Add the following rational numbers- i -5-7 and 3-7 ii -15-4-and-7-4 iii -8-11-and-4-11 iv 6-13-and-9-13

(i) 5/7 and 3/7 5/7 and 3/7= 5/7+3/7= 5+3/7= 2/7 (ii) 15/4 and 7/4 = 15/4+7/4= 15+7/4= 8/4 = 8 ÷ 4/4 ÷ 4= 2 (iii) 8/11 and 4/11 = 8/11+ 4/11= 8 4/11 = ...

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Standard VII

Mathematics

Addition of Rational Numbers

Add the follo...

Question

Add the following rational numbers:

(i) $\frac{- 5}{7} a n d \frac{3}{7}$

(ii) $\frac{- 15}{4} a n d \frac{7}{4}$

(iii) $\frac{- 8}{11} a n d \frac{- 4}{11}$

(iv) $\frac{6}{13} a n d \frac{- 9}{13}$

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Solution

(i) $\frac{- 5}{7} a n d \frac{3}{7}$

$\frac{- 5}{7} a n d \frac{3}{7} = \frac{- 5}{7} + \frac{3}{7} = \frac{- 5 + 3}{7} = \frac{- 2}{7}$

(ii) $\frac{- 15}{4} a n d \frac{7}{4} = \frac{- 15}{4} + \frac{7}{4} = \frac{- 15 + 7}{4} = \frac{- 8}{4} = \frac{- 8 \div 4}{4 \div 4} = - 2$

(iii) $\frac{- 8}{11} a n d \frac{- 4}{11} = \frac{- 8}{11} + \frac{- 4}{11} = \frac{- 8 - 4}{11} = \frac{- 12}{11}$

(iv) $\frac{6}{13} a n d \frac{- 9}{13} = \frac{6}{13} + \frac{- 9}{13} = \frac{6 - 9}{13} = \frac{- 3}{13}$

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Similar questions

Q. Add the following rational numbers:

(i)

\frac{12}{7} and \frac{3}{7}

(ii)

\frac{- 2}{5} and \frac{1}{5}

(iii)

\frac{3}{- 8} and \frac{1}{8}

(iv)

\frac{- 5}{11} and \frac{7}{- 11}

(v)

\frac{9}{- 13} and \frac{- 11}{- 13}

(vi)

\frac{- 2}{9} and \frac{- 5}{9}

(vii)

\frac{- 17}{9} and \frac{- 11}{9}

(viii)

\frac{- 3}{7} and \frac{5}{- 7}

Add the following rational numbers :

(i) $\frac{- 2}{5}$ and $\frac{4}{5}$ (ii) $\frac{- 6}{11}$ and $\frac{- 4}{11}$ (iii) $\frac{- 11}{8}$ and $\frac{5}{8}$

(iv) $\frac{- 7}{3}$ and $\frac{1}{3}$ (v) $\frac{5}{6}$ and $\frac{- 1}{6}$ (iv) $\frac{- 17}{15}$ and $\frac{- 1}{15}$

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

Verify commutativity of addition of rational numbers for each of the following pairs of rational numbers: (i) $\frac{- 11}{5} a n d \frac{4}{7}$ (ii) $\frac{4}{9} a n d \frac{7}{- 12}$ (iii) $\frac{- 3}{5} a n d \frac{- 2}{- 15}$ (iv) $\frac{2}{- 7} a n d \frac{12}{- 35}$ (v) $4 a n d \frac{- 3}{5}$ (vi) $- 4 a n d \frac{4}{- 7}$

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

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Add the following rational numbers: (i) −57and37 (ii) −154 and 74 (iii) −811 and −411 (iv) 613 and −913

(i) −57and37 −57 and 37=−57+37=−5+37=−27 (ii) −154 and 74=−154+74=−15+74=−84=−8÷44÷4=−2 (iii) −811 and −411=−811+−411=−8−411=−1211 (iv) 613 and −913=613+−913=6−913=−313

Add the following rational numbers:

(i) $\frac{- 5}{7} a n d \frac{3}{7}$

(ii) $\frac{- 15}{4} a n d \frac{7}{4}$

(iii) $\frac{- 8}{11} a n d \frac{- 4}{11}$

(iv) $\frac{6}{13} a n d \frac{- 9}{13}$