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Percentage Equivalence Insights

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Percentage Equivalence Insights

Use the equivalence rule: a% of b has the same value as b% of a. Show your working where asked.

Understanding percentage equivalence

1.Calculate 35% of 24 by writing 35% as a decimal and multiplying.

2.Calculate 24% of 35 by writing 24% as a decimal and multiplying.

3.Compare your answers for 35% of 24 and 24% of 35. What do you notice?

4.Decide whether 45% of 20 equals 20% of 45.

TrueFalse

5.Decide whether 16% of 75 equals 75% of 16.

TrueFalse

6.Fill the blank to make an equivalent calculation: 18% of 40 = 40% of .

7.Complete the equivalence: % of 32 = 32% of 25.

8.Match each calculation with the equivalent one.

14% of 50
32% of 25
60% of 15

25% of 32
15% of 60
50% of 14

Models and problem solving

9.Use a bar model to show that 30% of 40 is equal to 40% of 30. Label both calculations and their shared result.

10.At a dinosaur dig, 15% of 80 labelled fossil fragments are set aside for careful cleaning. Tane says this is the same number as 80% of 15. Is he correct? Calculate both amounts.

Calculation A: 28% of 25

Equivalent calculation: 25% of ____

Shared answer: ____

Calculation A: ____% of 45

Equivalent calculation: 45% of 16

Shared answer: ____

Calculation A: 42% of 30

Equivalent calculation: ____% of ____

Shared answer: ____

11.Explain why 35% of 60 equals 60% of 35. Use the words decimal, multiplication, equivalent and proportion in your explanation.

12.At a dinosaur-dig fundraiser, 24% of the NZ$75 total came from fossil-print sales. Manaia says that amount is equal to 75% of NZ$24. Calculate both amounts and decide whether Manaia is correct.

13.Calculate 32% of 25 and 25% of 32. Show each multiplication and confirm whether the answers are equivalent.