Podcast
Questions and Answers
What is the first step in simplifying complex fractions?
What is the first step in simplifying complex fractions?
The process of reducing a complex fraction to its lowest terms is optional.
The process of reducing a complex fraction to its lowest terms is optional.
False (B)
What does LCD stand for in the context of fractions?
What does LCD stand for in the context of fractions?
Least Common Denominator
A decimal number has its whole number part and the fractional part separated by a __________.
A decimal number has its whole number part and the fractional part separated by a __________.
Signup and view all the answers
Match the following steps with their corresponding actions in the process of adding or subtracting two fractions.
Match the following steps with their corresponding actions in the process of adding or subtracting two fractions.
Signup and view all the answers
What is the final step after performing the Keep, Change, Flip process?
What is the final step after performing the Keep, Change, Flip process?
Signup and view all the answers
When reading a decimal number, the decimal part is read as one complete number followed by its place value.
When reading a decimal number, the decimal part is read as one complete number followed by its place value.
Signup and view all the answers
What would you call a fraction whose numerator and/or denominator contains fractions?
What would you call a fraction whose numerator and/or denominator contains fractions?
Signup and view all the answers
What is the decimal equivalent of 723.29%?
What is the decimal equivalent of 723.29%?
Signup and view all the answers
If 60 is a part of 80, what percent does this represent?
If 60 is a part of 80, what percent does this represent?
Signup and view all the answers
What is the general form of representing a ratio between two quantities 'a' and 'b'?
What is the general form of representing a ratio between two quantities 'a' and 'b'?
Signup and view all the answers
What defines a unit ratio?
What defines a unit ratio?
Signup and view all the answers
What does the term 'percent' derive from?
What does the term 'percent' derive from?
Signup and view all the answers
What is the process to convert a decimal value to a percentage?
What is the process to convert a decimal value to a percentage?
Signup and view all the answers
When converting from percent to decimal, how is the conversion performed?
When converting from percent to decimal, how is the conversion performed?
Signup and view all the answers
It is defined as the comparison of two quantities of the same units.
It is defined as the comparison of two quantities of the same units.
Signup and view all the answers
What is the correct algebraic expression for 'the sum of a number and 5'?
What is the correct algebraic expression for 'the sum of a number and 5'?
Signup and view all the answers
Which of the following represents 'decreased by' in algebraic expressions?
Which of the following represents 'decreased by' in algebraic expressions?
Signup and view all the answers
What is the result of the algebraic expression -18m - 2m?
What is the result of the algebraic expression -18m - 2m?
Signup and view all the answers
Which option defines the term 'the product of a number and 6'?
Which option defines the term 'the product of a number and 6'?
Signup and view all the answers
What does the term 'algebra' derive from, and what does it signify?
What does the term 'algebra' derive from, and what does it signify?
Signup and view all the answers
When performing addition on integers with the same sign, what is the rule to follow?
When performing addition on integers with the same sign, what is the rule to follow?
Signup and view all the answers
In the expression -23 + -13, what result do you obtain?
In the expression -23 + -13, what result do you obtain?
Signup and view all the answers
Which of the following describes a monomial?
Which of the following describes a monomial?
Signup and view all the answers
There are 47 boys in the class. This is three more than four times the number of girls. How many girls are there in the class?
There are 47 boys in the class. This is three more than four times the number of girls. How many girls are there in the class?
Signup and view all the answers
The sum of two consecutive numbers is 41. What are the numbers?
The sum of two consecutive numbers is 41. What are the numbers?
Signup and view all the answers
Study Notes
Complex Fractions
- A complex fraction is a fraction where the numerator or denominator, or both, contains a fraction.
Simplifying Complex Fractions
- Step 2: Keep, Change, Flip.
- Step 3: Multiply the numerators and denominators.
Adding or Subtracting Unlike Denominators
- Step 1: Solve each fraction separately.
- Step 2: Find the Least Common Denominator (LCD) of the denominators.
- Step 3: Multiply the numerator and denominator of each fraction by the number needed to get the LCD.
- Step 4: Add or subtract the numerators.
- Step 5: Write the result as a new fraction with the LCD as the denominator.
- Step 6: Keep, change, flip.
- Step 7: Reduce your answer to the lowest terms if necessary.
Adding or Subtracting Fractions with the Same Denominator
- Step 1: Solve each fraction separately.
- Step 2: Keep the common denominator.
- Step 3: Add or subtract the numerators.
- Step 4: Write the result as a new fraction.
- Step 5: Simplify the fraction to the lowest terms.
Decimal Numbers
- A decimal number has a whole number part and a fractional part separated by a decimal point.
- Each position after the decimal point is 10 times smaller than the previous position.
Rounding Decimals
- Locate the digit to be rounded.
- Look at the digit to the right.
- If the digit to the right is less than 5, keep the digit the same and remove the rest of the digits.
- If the digit to the right is greater than or equal to 5, add 1 to the digit being rounded and remove the rest of the digits.
Converting Fractions to Decimals
- Divide the numerator by the denominator.
Converting Decimals to Fractions:
- Identify the place value of the digits after the decimal.
- Use that value to determine the denominator.
- Remove the decimal point.
- Simplify.
- Express as the lowest equivalent fraction
Adding and Subtracting Decimals
- Line up the decimal points vertically.
- Add or subtract as if the numbers were whole numbers.
- Place the decimal point in the result vertically with the numbers.
Multiplying Decimals
- Initially, ignore the decimal points, and multiply the numbers as if they were whole numbers.
- Count the total number of decimal places in both numbers.
- Place the decimal point in the product so that it has the same number of decimal places.
Dividing Decimals
- Convert the divisor into a whole number by moving the decimal point to the right.
- Move the decimal point in the dividend the same number of places to the right.
- Divide as if the numbers were whole numbers.
- Place the decimal point in the quotient directly above the decimal point in the dividend.
Ratio
- Ratio is a comparison of two quantities or numbers, frequently showing the relationship between them.
- In a ratio form, a:b or a/b, the quantity a comes before b.
Ratio Formula
- Formula: percent(%) = part/whole.
Percentage
- Percentage is a number or ratio expressed as a fraction of 100.
- Percentage values represent proportions based on a total value of 100.
Converting Percentage to Decimal
- Remove the percentage symbol.
- Divide by 100.
- Move the decimal point two places to the left.
Converting Decimal to Percent
- Multiply by 100
- Move the decimal point two places to the right.
Converting Fraction to Percent
- Multiply the fraction by 100.
- Simplify.
Converting Percent to Fraction
- Remove the percentage symbol
- Divide by 100.
- Simplify.
Proportion
- A proportion is an equation in which two ratios are set equal to each other.
Solving Proportions
- Calculate the cross products.
- Set the cross products equal to each other.
- Solve the equation for the unknown.
Solving Percentage Problems using Proportion
- Set up a proportion with the known values.
- Cross-multiply to find the unknown value.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
This quiz covers the essentials of complex fractions, including the methods for simplifying, adding, and subtracting fractions with both like and unlike denominators. You'll learn the steps for using the Least Common Denominator and how to reduce fractions to their simplest form. Test your understanding of these fundamental concepts in fraction operations.
