)</p> Signup and view all the answers

When multiplying fractions, what do you do with the numerators and denominators?

<p>Multiply them (B)</p> Signup and view all the answers

What is the first step in multiplying $\frac{1}{3} \times \frac{1}{4}$ using a rectangular diagram?

<p>Draw a rectangle (B)</p> Signup and view all the answers

When using a rectangular diagram to multiply fractions, what does the number of squares shaded twice represent?

<p>The numerator (A)</p> Signup and view all the answers

When multiplying a fraction by a whole number, what is the first step?

<p>Convert the whole number to a fraction (A)</p> Signup and view all the answers

Which of the following represents 4 as a fraction?

<p>$\frac{4}{1}$ (C)</p> Signup and view all the answers

What do you do after converting a whole number into a fraction?

<p>Multiply numerators and denominators separately (B)</p> Signup and view all the answers

To divide a fraction by a whole number, you must first convert the whole number into a fraction. What denominator should this converted fraction have?

<p>1 (D)</p> Signup and view all the answers

In the 'teacher divides the circle' example, what operation is used to describe the action?

<p>Division (D)</p> Signup and view all the answers

What is the next step when dividing fractions by fractions after converting the dividend into a fraction with '1' as the denominator?

<p>Change the denominator to the numerator and the numerator to the denominator (C)</p> Signup and view all the answers

What is the rule when dividing fractions by fractions?

<p>Invert the second fraction and multiply (A)</p> Signup and view all the answers

What becomes of the divisor when dividing fractions with different denominators?

<p>The denominator and numerator are switched (A)</p> Signup and view all the answers

What is the result of $\frac{3}{8} \div \frac{4}{6}$ after converting the divisor?

<p>$\frac{3}{8} \times \frac{6}{4}$ (A)</p> Signup and view all the answers

What does dividing all the boxes in the diagram accomplish when dividing fractions with diagrams?

<p>Creates parts that fit into the original (C)</p> Signup and view all the answers

What does the acronym 'LCM' stand for in mathematics?

<p>Lowest Common Multiple (C)</p> Signup and view all the answers

If Eliud had 20 sacks of millet and gave $\frac{1}{2}$ to his brother, how many sacks did his brother receive?

<p>10 (A)</p> Signup and view all the answers

If a guest house has 48 beds and $\frac{1}{8}$ of those beds are metal, how many beds are metal?

<p>6 (A)</p> Signup and view all the answers

A kangaroo ran $\frac{1}{3}$ of a distance of 15 kilometers. How far did it run?

<p>5 km (B)</p> Signup and view all the answers

If a school expected to register 160 pupils and $\frac{1}{4}$ were not registered, how many pupils were not registered?

<p>40 (D)</p> Signup and view all the answers

A grandfather drinks $\frac{1}{2}$ a litre of milk each day. How much milk does he drink in 4 weeks (28 days)?

<p>14 litres (C)</p> Signup and view all the answers

What is the first step to solving $\frac{1}{4} \div 1$

<p>Convert 1 into $\frac{1}{1}$ (B)</p> Signup and view all the answers

What is switch and multiply?

<p>Method of solving a division problem (D)</p> Signup and view all the answers

What is $\frac{4}{8} \div 16$?

<p>$\frac{1}{32}$ (A)</p> Signup and view all the answers

Which of the following defines multiplication and division of fractions?

<p>Activity (C)</p> Signup and view all the answers

Which activity helps to understand fractions?

<p>Use reliable online programs such as Khan Academy to Learn More Fractions (D)</p> Signup and view all the answers

Multiply $\frac{3}{4} \times $?

<p>Cannot be determined (C)</p> Signup and view all the answers

What is the result for $\frac{2}{3} + \frac{4}{1}$?

<p>Cannot be determined (D)</p> Signup and view all the answers

True or False: $\frac{1}{3} \leq \frac{6}{5}$

<p>True (A)</p> Signup and view all the answers

Solve $\frac{2}{3}$ [ ] $\frac{1}{2}$

<blockquote> <p>(B)</p> </blockquote> Signup and view all the answers

What is 21 x $\frac{5}{9}$?

