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Cambridge IGCSE Mathematics — 0580 Extended

Topic 1.5: Number — Four Operations

Negative numbers

Sign rules

Multiplying / dividing same signs

Answer is positive: \((-3) \times (-4) = +12\)

Multiplying / dividing different signs

Answer is negative: \((-3) \times 4 = -12\)

Subtracting a negative

Add the positive: \(5 - (-3) = 5 + 3 = 8\)

Evaluate \((-4) + (-7) - (-5)\).

Worked solution: negative four plus negative seven minus negative five equals negative six
Negative arithmetic: \((-4) + (-7) - (-5) = -6\)

Fractions and mixed numbers

Method

  1. +/− — common denominator, then add/subtract numerators.
  2. \(\times\) — multiply numerators and denominators; cancel before multiplying if possible.
  3. \(\div\) — multiply by the reciprocal of the second fraction.
  4. Convert mixed numbers to improper fractions before calculating.

Evaluate \(2\dfrac{1}{3} - 1\dfrac{5}{6}\).

Worked solution: two and one third minus one and five sixths equals one half
Mixed subtraction: \(2\dfrac{1}{3} - 1\dfrac{5}{6} = \dfrac{1}{2}\)

Evaluate \(\dfrac{2}{5} \times 1\dfrac{1}{4}\).

Worked solution: two fifths times one and one quarter equals one half
Fraction multiplication: \(\dfrac{2}{5} \times 1\dfrac{1}{4} = \dfrac{1}{2}\)

Paper 2 (non-calculator)

Cancel common factors before multiplying — it keeps numbers small and reduces arithmetic errors.

Try this

Evaluate \(\dfrac{3}{4} + \dfrac{5}{6}\).

Show answer
Answer

  1. Lowest common denominator is 12

    \[ \dfrac{3}{4} + \dfrac{5}{6} \]

  2. Rewrite each fraction over 12

    \[ \dfrac{3}{4} = \dfrac{9}{12},\quad \dfrac{5}{6} = \dfrac{10}{12} \]

  3. Add the numerators

    \[ \dfrac{9}{12} + \dfrac{10}{12} = \dfrac{19}{12} \]

  4. Answer

    \[ \dfrac{19}{12} = 1\dfrac{7}{12} \]

BIDMAS

Order of operations: Brackets → Indices → Division & Multiplication (left to right) → Addition & Subtraction (left to right).

Evaluate \(3 + 4 \times 2^2 - 6 \div 2\).

Worked solution: three plus four times two squared minus six divided by two equals sixteen
BIDMAS: \(3 + 4 \times 2^2 - 6 \div 2 = 16\)

Evaluate \(-2 \times (5 - 8)^2 + 4\).

Worked solution: negative two times five minus eight squared plus four equals negative fourteen
BIDMAS with brackets: \(-2 \times (5 - 8)^2 + 4 = -14\)

Exam Traps

  • \(-3^2 = -(3^2) = -9\), but \((-3)^2 = 9\) — brackets change the sign.
  • Division and multiplication have equal priority — work left to right, not division first.

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