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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

📐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

Writing a Ratio

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

Simplifying Ratios

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

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

Using Equivalent Ratios

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

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

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

Printable Ratios practice

Need more than a few examples? Create a printable ratios test with a worked answer key, balanced difficulty, and a teacher-reviewed PDF.

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Worked Examples

Ratio Problem Examplemedium

Proportions Fractions Percentages Scale Factor

Curriculum Alignment

CommonCore (6.RP.A.1)KS3KMK

Classroom assessment context

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