<p>$\frac{35}{3}$ (B)</p> Signup and view all the answers

What is $\frac{2}{3} \div \frac{4}{4}$?

<p>$\frac{2}{3}$ (A)</p> Signup and view all the answers

There are 100 pupils, but only $\frac{1}{4}$ are boys. How many girls are there?

<p>75 (D)</p> Signup and view all the answers

Masalu had 88 mangoes and sold $\frac{7}{8}$, how many were sold?

<p>77 (A)</p> Signup and view all the answers

There are 445 math books to 3 schools, but 1 school gets $\frac{2}{5}$ of the books. How many book does this school get?

<p>178 (D)</p> Signup and view all the answers

A pupil eats $\frac{1}{8}$ kilogram of meat and must weigh 64 kilograms. How many pupils eat meat?

<p>512 (A)</p> Signup and view all the answers

How many $\frac{1}{1000}$ are in $\frac{1}{10}$?

<p>100 (B)</p> Signup and view all the answers

The households of a village share 2 tonnes of maize. Each household was given $\frac{1}{20}$ of a tonne, how many households are in that village?

<p>40 households (D)</p> Signup and view all the answers

If a board is 75 meters long and needs to be cut in $\frac{5}{4}$ metres long, how many pieces can it be cut into?

<p>60 (B)</p> Signup and view all the answers

What sign is used to show that fractions are equivalent?

<p>= (equal to) (A)</p> Signup and view all the answers

What happens to the value of a fraction if you multiply it by 1?

<p>It stays the same (B)</p> Signup and view all the answers

Which operation is used to find equivalent fractions?

<p>Multiplication (C)</p> Signup and view all the answers

According to the fraction chart, how does the shaded area relate to the size of the fraction?

<p>The shaded area represents the size of the fraction. (D)</p> Signup and view all the answers

What do you multiply when multiplying fractions?

<p>Multiply numerators and denominators separately (A)</p> Signup and view all the answers

In the rectangular diagram method for multiplying fractions what do the rectangles represent?

<p>The product of the fractions (C)</p> Signup and view all the answers

When a whole number is converted into fraction what is the denominator?

<p>1 (C)</p> Signup and view all the answers

When dividing fractions, what do you do with the second fraction?

<p>Flip it (C)</p> Signup and view all the answers

In the division of fractions what happens to the divisor?

<p>The divisor changes (A)</p> Signup and view all the answers

What happens to the division operation when dividing fractions?

<p>Becomes multiplication (B)</p> Signup and view all the answers

What is the reciprocal of $\frac{5}{3}$?

<p>$\frac{3}{5}$ (D)</p> Signup and view all the answers

What is the result of $\frac{1}{1}$?

<p>1 (C)</p> Signup and view all the answers

What is the denominator of 4 when written as a fraction?

<p>1 (A)</p> Signup and view all the answers

What should you do before multiplying numerators and denominators?

<p>The multiplication can start immediately (A)</p> Signup and view all the answers

What is $\frac{1}{4} \times \frac{1}{3}$

<p>$\frac{1}{12}$ (D)</p> Signup and view all the answers

When using a rectangular diagram to multiply $\frac{1}{3} \times \frac{1}{4}$, what does the total number of squares in the diagram represent?

<p>The product of the denominators (A)</p> Signup and view all the answers

What is the result of $\frac{1}{3} \div 1$?

<p>$\frac{1}{3}$ (A)</p> Signup and view all the answers

What is $4 \div \frac{1}{2}$?

<p>8 (D)</p> Signup and view all the answers

A class divided a sheet into 6 parts, if 3 people took a sheet each. How many sheets were used?

<p>2 (D)</p> Signup and view all the answers

What is the primary purpose of learning about fractions, including comparing, multiplying, and dividing them?

