Mathematics • Year 7 • Unit 1 • Lesson 11
Operations with Decimals
Build fluency with the four operations on decimals. Line up the dots for + and −, count decimal places for ×, and shift dots equally for ÷. Estimate first, then calculate.
1. I do — fully worked example
Watch a worked decimal multiplication. Every step shows what you do and why it works.
Problem. Calculate 0.25 × 1.6.
Step 1 — Estimate first.
0.25 ≈ 0.25 and 1.6 ≈ 1.5 → 0.25 × 1.5 ≈ 0.375.
Reason: we use the estimate to check our final answer is in the right ballpark.
Step 2 — Ignore the dots and multiply as whole numbers.
25 × 16 = 400.
Reason: temporarily treating decimals as whole numbers turns it into ordinary multiplication.
Step 3 — Count the total decimal places in the question.
0.25 has 2 d.p. and 1.6 has 1 d.p. → total = 3 d.p.
Reason: when we ignored the dots we multiplied by powers of 10. We now have to undo those by placing the dot back.
Step 4 — Place the decimal in the answer.
400 with 3 d.p. → 0.400 = 0.4.
Reason: 0.4 matches our estimate of 0.375, so the placement is right. Drop trailing zeros.
Answer: 0.25 × 1.6 = 0.4.
2. We do — fill in the missing steps
Same structure as Section 1, but with the working faded. Fill in each blank line. 4 marks
Problem. Calculate 4.32 ÷ 0.6.
Step 1 — Estimate first:
4.32 ÷ 0.6 ≈ 4 ÷ 0.6 ≈ _______.
Step 2 — Make the divisor a whole number. Shift both dots ___ place to the right:
4.32 ÷ 0.6 → _______ ÷ _______
Step 3 — Divide using short division. 6 into 43 = ___ remainder ___. Bring down the 2 to make ___. 6 into ___ = ___.
Quotient: _______ . _______
Step 4 — Check against your estimate:
My answer = _______ ; Estimate was _______ ; in the same ballpark? _______
3. You do — independent practice
Show working under each problem. The first four are foundation, the middle two are standard, and the last two are extension.
Foundation — single step
3.1 Calculate 5.74 + 2.8. Line up the dots. 1 mark
3.2 Calculate 9.6 − 4.35. Show the borrowing. 1 mark
3.3 Calculate 0.6 × 0.7. State the total decimal places. 1 mark
3.4 Calculate 8.4 ÷ 0.2. Shift both dots first. 1 mark
Standard — combine two ideas
3.5 Calculate 6.35 + 2.8 + 0.75. Add a trailing zero so all three lines have two decimal places. 2 marks
3.6 Calculate 1.25 × 0.04. Show the ignore-dots multiplication and the total decimal places. 2 marks
Extension — push your thinking
3.7 Calculate 7.56 ÷ 0.09. Shift both dots, then divide. Show every step. 3 marks
3.8 Calculate (3.2 + 1.8) × 0.25 in two steps: first the brackets, then the multiplication. State your estimate, then your final answer. 2 marks
How did this worksheet feel?
What I'll revisit before next class:
Section 2 — We do (4.32 ÷ 0.6)
Step 1: 4 ÷ 0.6 ≈ 6 or 7.
Step 2: shift 1 place → 43.2 ÷ 6.
Step 3: 6 into 43 = 7 rem 1. Bring down 2 → 12. 6 into 12 = 2. Quotient: 7.2.
Step 4: 7.2 vs estimate ≈ 6-7 ✓ same ballpark.
3.1 — 5.74 + 2.8
Add trailing zero: 5.74 + 2.80. Hundredths: 4+0 = 4. Tenths: 7+8 = 15, write 5 carry 1. Ones: 5+2+1 = 8. Answer: 8.54.
3.2 — 9.6 − 4.35
Add trailing zero: 9.60 − 4.35. Hundredths: 0−5 borrow, 10−5 = 5. Tenths: 5−3 = 2 (after borrow). Ones: 9−4 = 5. Answer: 5.25.
3.3 — 0.6 × 0.7
6 × 7 = 42. Total d.p. = 1 + 1 = 2. So 0.42. Answer: 0.42.
3.4 — 8.4 ÷ 0.2
Shift both 1 place: 84 ÷ 2 = 42. Answer: 42.
3.5 — 6.35 + 2.8 + 0.75
Trailing zeros: 6.35 + 2.80 + 0.75. Hundredths: 5+0+5 = 10, write 0 carry 1. Tenths: 3+8+7+1 = 19, write 9 carry 1. Ones: 6+2+0+1 = 9. Answer: 9.90.
3.6 — 1.25 × 0.04
Ignore dots: 125 × 4 = 500. Total d.p. = 2 + 2 = 4. So 0.0500 = 0.05. Estimate check: 1 × 0.04 = 0.04. Close.
3.7 — 7.56 ÷ 0.09
Shift both 2 places right: 756 ÷ 9. 9 × 80 = 720. 756 − 720 = 36. 9 × 4 = 36. So 80 + 4 = 84. Estimate check: 7.5 ÷ 0.1 = 75, answer 84 is in the right ballpark.
3.8 — (3.2 + 1.8) × 0.25
Brackets first: 3.2 + 1.8 = 5.0. Then 5.0 × 0.25. Ignore dots: 50 × 25 = 1250. Total d.p. = 1 + 2 = 3 → 1.250 = 1.25. (Or use mental: 0.25 is a quarter, so 5 ÷ 4 = 1.25.) Estimate: 5 × 0.25 ≈ 1.25 ✓.