Using commutativity and associativity of addition of rational numbers, express the following as a rational number. [3 marks]
$\frac{4}{5} + \frac{9}{4} + \frac{- 7}{5} + \frac{- 1}{4}$

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Solution

Given: $\frac{4}{5} + \frac{9}{4} + \frac{- 7}{5} + \frac{- 1}{4}$

Using associative property, grouping the given rational numbers with the same denominators together,

$∴ \frac{4}{5} + \frac{9}{4} + \frac{- 7}{5} + \frac{- 1}{4} = (\frac{4}{5} + \frac{- 7}{5}) + (\frac{9}{4} + \frac{- 1}{4})$ (1 mark)
$= (\frac{4 - 7}{5}) + (\frac{9 - 1}{4})$
$= \frac{- 3}{5} + \frac{8}{4}$
$= \frac{- 3 \times 4}{5 \times 4} + \frac{8 \times 5}{4 \times 5}$ (1 mark)
$= \frac{- 12}{20} + \frac{40}{20}$
$= \frac{- 12 + 40}{20}$
$= \frac{28}{20}$
$= \frac{7}{5}$ (1 mark)

Hence, $\frac{4}{5} + \frac{9}{4} + \frac{- 7}{5} + \frac{- 1}{4} = \frac{7}{5}$

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Using commutativity and associativity of addition of rational numbers, express the following as a rational number. [3 marks]
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