Fractions

A standard method from Number and algebra basics: the steps and worked examples.

Steps

To add or subtract, make the denominators the same (use the L.C.M.).
To multiply, multiply tops and bottoms; cancel first if you can.
To divide, multiply by the reciprocal.

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Worked examples

Example 1: Algebraic fractions: simplify 1/(x − 1) − 1/(x + 2).

= (x + 2)/[(x − 1)(x + 2)] − (x − 1)/[(x − 1)(x + 2)]
= [(x + 2) − (x − 1)] / [(x − 1)(x + 2)]
= 3 / [(x − 1)(x + 2)]

Example 2: Fractions: work out 2/3 + 3/4 and 5/6 ÷ 10/9.

2/3 + 3/4  = 8/12 + 9/12 = 17/12 = 1 5/12      L.C.M. of 3 and 4 is 12
5/6 ÷ 10/9 = 5/6 × 9/10                        multiply by the reciprocal
           = 45/60 = 3/4

For the whole topic, read Number and algebra basics: key points, common mistakes and how the DSE tests it.

Steps

Worked examples

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