Ratio Sharing

We can share a total amount into a specific ratio using a three-step method: Add, Divide, Multiply.

Add: Add the numbers in the ratio together to work out the total number of parts
Divide: Divide the total quantity by the total parts to work out the value of one part
Multiply: Multiply the value of one part by each number in the original ratio

Add: 3 + 2 = 5 total parts

Divide: to work out the value of one part
$400 ÷ 5 = $80 (one part is worth $80)

Multiply: to work out the shares
3 × $80 = $240
2 × $80 = $160

Check: $240 + $160 = $400. (It adds up correctly!)

Note: as fractions one person gets 35 and the other gets 25 for a total of 55

Imagine you invest $10,000 and your friend invests $30,000 in a business, how many times more money did your friend invest?

How should you both share the profits?

Sam and Alex invest money into a company. It is only fair that they share the profits based on how much they each put in.

Sam invests $10,000 and Alex invests $30,000. The company makes a profit of $12,000.

First Simplify the Ratio: $10,000 to $30,000 is 1:3

Add: 1 + 3 = 4 parts.

Divide into parts:
Profit of $12,000 ÷ 4 = $3,000.

Multiply to get the Final Share:
Sam gets: 1 × $3,000 = $3,000
Alex gets: 3 × $3,000 = $9,000

The plaster mix needs 3 parts cement, 1 part sand and 4 parts water by volume. We need 40 liters.

Add: 3 + 1 + 4 = 8 total parts

Divide to work out the value of one part
40 ÷ 8 = 5 (one part is 5 liters)

Multiply: to work out the shares:
3 × 5 = 15 liters cement
1 × 5 = 5 liters sand
4 × 5 = 20 liters water

Check: 15 + 5 + 20 = 40 liters. (It adds up correctly!)