Which of the following sum is in the simplest form?

\frac{4}{9} + \frac{- 5}{9}

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\frac{- 2}{5} + \frac{13}{20}

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\frac{- 5}{12} + \frac{11}{- 12}

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\frac{- 7}{8} + \frac{1}{12} + \frac{2}{3}

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Solution

The correct option is B $\frac{4}{9} + \frac{- 5}{9}$
A. $\frac{4}{9} + \frac{- 5}{9} = \frac{- 1}{9}$ Simplest Form

B. $\frac{- 2}{5} + \frac{13}{20} = \frac{- 8 + 13}{20} = \frac{5}{20}$ Not the simplest form

C. $\frac{- 5}{12} + \frac{11}{- 12} = \frac{- 5 - 11}{12} = \frac{- 16}{12}$ Not the simplest form

D. $\frac{- 7}{8} + \frac{1}{12} + \frac{2}{3} = \frac{- 21 + 2 + 16}{24} = \frac{- 3}{24}$ Not the simplest form

$\Rightarrow$ Only A gives answer in simplest form

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Similar questions

Re-arrange suitably and find the sum in each of the following :

(i) $\frac{11}{12} + \frac{- 17}{3} + \frac{11}{2} + \frac{- 25}{2}$

(ii) $\frac{- 6}{7} + \frac{- 5}{6} + \frac{- 4}{9} + \frac{- 15}{7}$

(iii) $\frac{3}{5} + \frac{7}{3} + \frac{9}{5} + \frac{- 13}{15} + \frac{- 7}{3}$

(iv) $\frac{4}{13} + \frac{- 5}{8} + \frac{- 8}{13} + \frac{9}{13}$

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

(vi) $\frac{1}{8} + \frac{5}{12} + \frac{2}{7} + \frac{7}{12} + \frac{9}{7} + \frac{- 5}{16}$

Evaluate :

$(i) \frac{3}{7} + \frac{- 4}{9} + \frac{- 11}{7} + \frac{7}{9} (i i) \frac{2}{3} + \frac{- 4}{5} + \frac{1}{3} + \frac{2}{5} (i i i) \frac{4}{7} + 0 + \frac{- 8}{9} + \frac{- 13}{7} + \frac{17}{9} (i v) \frac{3}{8} + \frac{- 5}{12} + \frac{3}{7} + \frac{3}{12} + \frac{- 5}{8} + \frac{- 2}{7}$

Verify each of the following :

(i) $\frac{3}{7} \times \frac{- 5}{9} = \frac{- 5}{9} \times \frac{3}{7}$

(ii) $\frac{- 8}{7} \times \frac{13}{9} = \frac{13}{9} \times \frac{- 8}{7}$

(iii) $\frac{- 12}{5} \times \frac{7}{- 36} = \frac{7}{- 36} \times \frac{- 12}{5}$

(iv) $- 8 \times \frac{- 13}{12} = \frac{- 13}{12} \times (- 8)$

Fill in the blanks:

$(i) - 4 \times \frac{7}{9} = \frac{7}{9} \times$ ___

$(i i) \frac{5}{11} \times \frac{- 3}{8} = \frac{- 3}{8} \times$ ___

$(i i i) \frac{1}{2} \times (\frac{3}{4} + \frac{- 5}{12}) = \frac{1}{2} \times$ ____ $+ (\times) \frac{- 5}{12}$

$(i v) \frac{- 4}{5} \times \frac{5}{7} \times$ ___ $= (\frac{- 4}{5} \times \frac{5}{7}) \times \frac{- 8}{9}$

Verify the following

(i) $\frac{- 12}{5} + \frac{2}{7} = \frac{2}{7} + \frac{- 12}{5}$

(ii) $\frac{- 5}{8} + \frac{- 9}{13} = \frac{- 9}{13} + \frac{- 5}{8}$

(iii) $3 + \frac{- 7}{12} = \frac{- 7}{12} + 3$

(iv) $\frac{2}{- 7} + \frac{12}{- 35} = \frac{12}{- 35} + \frac{2}{- 7}$

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Which of the following sum is in the simplest form?

The correct option is B 49+−59A. 49+−59=−19 Simplest FormB. −25+1320=−8+1320=520 Not the simplest formC. −512+11−12=−5−1112=−1612 Not the simplest formD. −78+112+23=−21+2+1624=−324 Not the simplest form⇒ Only A gives answer in simplest form