What Is the Ratios?(With Examples)

A ratio is a comparison of two or more quantities showing the relative size of one quantity to another. It can be written as a:b, a/b, or "a to b" and tells you how many times one value contains another.

Grades 6-7Key Stage 3 (Year 7-9)Årskurs 6-8Klasse 6-7

📖Definition

A ratio is a comparison of two or more quantities showing the relative size of one quantity to another. It can be written as a:b, a/b, or "a to b" and tells you how many times one value contains another.

📐Formula

a : b or a/b

The ratio a:b means for every "a" units of one quantity, there are "b" units of another. For example, a ratio of 3:2 means for every 3 of one thing, there are 2 of another.

📝Step-by-Step Guide

1

Writing a Ratio

Identify the quantities being compared and write them in the correct order. Order matters in ratios!

2

Simplifying Ratios

Divide both parts of the ratio by their greatest common factor (GCF).

Example: 12:8 = 3:2 (divide both by 4)
3

Using Equivalent Ratios

Multiply or divide both parts by the same number to find equivalent ratios.

2:3 = 4:6 = 6:9 = 8:12
4

Solving Ratio Problems

Set up a proportion (two equal ratios) and cross-multiply to find the unknown value.

If a:b = c:x, then a × x = b × c

⚠️Common Mistakes to Avoid

  • Mixing up the order of quantities in a ratio
  • Not simplifying ratios to lowest terms
  • Adding instead of multiplying when finding equivalent ratios
  • Confusing ratios with fractions (ratios compare parts, fractions show part of whole)

✏️Practice Problems

Easy

Simplify the ratio 15:20

Answer: 3:4

Medium

If the ratio of boys to girls is 3:5 and there are 24 boys, how many girls are there?

Answer: 40 girls

Hard

A recipe uses flour and sugar in the ratio 5:2. If you have 350g of flour, how much sugar do you need?

Answer: 140g

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Worked Examples

Curriculum Alignment

CommonCore (6.RP.A.1)KS3KMK