1 (a) Work out $\frac{2}{7} + \frac{1}{4}$ (b) Work out $\frac{1}{5} - \frac{3}{4}$ Give your answer as a mixed number in its simplest form. - Edexcel - GCSE Maths - Question 1 - 2018 - Paper 1

To subtract the fractions $\frac{1}{5}$ and $\frac{3}{4}$, we again need a common denominator. The least common multiple of 5 and 4 is 20.

Convert each fraction:

$\frac{1}{5} = \frac{1 \times 4}{5 \times 4} = \frac{4}{20}$

$\frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20}$

Now subtract the two fractions:

$\frac{4}{20} - \frac{15}{20} = \frac{4 - 15}{20} = \frac{-11}{20}$

To express $\frac{-11}{20}$ as a mixed number, we note that it is less than 0 and cannot be expressed as a mixed number in positive terms. Thus, the result is $-\frac{11}{20}$.