Write an equivalent ratio

Key Notes :

1. What is an Equivalent Ratio?

  • Definition: Equivalent ratios are two ratios that express the same relationship between two quantities.
  • Example: The ratios 2:3 and 4:6 are equivalent because both represent the same proportion.

2. How to Find Equivalent Ratios

  • To create equivalent ratios, multiply or divide both terms of a ratio by the same non-zero number.
  • Example 1:
    Given ratio: 2:3
    Multiply both terms by 2:
    2 × 2 = 4, 3 × 2 = 6
    So, 2:3 is equivalent to 4:6.
  • Example 2:
    Given ratio: 6:9
    Divide both terms by 3:
    6 ÷ 3 = 2, 9 ÷ 3 = 3
    So, 6:9 is equivalent to 2:3.

3. Using Cross-Multiplication to Check for Equivalence

  • To check if two ratios are equivalent, cross-multiply and compare the results.
  • Example:
    Are 2:3 and 4:6 equivalent?
    Cross-multiply:
    2 × 6 = 12
    3 × 4 = 12
    Since both products are equal, the ratios 2:3 and 4:6 are equivalent.

4. Simplifying Ratios

  • To simplify a ratio, divide both terms by their greatest common divisor (GCD).
  • Example:
    Given ratio: 8:12
    GCD of 8 and 12 is 4.
    Divide both terms by 4:
    8 ÷ 4 = 2, 12 ÷ 4 = 3
    So, 8:12 simplifies to 2:3, which is an equivalent ratio.

Learn with an example

✈️ Find the number that makes the ratio equivalent to 1:3.

5: ____

Complete the ratio 5:____ so that it is equivalent to 1:3.

The second number is missing from 5:___. So, compare the first numbers of the two ratios.

1:3

5:__

To get 5 from 1, multiply by 5.

So, to get ____ from the second number in 1:3, multiply by 5.

3 . 5=15

This means 5:15 and 1:3 are equivalent ratios.

✈️ Find the number that makes the ratio equivalent to 1:2.

9: ____

Complete the ratio 9:_____ so that it is equivalent to 1:2.

The second number is missing from 9:_____. So, compare the first numbers of the two ratios.

1:2

9:___

To get 9 from 1, multiply by 9.

So, to get _____ from the second number in 1:2, multiply by 9.

2 . 9=18

This means 9:18 and 1:2 are equivalent ratios.

✈️ Find the number that makes the ratio equivalent to 1:8.

8:____

Complete the ratio 8______: so that it is equivalent to 1:8.

The second number is missing from 8:____. So, compare the first numbers of the two ratios.

1:8

8:_____

To get 8 from 1, multiply by 8.

So, to get _____ from the second number in 1:8, multiply by 8.

This means 8:64 and 1:8 are equivalent ratios.

Let’s practice! 🖊️