Decimal Arithmetic
Decimal arithmetic forms the foundation of financial literacy and measurement skills that Year 4 and 5 pupils need to master. When students struggle with adding 12.5 + 3.75 or calculating the cost of 2.3kg of apples at £1.45 per kg, they're missing crucial life skills that extend far beyond the classroom.
Try it right now
Click “Generate a problem” to see a fresh example of this technique.
Why it matters
Decimal arithmetic appears in countless real-world situations that children encounter daily. When shopping at Tesco, calculating that 3 items costing £2.45 each totals £7.35 requires decimal multiplication. Measuring ingredients for a Victoria sponge cake demands precision with decimals like 2.5 cups of flour or 1.25 teaspoons of vanilla extract. Sports statistics rely heavily on decimals — a footballer's average of 2.3 goals per match or a swimmer's time of 54.67 seconds. The UK National Curriculum emphasises these skills in Year 4 with recognition of tenths and hundredths, progressing to Year 5's three decimal place comparisons. Students who master decimal arithmetic by age 10 show significantly better performance in GCSE mathematics, particularly in topics involving money, measurement, and data handling where decimal calculations are fundamental.
How to solve decimal arithmetic
Decimal Arithmetic
- For +/−: line up the decimal points, then compute.
- For ×: ignore decimals, multiply, then count total decimal places.
- For ÷: make divisor whole by shifting decimal, then divide.
Example: 2.5 × 1.2: 25 × 12 = 300, two decimal places → 3.00.
Worked examples
0.5 + _______ = 1.5
Answer: 1
- Find the missing number → 1.5 − 0.5 — Subtract 0.5 from 1.5 to find the blank.
- Calculate → = 1 — The missing number is 1.
8.3 + 8.5 = _______
Answer: 16.8
- Line up the decimal points → 8.3 + 8.5 — Align by the decimal point.
- Add → = 16.8 — Operate column by column.
- Verify → 8.3 + 8.5 = 16.8 ✓ — Check.
35.88 − 3.43 = _______
Answer: 32.45
- Line up the decimal points → 35.88 − 3.43 — Align by the decimal point.
- Subtract → = 32.45 — Operate column by column.
- Verify → 35.88 − 3.43 = 32.45 ✓ — Check.
Common mistakes
- Ignoring decimal point alignment during addition leads to errors like 12.3 + 4.56 = 16.86 instead of the correct 16.86 when students write 123 + 456 = 579 and randomly place the decimal
- When multiplying decimals, students often place the decimal point incorrectly, calculating 2.4 × 1.3 = 31.2 instead of 3.12 by forgetting to count total decimal places
- During subtraction, borrowing across decimal points causes confusion, with 5.2 - 1.67 becoming 4.55 instead of 3.53 when students mishandle regrouping
- Students frequently round too early in multi-step problems, turning 3.67 + 2.84 ÷ 2 into 3.67 + 1.4 = 5.07 instead of the correct 5.09