Year 7AC9M7N08

Dividing a Quantity in a Ratio

Recognise, represent and solve problems involving ratios.

Sharing in a ratio is a three-step routine: count the parts, find one part, then build each share. It never varies.

Builds onYr 7 · Ratios and Simplifying

Method

Add the parts to get the total

3:2 \ \Rightarrow\ 5 \text{ parts}

This tells you how many equal pieces to split the amount into.

One part is the amount divided by the total parts

Check by adding the shares back

They must total the original amount. This catches almost every error.

e.g.

\text{Share } \$200 \text{ in the ratio } 3:2

Add the parts. $3 + 2 = 5 \text{ parts}$
Divide the amount by the number of parts. $200 \div 5 = 40 \quad \text{(one part)}$
Multiply for the first share. $3 \times 40 = 120$
Multiply for the second share. $2 \times 40 = 80$
Check the shares add back to the total. $120 + 80 = 200 \quad\checkmark$

Count the parts, find one part, then build each share.

\text{Share } 60 \text{ in } 1:3

Answer

15 \text{ and } 45

\text{Share } 350 \text{ in } 4:3

Answer

200 \text{ and } 150

\text{Share } 96 \text{ in } 1:2:5

Answer

12,\ 24,\ 60

\text{Two people share in } 5:3. \text{ The larger share is } 250. \text{ Find the total.}

Answer

\text{one part } = 50 \quad\therefore\quad 400

\text{Concrete is } 1:2:4 \text{ cement, sand, stone. In } 21 \text{ kg, how much sand?}

Answer

6 \text{ kg}