Do the ratios form a proportion?

Key Notes :

Definition of Proportion:

  • A proportion is an equation that shows two ratios are equal.
  • Example: 23/ = 4/6

Understanding Ratios:

  • A ratio is a comparison of two numbers, written as a:b, a/b, or a to b.
  • Example: The ratio of apples to oranges is 3:5.

Methods to Check if Ratios Form a Proportion:

Cross Multiplication Method:

If a/b = c/d, then a×d = b×c.

Example: Check if 4/6 = 6/9​:

  • 4×9 = 6×6
  • 36 = 36(True, so it’s a proportion).

Simplifying Method:

Simplify both ratios and see if they are equal.

Example: 10/15 = 20/30

  • 10/15 = 2/3​
  • 20/30 = 2/3

Since both are equal, they form a proportion.

Examples of Proportions:

  • 3/5 = 6/10
  • 8/12 = 2/3

Examples of Non-Proportions:

  • 4/7 ≠ 6/10​
  • 5/9 ≠ 10/15

Real-Life Applications:

  • Cooking: Using recipe ratios correctly.
  • Maps: Understanding scale ratios.
  • Speed: Comparing distance and time in driving.

Learn with an example

👉 Do the ratios 3/2 and 15/10  form a proportion?

  • yes
  • no

To determine whether the two ratios 3/2 and 15/10 form a proportion, you can compare them 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 3/2 with a denominator of 10.

3/2 = 3 . 5 / 2 .5 = 15 / 10

So, 3/2 and 15/10 are equal.

This means that the ratios form a proportion.

👉 Do the ratios 1/2 and 7/14 form a proportion?

  • yes
  • no

To determine whether the two ratios 1/2 and 7/14 form a proportion, you can compare them 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 1/2 with a denominator of 14.

1/2 = 1 . 7 / 2 . 7 = 7/14

So,  1/2 and 7/14 are equal.

This means that the ratios 1/2 and 7/14 form a proportion.

👉 Do the ratios 2/1 and 16/8 form a proportion?

  • yes
  • no

To determine whether the two ratios 2/1 and 16/8 form a proportion, you can compare them using a common denominator.

The denominators are 1 and 8. You can use 8 as the common denominator since 8 is a multiple of 1.

Write 2/1 with a denominator of 8.

2/1 = 2 . 8 / 1 . 8 = 16/8

So, 2/1 and 16/8  are equal.

This means that the ratios 2/1 and 16/8 form a proportion.

let’s practice! 🖊️