IGCSE Maths / Fractions, decimals and rounding

Directed numbers

Edexcel International GCSE Maths (4MA1), chapter 1: Fractions, decimals and rounding, specification point 1.1c. Free lesson.

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Directed numbers are positive and negative numbers. Use the right rule for each operation, then check how the answer relates to zero.

Use different rules for different operations

For addition and subtraction, subtracting a negative is the same as adding. For multiplication and division, matching signs give a positive answer and different signs give a negative answer. Keep these rules separate. 5 − (−3) = 5 + 3 −2 + (−6) = −2 − 6 (−4) × (−3) = 12 (−12) ÷ 3 = −4

Subtracting a negative moves you right

When a subtraction sign is followed by a negative number, the signs are side by side, so subtracting the negative becomes adding. On a number line, adding a positive number means moving right. You may pass zero and end up positive. Start at the first number. Move right by the amount being added.

Count minus signs when multiplying or dividing

For a chain of multiplications, work out the numbers without their signs first. Then count the minus signs: an even number gives a positive answer, while an odd number gives a negative answer. The same-sign rule also applies to division. Even number of minus signs: positive answer. Odd number of minus signs: negative answer.

A subtraction is a move left

The multiplying rule does not apply just because an expression contains two minus signs. In −3 − 4, the second minus means subtract 4, so start at −3 and move four places left. The answer becomes more negative. Use the subtracting-a-negative rule only when a subtraction sign is followed by a negative number, as in −6 − (−10). Multiplying by a negative can flip a number to the other side of zero. For example, 5 × −2 = −10, which is smaller than 5.

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