Write an equivalent ratio

Key Notes :

Definition of Ratio

A ratio is a comparison of two quantities.

It can be written in three forms:

  • Fraction form (3/4)
  • Colon form (3:4)
  • Word form (3 to 4)

What are Equivalent Ratios?

  • Equivalent ratios have the same relationship between numbers but may use different values.
  • Example: 2:3, 4:6, and 6:9 are equivalent ratios.

Finding Equivalent Ratios

  • Multiply or divide both terms of the ratio by the same non-zero number.
  • Example: To find an equivalent ratio of 3:5, multiply both by 2 → (3×2):(5×2) = 6:10.

Using Cross Multiplication to Check Equivalence

Two ratios are equivalent if their cross products are equal.

Example: Check if 3:4 and 6:8 are equivalent.

  • Cross multiply: 3 × 8 = 24, 4 × 6 = 24 → Since they are equal, the ratios are equivalent.

Simplifying Ratios

Find the Greatest Common Factor (GCF) of both terms and divide.

Example: 10:15

  • GCF of 10 and 15 is 5.
  • Divide both by 5 → (10÷5):(15÷5) = 2:3.

Real-Life Examples of Equivalent Ratios

  • Recipes: A cake recipe uses a 2:3 ratio of sugar to flour. Doubling the recipe makes it 4:6.
  • Maps: A 1:50 scale means 1 cm on the map is 50 cm in real life.

Practice Writing Equivalent Ratios

Complete the missing numbers:

  • 5:7 = __:14
  • 8:12 = 4:__

Learn with an example

▶️ Find the number that makes the ratio equivalent to 1:4.

8: ______

Complete the ratio 8: ___ so that it is equivalent to 1:4.The second number is missing from 8: ____. 

So, compare the first numbers of the two ratios.

1:4

8: ___

To get 8 from 1, multiply by 8.

So, to get ____ from the second number in 1:4, multiply by 8.

4 . 8 = 32

This means 8:32 and 1:4 are equivalent ratios.

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

9: ______

Complete the ratio 9: ____ so that it is equivalent to 1:3.The second number is missing from 9:____. 

So, compare the first numbers of the two ratios.

1:3

9: ___

To get 9 from 1, multiply by 9.

So, to get ___ from the second number in 1:3, multiply by 9.

3 . 9 = 27

This means 9:27 and 1:3 are equivalent ratios.

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

6:________

Complete the ratio 6: ___ so that it is equivalent to 1:2.

The second number is missing from 6: ___. 

So, compare the first numbers of the two ratios.

1:2

6: ____

To get 6 from 1, multiply by 6.

So, to get ______ from the second number in 1:2, multiply by 6.

2 . 6 = 12

This means 6:12 and 1:2 are equivalent ratios.

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