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Year 9 Number Operations

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Year 9 Number Operations

Show your working where appropriate. Simplify fractions fully and include units in word-problem answers.

Order of Operations and Integers

1.Evaluate 18 − 2 × 3² + 5.

2.Work out (30 ÷ 5) × 4 − 2³.

3.Calculate −11 + 17.

4.Calculate −15 − (−9).

5.Calculate (−7) × 8.

6.Calculate 42 ÷ (−6).

7.A number line shows a starting value of −6. Move 9 units to the right, then 4 units to the left. What value do you finish on?

8.At dawn in Tekapo, the temperature was −5°C. It warmed by 11°C during the day and then cooled by 7°C overnight. What was the temperature after it cooled?

Fractions, Decimals and Percentages

9.Write 0.45 as a percentage and as a fraction in simplest form.

10.Convert 7/8 to a decimal and a percentage.

11.The fraction bar is divided into 10 equal parts, with 3 parts shaded. What fraction and percentage of the bar are shaded?

12.Find 5/6 + 1/4. Give your answer in simplest form.

13.Find 7/10 − 1/4. Give your answer in simplest form.

14.A rain jacket is priced at $96. It is reduced by 20%. What is its sale price?

15.Mei uses 2/5 of her savings for a book and 1/6 for a bus pass. What fraction of her savings does she use altogether? Give the answer in simplest form.

Prime Factors and Problem Solving

16.Write 84 as a product of prime factors, using index notation where possible.

17.Find the highest common factor (HCF) and lowest common multiple (LCM) of 20 and 30.

18.Estimate 31.6 × 5.2 by rounding each number to the nearest whole number, then calculate the exact product.

19.A club has 42 junior members and 56 senior members. They are to be split into the greatest possible number of identical teams, with no one left over and the same number of juniors and seniors in every team. How many teams can be made, and how many members from each group will be in each team?