NZ Level 5
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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 $5$5 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 $5$5, so we can multiply this by $5$5.

Do: $1.84\times5=\$9.20$1.84×5=$9.20.

This means $5$5 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 $20$20 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 $60$60c.

Do: $0.6\times20=\$12$0.6×20=$12

$20$20 bread rolls cost $\$12$$12

Question 4

 

Buzz bought $6$6 stamps for $24.

  1. What is the price for 1 stamp?

  2. How much would it cost him if he only wants to buy $2$2 stamps?

Question 5

$3$3 workers can build $5$5 tables in $8$8 minutes.

  1. How long would it take for 1 worker to build $5$5 tables?

  2. How long would it take for $2$2 workers to build the same number of tables ?

 

 

Outcomes

NA5-1

Reason with linear proportions.

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