Year 7AC9M7N08

Ratios and Simplifying

Recognise, represent and solve problems involving ratios.

A ratio compares two amounts of the same kind. It behaves almost exactly like a fraction, and it simplifies the same way.

Method

Order matters

3:2 \neq 2:3

The first number goes with the first thing named.

Simplify by dividing both parts

12:18 = 2:3

Divide by the highest common factor, just like a fraction.

Units must match first

1\text{ m}:50\text{ cm} = 100:50 = 2:1

Convert to the same unit before simplifying.

e.g.

\text{Simplify } 45:60

Check both parts are in the same unit. $\text{both plain numbers} \quad\checkmark$
Find the highest common factor. $HCF(45,60) = 15$
Divide the first part by it. $45 \div 15 = 3$
Divide the second part by the same number. $60 \div 15 = 4$
Write the simplified ratio. $45:60 = 3:4$

Match the units first, then simplify.

\text{Simplify } 20:35

Answer

4:7

\text{Simplify } 8:12:20

Answer

2:3:5

\text{Simplify } 2\text{ km}:500\text{ m}

Answer

2000:500 = 4:1

\text{Simplify } 0{,}5:1{,}5

Answer

1:3

\text{A class has } 12 \text{ boys and } 15 \text{ girls. Ratio of boys to girls?}

Answer

4:5