Ratios and Proportions
A ratio compares two quantities of the same kind. Proportions state that two ratios are equal. These concepts are used in recipes, scale drawings, and comparing quantities in everyday life.
What You Need to Know
Key Concept Diagram
A ratio compares two or more quantities using the notation a:b (read as "a to b")
Ratios can be simplified by dividing all parts by their HCF
A proportion states that two ratios are equal: a/b = c/d
To divide a quantity in a given ratio: find the total parts, then calculate each share
Unit rate (unitary method): find the value for one unit, then scale up
Key Vocabulary
Ratio
A comparison of two quantities of the same type, written as a:b or a/b
Proportion
An equation stating that two ratios are equal: a:b = c:d
Simplify
To write a ratio in its lowest terms by dividing by the HCF of all parts
Unitary Method
Finding the value for one unit first, then multiplying to find any quantity
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
Simplify the ratio 15:25.
Question 2
Divide $60 in the ratio 2:3.
Question 3
If 4 apples cost $2.80, how much do 7 apples cost?
Key Concepts Summary
- ●A ratio compares two or more quantities using the notation a:b (read as "a to b")
- ●Ratios can be simplified by dividing all parts by their HCF
- ●A proportion states that two ratios are equal: a/b = c/d
- ●To divide a quantity in a given ratio: find the total parts, then calculate each share
- ●Unit rate (unitary method): find the value for one unit, then scale up