Grade 6 Ratios & Rates: Introduction to Ratios

Learn to write and understand ratios

What You'll Learn

Write a ratio from a picture (part to part and part to whole)
Write ratios in simplest form

📖Ratios

A ratio compares two quantities. In ● ● ● ● ● ● ▲ ▲ ▲ ▲ there are 6 circles and 4 triangles: circles to triangles is 6:4 = 3:2, and circles to all the shapes is 6:10 = 3:5.

Worked examples

Real problems from the practice worksheets, solved one step at a time.

Example 1
Simplify the ratio 54:36
1. Find the greatest common factor of 54 and 36: the biggest number that divides both is 18.
2. Divide both parts by 18: 54 ÷ 18 = 3 and 36 ÷ 18 = 2.
3. So 54:36 simplifies to 3:2.
Answer: 3:2
Example 2
Count the shapes. Write the ratio of hearts to all the shapes in simplest form: ♥ ♥ ♥ ▲ ▲ ▲ ▲ ▲ ▲ ▲ ▲
1. Count: 3 hearts out of 11 shapes in all, so hearts to all the shapes is 3:11.
2. 3 and 11 have no common factor bigger than 1.
3. So 3:11 is already in simplest form: 3:11.
Answer: 3:11
Example 3
Count the shapes. Write the ratio of circles to all the shapes in simplest form: ● ● ● ● ● ● ● ● ● ● ★ ★ ★ ★
1. Count: 10 circles out of 14 shapes in all, so circles to all the shapes is 10:14.
2. Find the greatest common factor of 10 and 14: the biggest number that divides both is 2.
3. Divide both parts by 2: 10 ÷ 2 = 5 and 14 ÷ 2 = 7.
4. So 10:14 simplifies to 5:7.
Answer: 5:7