Four operations: integers, decimals, fractions
This is the bedrock of Foundation arithmetic. On Paper 1F (non-calculator), every paper has at least one column-method calculation worth 3–4 marks.
Integers — column methods
Addition / subtraction: stack place values, carry/borrow as needed. 1428 + 5736 = 7164.
Multiplication: long multiplication, grid method, or lattice. Edexcel marks any valid method. 234 × 12: 234 × 10 + 234 × 2 = 2340 + 468 = 2808.
Division: bus stop / short division for divisors ≤ 12; long division for larger. 672 ÷ 4 = 168.
Decimals — line up the decimal point
For addition/subtraction, align decimal points, padding with zeros. 3.4 + 2.78 = 3.40 + 2.78 = 6.18.
For multiplication: ignore decimal points, multiply as integers, then count total decimal places in inputs and place the point that many in from the right. 0.4 × 0.7 = 4 × 7 = 28; 1 + 1 = 2 decimal places ⇒ 0.28.
For division: convert the divisor to a whole number by multiplying both numbers by a power of 10. 6.4 ÷ 0.8 → 64 ÷ 8 = 8.
Fractions — common denominators
Addition / subtraction: find LCM of denominators. 2/3 + 1/4 = 8/12 + 3/12 = 11/12.
Multiplication: multiply tops and bottoms. 2/3 × 4/5 = 8/15.
Division: invert and multiply (multiply by the reciprocal). 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6.
Mixed numbers
Convert to improper fractions before operating. 2¾ × 1⅖ = 11/4 × 7/5 = 77/20 = 3 17/20.
Edexcel exam tip
For non-calc fraction operations: simplify before multiplying when possible. Cross-cancel. 4/9 × 3/8 = (4 × 3)/(9 × 8). Cancel 4 with 8 (giving 1 and 2) and 3 with 9 (giving 1 and 3) ⇒ 1/(3 × 2) = 1/6.
⚠Common mistakes— Common errors
- Decimals in addition without aligning the points: 3.4 + 0.78 written as 4.12 (forgetting the 4 was tenths, 8 was hundredths).
- Fraction addition by adding tops and bottoms: 1/2 + 1/3 ≠ 2/5.
- Division of fractions: forgetting to flip.
- Mixed-number multiplication: multiplying whole and fractional parts separately. Convert first.
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