The four operations on integers, decimals and fractions

This is the workhorse of Unit 1 (non-calculator). WJEC opens every Foundation paper with 6–10 marks of pure arithmetic, and Higher students lose marks here surprisingly often.

Integers

Use long methods: column addition/subtraction, long multiplication, short or long division. Show each carry/borrow line.

Negatives:

• Same signs → positive: (-3) × (-4) = 12.
• Different signs → negative: (-3) × 4 = -12.
• Subtracting a negative is adding: 7 − (-3) = 7 + 3 = 10.

Decimals — addition and subtraction

Line up the decimal points; pad with trailing zeros; then add/subtract column-by-column. Bring the decimal point straight down.

12.40 + 0.075 → 12.400 + 0.075 = 12.475.

Decimals — multiplication

Ignore the decimal points; multiply as integers; count the total number of decimal places in the inputs and put that many in the answer.

3.4 × 0.06 → 34 × 6 = 204; total 1 + 2 = 3 decimal places → 0.204.

Decimals — division

Multiply both numbers by the same power of 10 to make the divisor a whole number, then do long division.

7.2 ÷ 0.4 → 72 ÷ 4 = 18.

Fractions — add/subtract

Find a common denominator, convert, add/subtract numerators only, simplify.

2/3 + 1/4: LCM(3,4) = 12, so 8/12 + 3/12 = 11/12.

Fractions — multiply

Multiply numerators and denominators. Cancel before multiplying when possible.

2/3 × 9/10 = (2 × 9)/(3 × 10) = 18/30 = 3/5. (Cancel 2/10 → 1/5 first: 1/3 × 9/5 × 2/2... or simpler: 2/3 × 9/10 = (2×9)/(3×10) and cancel 2/10 = 1/5: 9/15 = 3/5.)

Fractions — divide

Multiply by the reciprocal: a/b ÷ c/d = a/b × d/c.

3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8 = 1 7/8.

Mixed numbers

Convert to top-heavy (improper) fractions before multiplying or dividing. 2 1/3 = 7/3.

WJEC exam tip

Foundation papers expect exact answers in lowest-form fractions for non-calc work, and answers to 2 d.p. or 3 s.f. for decimal contexts. Always state your method line clearly — Σ method marks are worth more than the final A1.