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 ✓.