Identify equivalent ratios

key notes :

1. Definition of Equivalent Ratios

  • Equivalent ratios are two ratios that express the same relationship between numbers, even if the numbers are different.
  • For example, the ratios 2:3 and 4:6 are equivalent because both represent the same proportion.

2. How to Identify Equivalent Ratios

  • Simplifying Ratios: To check if two ratios are equivalent, simplify each ratio to its simplest form and see if they are the same.
    • Example: 6:8 and 3:4 → Divide both terms of 6:8 by 2 to get 3:4.
  • Cross Multiplication: You can also use cross multiplication to verify if two ratios are equivalent.
    • Example: To check if 2:3 is equivalent to 4:6, cross-multiply:
      • 2×6=12
      • 3×4=12
      • Since the products are equal, the ratios are equivalent.

3. Using Multiplication to Find Equivalent Ratios

  • If you multiply both terms of a ratio by the same number, the resulting ratio will be equivalent.
    • Example: Multiply 3:5 by 2 → 6:10.
  • The ratios 3:5 and 6:10 are equivalent because both represent the same proportion.

Learn with an example

🔔 Are the ratios 4:2 and 20:10 equivalent?

  • yes
  • no

First, write the ratios as fractions.

The first number is the numerator. The second number is the denominator.

4:2 ➔ 4/2

20:10 ➔ 20/10

You can compare the fractions using a common denominator.

The denominators are 2 and 10. You can use 10 as the common denominator since 10 is a multiple of 2.

Write 4/2  with a denominator of 10.

4/2 = 4 . 5 / 2 . 5 = 20/50

So,  4/2 and 20/10  are equal.

This means that the ratios 4:2 and 20:10 are equivalent.

🔔 Are the ratios 15:12 and 10:6 equivalent?

  • yes
  • no

First, write the ratios as fractions.

The first number is the numerator. The second number is the denominator.

15:12 ➔ 15/12

10:6 ➔ 10/6

You can compare the fractions using a common denominator.

The denominators are 12 and 6. You can use 12 as the common denominator since 12 is a multiple of 6.

Write 10/6 with a denominator of 12.

10/6 = 10 . 2 / 6 . 2 = 20/10

So,  15/12 and 10/6  are not equal.

This means that the ratios 15:12 and 10:6 are not equivalent.

Are the ratios 5:1 and 10:2 equivalent?

  • yes
  • no

First, write the ratios as fractions.

The first number is the numerator. The second number is the denominator.

You can compare the fractions using a common denominator.

The denominators are 1 and 2. You can use 2 as the common denominator since 2 is a multiple of 1.

Write 5/1 with a denominator of 2.

So, 5/1 and 10/2 are equal.

This means that the ratios 5:1 and 10:2 are equivalent.

Let’s Practice!