Four operations: integers, decimals, fractions

OCR J560/01 (no calculator) routinely tests written-method arithmetic. The Foundation paper also has straight calculation marks at the start. Don't lose method marks by trying to do arithmetic in your head.

Integers — written methods

• Addition/subtraction: align in columns by place value; carry/borrow as needed.
• Long multiplication: e.g. 247 × 36. Multiply by 6 (units), then by 30 (tens, shift left). Add.
• Long division ("bus stop"): divide largest place first, bring down next digit, repeat.

Decimal calculation

• Addition/subtraction: line up decimal points (NOT right-edges).
• Multiplication: ignore decimal points, multiply as integers, then count total decimal places in the inputs and place the point.
  • 0.7 × 0.04. Integers: 7 × 4 = 28. Decimal places: 1 + 2 = 3. Answer: 0.028.
• Division: scale BOTH numbers by the same power of 10 to make the divisor an integer.
  • 4.5 ÷ 0.3 → 45 ÷ 3 = 15.

Fraction arithmetic

Addition/subtraction — common denominator first.

• 1/4 + 1/6 = 3/12 + 2/12 = 5/12.

Multiplication — multiply numerators and denominators directly. Cancel where possible.

• 2/3 × 9/10 = (2 × 9)/(3 × 10) = 18/30 = 3/5. Or cancel first: 2/3 × 9/10 = (1 × 3)/(1 × 5) = 3/5.

Division — flip and multiply (KFC: keep, flip, change).

• 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8 = 1⅞.

Mixed numbers

Convert to improper fractions before multiplying or dividing.

• 2¼ × 1⅓ = 9/4 × 4/3 = 36/12 = 3.

Order of operations (BIDMAS)

Brackets, Indices, Division/Multiplication (left to right), Addition/Subtraction (left to right).

Multiplication and division have equal priority — work left to right. Same with addition and subtraction.

Example: 12 − 3 × 2 = 12 − 6 = 6 (NOT 18).

OCR mark scheme conventions

• M1 for a correct method (long multiplication layout / common denominator shown).
• A1 for the correct final answer.
• Working must be shown for "use a written method" questions; bare answers without working can lose method marks even if correct.