<p>To apply the concepts in different real-world situations. (D)</p> Signup and view all the answers

When comparing fractions, which of the following mathematical symbols are used?

<p>=, &lt;, &gt; (C)</p> Signup and view all the answers

If a fraction is multiplied by 1, what happens to its value?

<p>The value remains the same. (D)</p> Signup and view all the answers

Which of the following fractions is equivalent to $\frac{3}{4}$?

<p>$\frac{6}{8}$ (B)</p> Signup and view all the answers

What is an accurate comparison of $\frac{1}{4}$ and $\frac{2}{5}$?

<p>$\frac{1}{4} &lt; \frac{2}{5}$ (D)</p> Signup and view all the answers

To multiply fractions with different denominators, what is the initial step?

<p>Multiply the numerators and the denominators separately. (A)</p> Signup and view all the answers

Using rectangular diagrams, which of the following statements is accurate when multiplying $\frac{1}{3} \times \frac{1}{4}$?

<p>Shade the rectangles $\frac{1}{3}$ vertically and $\frac{1}{4}$ horizontally. (D)</p> Signup and view all the answers

When using the rectangular diagram method for multiplying fractions, what does the number of squares shaded twice represent?

<p>The product of the fractions. (C)</p> Signup and view all the answers

What is the initial step in multiplying a whole number by a fraction?

<p>Convert the whole number into a fraction. (A)</p> Signup and view all the answers

If you need to divide a fraction by a whole number, what is the first step?

<p>Convert the whole number into a fraction. (B)</p> Signup and view all the answers

What happens to a whole number when it is converted into a fraction for division?

<p>It is placed over 1 as the denominator. (B)</p> Signup and view all the answers

When a teacher divides a sheet to share with pupils, what mathematical operation represents this action?

<p>Division (C)</p> Signup and view all the answers

In the division of fractions, what is the next step after converting the whole number into a fraction?

<p>Multiply by the reciprocal of the divisor. (A)</p> Signup and view all the answers

When dividing one fraction by another, what should be done with the second fraction (the divisor)?

<p>It should be inverted and multiplied. (A)</p> Signup and view all the answers

What is the reciprocal of a fraction?

<p>The fraction with its numerator and denominator interchanged. (D)</p> Signup and view all the answers

How does the text describe the process of dividing fractions using diagrams?

<p>By dividing all the boxes in the diagram. (B)</p> Signup and view all the answers

Eliud had 20 sacks of millet and he provided $\frac{2}{5}$ to his brother. How many sacks did his brother receive?

<p>8 sacks (C)</p> Signup and view all the answers

A guest house has 48 beds, where $\frac{3}{8}$ of the beds are metal. How many metal beds are in the guest house?

<p>18 (B)</p> Signup and view all the answers

A kangaroo ran $\frac{2}{3}$ of a distance of 15 kilometers. How far did the kangaroo run?

<p>10 kilometers (D)</p> Signup and view all the answers

In a school expecting 160 pupils, $\frac{3}{4}$ were registered. How many pupils were not registered?

<p>40 (A)</p> Signup and view all the answers

What initial transformation is required to calculate $\frac{3}{4} \div 1$?

<p>Convert 1 into the fraction $\frac{1}{1}$. (D)</p> Signup and view all the answers

What is 'switch and multiply' primarily referring to in fraction calculations?

<p>Division of fractions. (D)</p> Signup and view all the answers

What is the value of $\frac{8}{16} \div 4$?

<p>$\frac{1}{8}$ (D)</p> Signup and view all the answers

What is the appropriate method for understanding mathematical operations with fractions effectively?

<p>Using visual activities. (D)</p> Signup and view all the answers

Evaluate $\frac{2}{5} \times 15$?

<p>6 (A)</p> Signup and view all the answers

What results does $\frac{1}{4} + \frac{8}{1}$ yield?

