Four operations with integers, decimals and fractions

Integers — written methods

CCEA Foundation Paper M1 (NC) tests the standard column algorithms.

• Addition / subtraction: line up units; carry/borrow as needed.
• Multiplication: long or grid multiplication. E.g. 234 × 17.
• Division: bus stop / short division for single-digit divisors; long division for two-digit.

Always estimate first to spot order-of-magnitude errors (e.g. 234 × 17 ≈ 200 × 20 = 4000, so an answer of 397 is wrong).

Decimals — alignment is everything

• Adding/subtracting: line up decimal points, fill blanks with zeros.
• Multiplying: ignore decimal points, multiply, then count total decimal places in both factors and apply to answer.
  • 0.4 × 0.03 → 4 × 3 = 12; 1 + 2 = 3 dp → 0.012.
• Dividing by a decimal: multiply both numbers by powers of 10 to make the divisor whole.
  • 4.8 ÷ 0.6 = 48 ÷ 6 = 8.

Fractions

• Adding/subtracting: common denominator, then add/subtract numerators.
  • 1/4 + 2/3 = 3/12 + 8/12 = 11/12.
• Multiplying: multiply numerators and denominators; cancel common factors first if possible.
  • 2/3 × 9/10 = 18/30 = 3/5 (or cancel 2/10 → 1/5; 9/3 → 3; → 1×3 / 1×5 = 3/5).
• Dividing: keep, change, flip (multiply by the reciprocal).
  • 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.

Example: 2 1/3 × 1 1/2 = 7/3 × 3/2 = 21/6 = 7/2 = 3 1/2.

Common CCEA exam tip

Show the working step that converts to a common denominator (or flips the second fraction in a division). The M1 method mark depends on it — even if the final A1 is wrong because of an arithmetic slip, the M1 still scores.