Add the following rational numbers-i 34 and -58ii 5-9 and 73iii -3 and 35iv -727 and 1118v 31-4 and -58vi 536 and -712vii -516 and 724viii 7-18 and 827

(i) #160;Clearly, #160;denominators #160;of #160;the #160;given #160;numbers #160;are #160;positive. #160;The #160;L.C.M. #160;of #160;d ...

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Standard IV

Mathematics

Multiplication Trick for a Table

Add the follo...

Question

Add the following rational numbers:
(i) $\frac{3}{4} and \frac{- 5}{8}$
(ii) $\frac{5}{- 9} and \frac{7}{3}$
(iii) $- 3 and \frac{3}{5}$
(iv) $\frac{- 7}{27} and \frac{11}{18}$
(v) $\frac{31}{- 4} and \frac{- 5}{8}$
(vi) $\frac{5}{36} and \frac{- 7}{12}$
(vii) $\frac{- 5}{16} and \frac{7}{24}$
(viii) $\frac{7}{- 18} and \frac{8}{27}$

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Solution

$(i) Clearly, denominators of the given numbers are positive. The L.C.M. of denominators 4 and 8 is 8. Now, we will express \frac{3}{4} in the form in which it takes the denominator is 8 . \frac{3 \times 2}{4 \times 2} = \frac{6}{8} \frac{3}{4} + \frac{- 5}{8} = \frac{6}{8} + \frac{- 5}{8} = \frac{6 + (- 5)}{8} = \frac{6 - 5}{8} = \frac{1}{8} (ii) \frac{5}{- 9} + \frac{7}{3} = \frac{- 5}{9} + \frac{7}{3} The L.C.M. of denominators 9 and 3 is 9 . Now, we will express \frac{7}{3} in the form in which it takes the denominator is 9 . \frac{7 \times 3}{3 \times 3} = \frac{21}{9} \frac{- 5}{9} + \frac{7}{3} = \frac{- 5}{9} + \frac{21}{9} = \frac{(- 5) + 21}{9} = \frac{- 5 + 21}{9} = \frac{16}{9} (iii) - 3 + \frac{3}{5} = \frac{- 3}{1} + \frac{3}{5} The L.C.M. of denominators 1 and 5 is 5 . Now, we will express \frac{- 3}{1} in the form in which it takes the denominator 5 . \frac{- 3 \times 5}{1 \times 5} = \frac{- 15}{5} So \frac{- 3}{1} + \frac{3}{5} = \frac{- 15}{5} + \frac{3}{5} = \frac{- 15 + 3}{5} = \frac{- 12}{5} (iv) The L.C.M. of denominators 27 and 18 is 54 . Now, we will express \frac{- 7}{27} and \frac{11}{18} in the form in which they take the denominator 54 . \frac{- 7 \times 2}{27 \times 2} = \frac{- 14}{54} \frac{11 \times 3}{18 \times 3} = \frac{33}{54} \frac{- 7}{27} + \frac{11}{18} = \frac{- 14}{54} + \frac{33}{54} = \frac{- 14 + 33}{54} = \frac{19}{54} (v) We have \frac{31}{- 4} + \frac{- 5}{8} = \frac{- 31}{4} + \frac{- 5}{8} The L.C.M. of denominators 4 and 8 is 8 . Now, we will express \frac{- 31}{4} in the form in which it takes the denominator 8 . \frac{- 31 \times 2}{4 \times 2} = \frac{- 62}{8} So \frac{- 31}{4} + \frac{- 5}{8} = \frac{- 62}{8} + \frac{- 5}{8} = \frac{(- 62) + (- 5)}{8} = \frac{- 62 - 5}{8} = \frac{- 67}{8} (vi) The L.C.M. of denominators 36 and 12 is 36 . Now, we will express \frac{- 7}{12} in the form in whic h it takes the denominator 36 . \frac{- 7 \times 3}{12 \times 3} = \frac{- 21}{36} So \frac{5}{36} + \frac{- 7}{12} = \frac{5}{36} + \frac{- 21}{36} = \frac{5 + (- 21)}{36} = \frac{5 - 21}{36} = \frac{- 16}{36} = \frac{- 4}{9} (vii) The L.C.M. of denominators 16 and 24 is 48 . Now, we will express \frac{- 5}{16} and \frac{7}{24} in the form in which they take the denominator 48 . \frac{- 5 \times 3}{16 \times 3} = \frac{- 15}{48} \frac{7 \times 2}{24 \times 2} = \frac{14}{48} So \frac{- 5}{16} + \frac{7}{24} = \frac{- 15}{48} + \frac{14}{48} = \frac{(- 15) + 14}{48} = \frac{- 15 + 14}{48} = \frac{- 1}{48} (viii) \frac{7}{- 18} + \frac{8}{27} = \frac{- 7}{18} + \frac{8}{27} The L.C.M. of denominators 18 and 27 is 54 . Now, we will express \frac{- 7}{18} and \frac{8}{27} in the form in which they take the denominator 54 . \frac{- 7 \times 3}{18 \times 3} = \frac{- 21}{54} \frac{8 \times 2}{27 \times 2} = \frac{16}{54} So \frac{- 7}{18} + \frac{8}{27} = \frac{- 21}{54} + \frac{16}{54} = \frac{- 21 + 16}{54} = \frac{- 5}{54} = \frac{- 5}{54}$

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Similar questions

Q. Add the following rational numbers:

(i)

\frac{- 2}{5} and \frac{3}{4}

(ii)

\frac{- 5}{9} and \frac{2}{3}

(iii)

- 4 and \frac{1}{2}

(iv)

\frac{- 7}{27} and \frac{5}{18}

(v)

\frac{- 5}{36} and \frac{- 7}{12}

(vi)

\frac{1}{- 9} and \frac{4}{- 27}

(vii)

\frac{- 9}{24} and \frac{- 1}{8}

(viii)

\frac{27}{- 4} and \frac{- 15}{8}

Add the following rational numbers:
(i) $\frac{3}{4}$ and $\frac{- 3}{5}$
(ii) $\frac{5}{8}$ and $\frac{- 7}{12}$
(iii) $\frac{- 8}{9}$ and $\frac{11}{6}$
(iv) $\frac{- 5}{16}$ and $\frac{7}{24}$
(v) $\frac{7}{- 18}$ and $\frac{8}{27}$
(vi) $\frac{1}{- 12}$ and $\frac{2}{- 15}$
(vii) $- 1$ and $\frac{3}{4}$
(viii) $2$ and $\frac{- 5}{4}$
(ix) $0$ and $\frac{- 2}{5}$