<p>$\frac{33}{4}$ (B)</p> Signup and view all the answers

State whether the following statement is correct; $\frac{2}{5} \leq \frac{8}{9}$

<p>True (A)</p> Signup and view all the answers

Which symbol could replace the [ ] to show the relationship between $\frac{3}{4}$ [ ] $\frac{6}{8}$?

<p>= (C)</p> Signup and view all the answers

Determine the product of 42 x $\frac{2}{9}$?

<p>$\frac{28}{3}$ (B)</p> Signup and view all the answers

Among 200 students, $\frac{3}{5}$ are girls. How many boys are there?

<p>80 (C)</p> Signup and view all the answers

From a collection of 132 guavas, $\frac{5}{6}$ were sold. How many were sold?

<p>110 (C)</p> Signup and view all the answers

Of 660 text books divided among schools, one school gets $\frac{3}{5}$ of the books. What is the allocation of the books to this school?

<p>396 (A)</p> Signup and view all the answers

A student eats $\frac{1}{10}$ kg of rice and there are 90 kg of rice. How many students can eat?

<p>900 (B)</p> Signup and view all the answers

The people share 4 ton of rice where each person gets a share of $\frac{1}{8}$ of a ton. How many people are there?

<p>32 (B)</p> Signup and view all the answers

A timber is 150 m long and is cut into pieces that are $\frac{5}{4}$ m long. How many pieces could be cut?

<p>120 (C)</p> Signup and view all the answers

In the list of fractions, $\frac{8}{10}$, $\frac{4}{5}$, $\frac{2}{3}$, $\frac{16}{20}$, which fractions are equivalent?

<p>$\frac{8}{10}$, $\frac{4}{5}$, and $\frac{16}{20}$ (B)</p> Signup and view all the answers

What is the primary focus of the chapter on fractions?

<p>Comparing, multiplying, and dividing fractions with different denominators, and by whole numbers. (A)</p> Signup and view all the answers

Which mathematical symbols are primarily used to compare fractions?

<p>=, &lt;, &gt; (A)</p> Signup and view all the answers

What remains the same when a fraction is multiplied by 1?

<p>The value of the fraction. (A)</p> Signup and view all the answers

What is the equivalent fraction of $\frac{3}{4}$ when both numerator and denominator are multiplied by 2?

<p>$\frac{6}{8}$ (A)</p> Signup and view all the answers

According to the fraction chart, which fraction is greater, $\frac{2}{5}$ or $\frac{2}{6}$?

<p>$\frac{2}{5}$ is greater. (D)</p> Signup and view all the answers

What should you do with the numerators and denominators when multiplying fractions?

<p>Multiply the numerators and denominators separately. (A)</p> Signup and view all the answers

In the rectangular diagram method for multiplying fractions, what do the horizontal and vertical rectangles represent?

<p>The numerators and denominators of each fraction. (A)</p> Signup and view all the answers

When multiplying a whole number by a fraction, what is the initial step?

<p>Convert the whole number into a fraction. (B)</p> Signup and view all the answers

To divide a fraction by a whole number, what is the first necessary step?

<p>Express the whole number as a fraction. (B)</p> Signup and view all the answers

What transformation is applied to the divisor when dividing fractions with different denominators?

<p>It is inverted (reciprocal found). (C)</p> Signup and view all the answers

What fundamental change occurs to the division operation when dividing one fraction by another?

<p>It is converted to multiplication. (A)</p> Signup and view all the answers

What represents the reciprocal of the fraction$\frac{a}{b}$?

<p>$\frac{b}{a}$ (C)</p> Signup and view all the answers

$\frac{1}{3} \times \frac{1}{4} = $?

<p>$\frac{1}{12}$ (A)</p> Signup and view all the answers

When dividing $\frac{1}{3}$ by 1, what is the result?

<p>$\frac{1}{3}$ (B)</p> Signup and view all the answers

Calculate the result of $4 \div \frac{1}{2}$?

<p>8 (D)</p> Signup and view all the answers

Eliud provides $\frac{2}{5}$ of his 20 sacks of millet to his brother. Determine how many sacks the brother receives.

