Simplify -3-10-7-15-3-20-9-10-13-15-13-20

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Addition of Fractions

Simplify -3...

Question

Simplify $\frac{- 3}{10} + \frac{7}{15} + \frac{3}{- 20} + \frac{- 9}{10} + \frac{13}{15} + \frac{13}{- 20}$

\frac{- 2}{3}

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\frac{3}{5}

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\frac{4}{5}

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\frac{1}{3}

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Solution

The correct option is A $\frac{- 2}{3}$
Re-arranging and grouping the numbers in pairs such that each group contains a pair of rational numbers with equal denominators, we have
$\frac{- 3}{10} + \frac{7}{15} + \frac{3}{- 20} + \frac{- 9}{10} + \frac{13}{15} + \frac{13}{- 20}$
$= (\begin{matrix} \frac{- 3}{10} + \frac{- 9}{10} \end{matrix}) + (\begin{matrix} \frac{7}{15} + \frac{13}{15} \end{matrix}) + (\begin{matrix} \frac{3}{- 20} + \frac{13}{- 20} \end{matrix})$
$= (\begin{matrix} \frac{- 3}{10} + \frac{- 9}{10} \end{matrix}) + (\begin{matrix} \frac{7}{15} + \frac{13}{15} \end{matrix}) + (\begin{matrix} \frac{- 3}{20} + \frac{- 13}{20} \end{matrix})$
$= \frac{(- 3) + (- 9)}{10} + \frac{7 + 13}{15} + \frac{(- 3) + (- 13)}{20}$
$= \frac{- 12}{10} + \frac{20}{15} + \frac{- 16}{20}$
$= \frac{- 6}{5} + \frac{4}{3} + \frac{- 4}{5}$
[Expressing each rational in lowest terms]
$= (\begin{matrix} \frac{- 6}{5} + \frac{- 4}{5} \end{matrix}) + \frac{4}{3}$
$= \frac{(- 6) + (- 4)}{5} + \frac{4}{3} = \frac{- 10}{5} + \frac{4}{3}$
$= - 2 + \frac{4}{3} = \frac{- 6 + 4}{3} = \frac{- 2}{3}$

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Similar questions

Q. Simplify:

(\frac{13}{15} - \frac{3}{5}) \div (\frac{13}{15} + \frac{3}{5})

Q. Simplify:

(1) (−8) + (−3)
(2) 13 − 15
(3) 6 − (−19)
(4) 10 + (−7)

Find each of the following products :

(i) $\frac{3}{5} \times \frac{- 7}{8}$ (ii) $\frac{- 9}{2} \times \frac{5}{4}$ (iii) $\frac{- 6}{11} \times \frac{- 5}{3}$

(iv) $\frac{- 2}{3} \times \frac{6}{7}$ (v) $\frac{- 12}{5} \times \frac{10}{- 3}$ (vi) $\frac{25}{- 9} \times \frac{3}{- 10}$

(vii) $\frac{5}{- 18} \times \frac{- 9}{20}$ (viii) $\frac{- 13}{15} \times \frac{- 25}{26}$ (ix) $\frac{16}{- 21} \times \frac{14}{5}$

(x) $\frac{- 7}{6} \times 24$ (xi) $\frac{7}{24} \times (- 48)$ (xii) $\frac{- 13}{5} \times (- 10)$

Prove that:
(i) $\frac{1}{3 + \sqrt{7}} + \frac{1}{\sqrt{7} + \sqrt{5}} + \frac{1}{\sqrt{5} + \sqrt{3}} + \frac{1}{\sqrt{3} + 1} = 1$
(ii) $\frac{1}{1 + \sqrt{2}} + \frac{1}{\sqrt{2} + \sqrt{3}} + \frac{1}{\sqrt{3} + \sqrt{4}} + \frac{1}{\sqrt{4} + \sqrt{5}} + \frac{1}{\sqrt{5} + \sqrt{6}} + \frac{1}{\sqrt{6} + \sqrt{7}} + \frac{1}{\sqrt{7} + \sqrt{8}} + \frac{1}{\sqrt{8} + \sqrt{9}} = 2$

Q. Simplify each of the following:

4 + \frac{1}{5} [\{- 10 \times (25 - 13 - 3)\} \div (- 5)]

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Simplify −310+715+3−20+−910+1315+13−20

Simplify $\frac{- 3}{10} + \frac{7}{15} + \frac{3}{- 20} + \frac{- 9}{10} + \frac{13}{15} + \frac{13}{- 20}$