Decimal Operations Mastery

Year 9 Mathematics — 2025 NZ Curriculum

Name:

Date:

🧠 Part 1: Mental Maths Warm-Up

Answer these quickly — use estimation to check your answers make sense. No calculator!

1. Calculate each of the following mentally. Write your answer and an estimate to show it is reasonable.

a) 1.3 + 0.2 = _______ Estimate: _______

b) 32.55 − 21.21 = _______ Estimate: _______

c) 4.8 + 3.15 = _______ Estimate: _______

d) 10.00 − 6.75 = _______ Estimate: _______

2. Circle the best estimate for 23.5 × 1.4 before you calculate.

About 20

About 33

About 46

About 60

Now calculate the exact answer: 23.5 × 1.4 = _______

➗ Part 2: Dividing Decimals by Whole Numbers

Use the column method. Show all working and express any remainder as a decimal.

3. Solve each division. Show your working in the box provided.

a) 8.4 ÷ 3 = _______

b) 6.4 ÷ 2 = _______

c) 5.7 ÷ 2 = _______

4. Which of the following correctly shows 9.3 ÷ 4? Circle your answer.

2.325

2.3 remainder 1

23.25

2.025

5. 🌍 Word Problem — Division with Remainder

You have 7.5 litres of paint. It takes 0.8 litres to paint one chair. How many chairs can you fully paint? How much paint is left over? Express the leftover amount as a decimal.

Number of chairs fully painted: _______ Leftover paint: _______ litres

6. 🛒 Word Problem — Sharing Equally

Three friends share a bag of kumara that weighs 8.4 kg equally. How much kumara does each person receive? Show your working using the column method.

Each person receives: _______ kg

✏️ Part 3: Applying Decimal Operations & Explanation

Use estimation, place value understanding, and mathematical language in your answers.

7. 💰 Multi-Step Word Problem

Aroha earns $135.50 babysitting and spends $48.75 on a new book and $23.90 on lunch. She then splits her remaining money equally between 4 savings jars. How much goes into each jar? Express your answer as a decimal.

Amount in each jar: $_______

8. Tick ALL the statements below that are correct about decimal operations.

When adding decimals, you must align the decimal points before calculating.

3.2 × 0.5 is the same as half of 3.2.

A remainder in a division problem must always be written as a whole number.

Estimating before calculating helps you check if your answer is reasonable.

5.7 ÷ 2 = 2.85 because 5.7 = 5 + 0.7, divided separately.

9. 🤔 Explanation Question

Explain why 5.7 ÷ 2 produces a decimal remainder. Give a real-life context where it would make sense to express the remainder as a decimal rather than rounding up or down.

10. 🏆 Extension Challenge

A running track is 250.11 metres long. A school group runs a total of 135.29 metres more than the full track length. What total distance did they run? Then divide this total equally among 5 students. How far did each student run?

Total distance: _______ m Each student's distance: _______ m