Write an equivalent ratio

key notes :

1. Understanding Ratios

  • A ratio represents a relationship between two numbers. It can be written in three ways:
    • As a fraction (e.g., 3/4)
    • Using a colon (e.g., 3:4)
    • Using the word “to” (e.g., 3 to 4).

2. What Are Equivalent Ratios?

  • Equivalent ratios are two ratios that express the same relationship or value.
  • Example: The ratio 2:3 is equivalent to 4:6 because both simplify to the same value (2 ÷ 3 = 4 ÷ 6 = 0.666…).

3. How to Find Equivalent Ratios

  • To find equivalent ratios, multiply or divide both terms of the ratio by the same non-zero number.
    • Multiplying: If you multiply both terms of a ratio by the same number, you create an equivalent ratio.
      • Example: To find an equivalent ratio of 2:5, multiply both terms by 3:
        (2×3):(5×3)=6:15
    • Dividing: If you divide both terms of a ratio by the same number, you create an equivalent ratio.
      • Example: To find an equivalent ratio of 8:12, divide both terms by 4:
        (8÷4):(12÷4)=2:3

4. Simplifying Ratios

  • To simplify a ratio, divide both terms by their greatest common divisor (GCD).
    • Example: Simplify 6:9. The GCD of 6 and 9 is 3, so:
      • (6÷3):(9÷3)=2:3

5. Practice with Equivalent Ratios

  • Example 1: Write equivalent ratios for 4:7.
    • Multiply by 2 → 8:14
    • Multiply by 3 → 12:21
    • Divide by 2 → 2:3.5
  • Example 2: Simplify the ratio 16:20.
    • The GCD of 16 and 20 is 4, so:
      • (16÷4):(20÷4)=4:5

Learn with an example

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

7: ______

Complete the ratio 7: ___ so that it is equivalent to 1:2.

The second number is missing from 7: ___ . So, compare the first numbers of the two ratios.

1:2

7 :

To get 7 from 1, multiply by 7

So, to get ___ from the second number in 1:2, multiply by 7

2 . 7 = 14

This means 7:14 and 1:2 are equivalent ratios.

🔔 Find the number that makes the ratio equivalent to 1:5.

9:_____

Complete the ratio 9: ______ so that it is equivalent to 1:5.

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

1:5

9:___

To get 9 from 1, multiply by 9.

So, to get ______ from the second number in 1:5, multiply by 9.

5 . 9 = 45

This means 9:45 and 1:5 are equivalent ratios.

🔔 Find the number that makes the ratio equivalent to 1:6.

6:____

Complete the ratio 6: ___ so that it is equivalent to 1:6 .

The second number is missing from 6:_____. So, compare the first numbers of the two ratios.

1:6

6:

To get 6 from 1, multiply by 6.

So, to get ___ from the second number in 1:6, multiply by 6.

6 . 6 = 36

This means 6:36 and 1:6 are equivalent ratios.

Let’s Practice!