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Integer Operations Practice

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Integer Operations Practice

Work through each question. Show your working where space is provided.

Operations with integers

Practise adding, subtracting, multiplying and dividing positive and negative numbers.

1.Calculate each integer operation: (a) (−9) + 4; (b) 6 − (−5); (c) (−7) × 3; (d) (−24) ÷ (−6).

2.At dawn, the temperature in Dunedin was −6°C. It increased by 11°C by lunchtime. What was the lunchtime temperature?

3.Which description correctly represents (−3) × 4?

Four groups of −3, giving −12
Four groups of 3, giving 12
Three groups of 4, giving 12
Four groups of −3, giving 12

4.A diver is 12 metres below sea level. They descend a further 31 metres, then rise 20 metres. What is their final position relative to sea level?

Fractions, decimals and properties

Apply integer rules to fractions and decimals, and identify familiar operation properties.

5.Work out each value: (a) (−2/3) + 5/6; (b) (−1.8) × 5; (c) 8 ÷ (−1/4).

6.Explain why dividing by 1/4 gives the same result as multiplying by 4. Use 3 ÷ 1/4 to support your explanation.

7.Match each equation with the property it demonstrates.

(−4) + 9 = 9 + (−4)
5 × (2 + 7) = (5 × 2) + (5 × 7)
[3 + (−6)] + 8 = 3 + [(−6) + 8]

Distributive property
Associative property
Commutative property

Explain and apply

Use reasoning to explain how integer operations work in everyday situations.

8.Without using a calculator, explain what happens to a positive number when you divide it by a positive number less than 1. Use 15 ÷ 0.5 as an example.

9.A bank account has a balance of −$38. After four identical deposits, its balance is $26. What was the amount of each deposit? Write an equation and solve it.

10.A lift is on level −2 and travels up 7 floors. Write an integer calculation for its new level and state the answer.