Express each of the following as a rational number with positive denominator:
(i) $\frac{- 15}{- 28}$
(ii) $\frac{6}{- 9}$
(iii) $\frac{- 28}{- 11}$
(iv) $\frac{19}{- 7}$

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Solution

Rational number with positive denominators:

(i) Multiplying the number by $-$ 1, we get:

$\frac{- 15}{- 28} = \frac{- 15 \times - 1}{- 28 \times - 1} = \frac{15}{28}$

(ii) Multiplying the number by $-$ 1, we get:

$\frac{6}{- 9} = \frac{6 \times - 1}{- 9 \times - 1} = \frac{- 6}{9}$

(iii) Multiplying the number by $-$ 1, we get:

$\frac{- 28}{- 11} = \frac{- 28 \times - 1}{- 11 \times - 1} = \frac{28}{11}$

(iv) Multiplying the number by $-$ 1, we get:

$\frac{19}{- 7} = \frac{19 \times - 1}{- 7 \times - 1} = \frac{- 19}{7}$

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Using commutativity and associativity of addition of rational numbers, express each of the following as a rational number:

(i) $\frac{2}{5} + \frac{7}{3} + \frac{- 4}{5} + \frac{- 1}{3}$

(ii) $\frac{3}{7} + \frac{- 4}{9} + \frac{- 11}{7} + \frac{7}{9}$

(iii) $\frac{2}{5} + \frac{8}{3} + \frac{- 11}{15} + \frac{4}{5} + \frac{- 2}{3}$

(iv) $\frac{4}{7} + 0 + \frac{- 8}{9} + \frac{- 13}{7} + \frac{17}{21}$

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