Equivalent Ratios and Fractions Operations

Questions and Answers

6/12

8/12 (correct)

8/9

6/9

5/12 (correct)

3/12

2/12

1/12

1/2

1/3

1/6 (correct)

5/6

4/9 Signup and view all the answers

0.75 Signup and view all the answers

24 Signup and view all the answers

1/2 Signup and view all the answers

4/3 Signup and view all the answers

3/8 Signup and view all the answers

Study Notes

Two fractions are equivalent if they have the same value
Equivalent fractions can be found by multiplying or dividing both numerator and denominator by the same number
Example: 1/2 = 2/4 = 3/6
To find an equivalent fraction, multiply or divide both numbers by the same number

To add or subtract fractions, they must have the same denominator
If the denominators are different, find the least common multiple (LCM) of the two denominators
Convert both fractions to have the LCM as the denominator
Add or subtract the numerators and keep the denominator the same
Example: 1/4 + 1/6 = 3/12 + 2/12 = 5/12

To multiply fractions, multiply the numerators and multiply the denominators
Example: 1/2 × 3/4 = (1 × 3) / (2 × 4) = 3/8
Multiplying by a whole number is the same as multiplying by an equivalent fraction
Example: 2 × 3/4 = 2/1 × 3/4 = 6/4 = 3/2

To divide fractions, invert the second fraction (i.e., flip the numerator and denominator) and then multiply
Example: 1/2 ÷ 3/4 = 1/2 × 4/3 = (1 × 4) / (2 × 3) = 4/6
Dividing by a whole number is the same as dividing by an equivalent fraction
Example: 3/4 ÷ 2 = 3/4 ÷ 2/1 = 3/4 × 1/2 = 3/8

A fraction can be converted to a decimal by dividing the numerator by the denominator
Example: 3/4 = 3 ÷ 4 = 0.75
Decimals can be converted back to fractions by finding the equivalent fraction
Example: 0.5 = 1/2

Equivalent fractions have the same value, and can be found by multiplying or dividing both numerator and denominator by the same number
Example of equivalent fractions: 1/2 = 2/4 = 3/6
Multiplying or dividing both numbers by the same number finds an equivalent fraction

Fractions must have the same denominator to add or subtract
If denominators differ, find the least common multiple (LCM) of both denominators to convert fractions
Add or subtract the numerators and keep the denominator the same after converting
Example: 1/4 + 1/6 = 3/12 + 2/12 = 5/12

Multiply the numerators and multiply the denominators to multiply fractions
Example: 1/2 × 3/4 = (1 × 3) / (2 × 4) = 3/8
Multiplying by a whole number is the same as multiplying by an equivalent fraction
Example: 2 × 3/4 = 2/1 × 3/4 = 6/4 = 3/2

Invert the second fraction (flip numerator and denominator) and then multiply to divide fractions
Example: 1/2 ÷ 3/4 = 1/2 × 4/3 = (1 × 4) / (2 × 3) = 4/6
Dividing by a whole number is the same as dividing by an equivalent fraction
Example: 3/4 ÷ 2 = 3/4 ÷ 2/1 = 3/4 × 1/2 = 3/8