<p>8 sacks (A)</p> Signup and view all the answers

In a guest house of 48 beds, $\frac{3}{8}$ are metal. How many beds are metal?

<p>18 beds (B)</p> Signup and view all the answers

A kangaroo covers $\frac{2}{3}$ of a 15 km distance. Calculate the distance covered.

<p>10 km (C)</p> Signup and view all the answers

Out of an expected 160 pupils, $\frac{3}{4}$ registered. How many pupils did not register?

<p>40 pupils (A)</p> Signup and view all the answers

Before performing the calculation $\frac{3}{4} \div 1$, which transformation is required?

<p>No transformation is necessary (A)</p> Signup and view all the answers

In the context of fraction calculations, what does 'switch and multiply' primarily refer to?

<p>Inverting the divisor and changing division to multiplication (C)</p> Signup and view all the answers

What is the simplified value of $\frac{8}{16} \div 4$?

<p>$\frac{1}{8}$ (D)</p> Signup and view all the answers

Which method aids effectively in understanding mathematical operations involving fractions?

<p>Using real-world examples and visual aids (A)</p> Signup and view all the answers

What does $\frac{2}{5} \times 15$ equal?

<p>6 (D)</p> Signup and view all the answers

Is the following statement correct? $\frac{2}{5} \leq \frac{8}{9}$

<p>True (A)</p> Signup and view all the answers

Which symbol correctly shows the relationship between $\frac{3}{4}$ and $\frac{6}{8}$?

<p>= (A)</p> Signup and view all the answers

What is the product of 42 and $\frac{2}{9}$?

<p>$\frac{84}{9}$ (D)</p> Signup and view all the answers

Out of 200 students, $\frac{3}{5}$ are girls. How many boys are there?

<p>80 (D)</p> Signup and view all the answers

Out of 132 guavas, $\frac{5}{6}$ were sold. How many guavas were sold?

<p>110 (C)</p> Signup and view all the answers

660 textbooks are divided among schools, and one school gets $\frac{3}{5}$ of the books. What is this school's allocation?

<p>396 (D)</p> Signup and view all the answers

If a student eats $\frac{1}{10}$ kg of rice and there are 90 kg of rice available, how many students can be fed?

<p>900 (C)</p> Signup and view all the answers

If 4 tons of rice are shared, and each person receives a share of $\frac{1}{8}$ of a ton, how many people are sharing?

<p>32 (C)</p> Signup and view all the answers

If a timber is 150 meters long and needs to be cut into pieces that are $\frac{5}{4}$ meters long, how many pieces can be cut?

<p>120 (B)</p> Signup and view all the answers

Given the fractions $\frac{8}{10}$, $\frac{4}{5}$, $\frac{2}{3}$, $\frac{16}{20}$, select the equivalent fractions:

<p>$\frac{8}{10}$, $\frac{4}{5}$ and $\frac{16}{20}$ (C)</p> Signup and view all the answers

Imagine dividing a pizza equally among friends. If you want each slice to be twice as big, what must you do to the number of friends?

<p>Halve the number of friends. (B)</p> Signup and view all the answers

If multiplying a fraction 'x' by another fraction results in a product greater than 'x', what must be true of the second fraction?

<p>It must be greater than 1. (A)</p> Signup and view all the answers

Suppose you have a recipe that calls for $\frac{2}{3}$ cup of sugar, but you only want to make half the recipe. How much sugar do you need?

<p>$\frac{1}{3}$ cup (C)</p> Signup and view all the answers

You are stacking books on a shelf. Each book is $\frac{3}{4}$ inch thick. If the shelf is 9 inches long, how many books can you fit?

<p>12 books (C)</p> Signup and view all the answers

A snail crawls $\frac{1}{16}$ of a meter in one minute. How long will it take the snail to crawl $\frac{1}{4}$ of a meter, assuming it maintains a constant speed?

