Identify equivalent ratios

Key Notes :

What are Ratios?

  • A ratio is a relationship between two numbers, showing how many times the first number contains the second. It is written in the form of a:b or a/b, where a and b are numbers.

Equivalent Ratios

  • Equivalent ratios are ratios that express the same relationship between numbers, even though the numbers themselves may be different.
  • For example, the ratios 2:4 and 3:6 are equivalent because both express the same relationship (both simplify to 1:2).

How to Identify Equivalent Ratios?

  1. Simplifying the Ratio:
    • To check if two ratios are equivalent, try simplifying both ratios to their lowest terms.
    • Example:
      • 4:8 → Simplified form is 1:2.
      • 2:4 → Simplified form is also 1:2.
      • Since both ratios simplify to 1:2, they are equivalent.
  2. Cross-Multiplication Method:
    • You can also use cross-multiplication to identify equivalent ratios.
    • For two ratios a:b and c:d, if a × d = b × c, the ratios are equivalent.
    • Example:
      • Compare 2:3 and 4:6.
      • Cross-multiply: 2 × 6 = 12 and 3 × 4 = 12.
      • Since both products are equal, the ratios are equivalent.
  3. Multiplying or Dividing Both Terms of a Ratio:
    • You can find equivalent ratios by multiplying or dividing both terms of a ratio by the same number.
    • Example:
      • Start with 3:5.
      • Multiply both terms by 2: 3 × 2 = 6 and 5 × 2 = 10, giving the equivalent ratio 6:10.
      • Multiply both terms by 3: 3 × 3 = 9 and 5 × 3 = 15, giving the equivalent ratio 9:15.

Learn with an example

👉 Are the ratios 4:2 and 12:6 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 2 and 6. You can use 6 as the common denominator since 6 is a multiple of 2.

Write 4/2 with a denominator of 6.

So, 4/2 and 12/6 are equal.

This means that the ratios 4:2 and 12:6 are equivalent.

👉 Are the ratios 15:5 and 3:1 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 5 and 1. You can use 5 as the common denominator since 5 is a multiple of 1.

Write 3/1 with a denominator of 5.

So, 15/5 and 3/1 are equal.

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

✈️ Are the ratios 1:2 and 7:14 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 2 and 14. You can use 14 as the common denominator since 14 is a multiple of 2.

Write 12 with a denominator of 14.

So, 1/2 and 7/14 are equal.

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

Let’s practice! 🖊️