# Proportion and rates - Unitary method for whole numbers

Lesson

This is a method of carrying out a calculation to find the value of a number of items by first finding the cost of one of them. This method of solving problems is often handy for solving word problems.

#### Examples

Let's look at how we can use the the unitary method to find the value of one item:

##### question 1

Evaluate: If $12$12 cans of paint weight $30$30kg, how much does one can weigh?

Think: To find the weight of one tin, we need to divide the total weight by $12$12.

Do: $30\div12=2.5$30÷​12=2.5kg

That means, one tin of paint weighs $2.5$2.5kg.

Once we need know the value of one item, we can use it to find the value of any other quantity.

##### question 2

Evaluate: If $3$3 tennis balls cost $\$5.52$$5.52, how much would 55 tennis balls cost? Think: We can find out the cost of one tennis ball by dividing \5.52$$5.52 by $3$3. So one tennis ball would cost $\$1.84$$1.84. What we really want though is the cost of 55, so we can multiply this by 55. Do: 1.84\times5=\9.201.84×5=9.20. This means 55 tennis balls cost \9.20$$9.20

##### question 3

Let's check out one more example.

Evaluate: If $18$18 bread rolls cost $\$10.80$$10.80, how much would 2020 bread rolls cost? Think: We can find the cost of one bread roll by dividing \10.80$$10.80 by $18$18. So one bread roll costs $\$0.60$$0.60 or 6060c. Do: 0.6\times20=\120.6×20=12 2020 bread rolls cost \12$$12

### Outcomes

#### 5.NN4.03

Demonstrate an understanding of simple multiplicative relationships involving whole-number rates, through investigation using concrete materials and drawings