<p>4 minutes (D)</p> Signup and view all the answers

Flashcards

Equivalent Fractions

Fractions with the same value, created by multiplying the numerator and denominator by the same number.

Fraction Chart

A visual aid where the shaded area represents the fraction's size, aiding in comparison.

Comparing fractions

Use either '<' (less than) or '>' (greater than) to show the relationship of fractions.

Multiplying Fractions

Multiply the numerators to get new numarator and denominators to get the new denominator.

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Fraction by Whole Number

Convert the whole number to a fraction and apply multiplication to fractions.

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Dividing Fractions

Convert the whole number into a fraction, then multiply by the reciprocal (switch the numerator and denominator).

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Dividing Fractions with unlike Denominators

Switch numerator and denominator of the second fraction, use multiplication to find an answer.

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Improper Fraction

A fraction where the numerator is greater than or equal to the denominator.

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Creating Equivalent Fractions

Multiplying the numerator and the denominator of a fraction by the same number.

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Mixed Number

A number consisting of a whole number and a fraction.

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Dividing Fractions Steps

Invert the second fraction and multiply.

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Rectangular Fraction Diagram

A diagram representing fractions as parts of a whole, aiding visualization.

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Multiplying by One

When a fraction is multiplied by 1, its value remains unchanged.

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Fraction

A part of a whole number.

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What is a fraction?

A number that represents a part of a whole, written as one number over another.

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What is comparison of fractions?

Using symbols like =, <, or > express a relationship between two fractions.

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What is 'scaling' fractions?

Multiplying the top and bottom numbers by same value doesn't change the fraction’s worth.

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Dividing fractions: Keep, Change, Flip

To simplify division, you can change the operation to multiplication using reciprocals.

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Rectangle Fraction Division

A diagram uses rectangles to show fractions of fractions.

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What are equivalent fractions?

Fractions expressed with different numerators and denominators but representing the same portion of a whole.

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What is comparing fractions?

Using mathematical symbols to express the relative size of two fractions.

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Multiplying a fraction by a whole number

Multiplying the numerator by the whole number

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Dividing fractions strategy

Turn the dividing fraction upside down and multiply.

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How do you multiply fractions?

Numbers written in fraction form are multiplied by multiplying the numerators and denominators

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Simplified Equivalent Fractions

Fractions simplified by equal division result in equivalent fractions

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The identity property

When multiplying or dividing by one, the original value stays the same.

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Study Notes

  • This chapter is about comparing, multiplying, and dividing fractions with different denominators and by whole numbers
  • Skills developed can be applied in various contexts

Comparing Fractions

  • Fractions can be compared using the equal sign (=), less than sign (<), and greater than sign (>)
  • Equivalent fractions are compared using the equal sign (=)
  • A fraction with the same worth as a whole has a value of 1
  • Multiplying a fraction by 1 doesn't change its value

Using the Equal Sign to Recognize Equivalent Fractions:

  • Comparing fractions using a fraction chart is possible, as shaded areas on the chart show the size of the fraction
  • Fractions with different values can be identified by chart
  • Fractions with different values can be compared using the symbols < (less than) or >
  • When multiplying fractions, numerators and denominators are multiplied separately to get the answer

Multiplying Fractions with Different Denominators

  • Multiplying fractions involves multiplying the numerators and denominators by the numerator and the denominator respectively
  • Multiplication of fractions can be done using rectangular diagrams

Multiply Fractions Using Rectangular Diagrams

  • Draw horizontal rectangles and vertical rectangles in the larger rectangle
  • Shade the rectangles vertically and horizontally
  • Number of squares shaded twice is the numerator
  • The total number of squares, is the denominator

Multiplication of Fractions by Whole Numbers

  • Convert the whole number into a fraction, then multiply

Division of Fractions by Whole Numbers

  • Convert the whole number into a fraction with 1 as the denominator, then multiply the fractions

Division of Fractions with Different Denominators

  • Interchange the denominator and numerator, then multiply

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