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

(i) 3/4 + ( 3/5 ) 15+( 12)/20=15 12/20=3/20 (LCM of 4, 5 = 20) (ii) 5/8 + 7/12 =15+( 14)/24=15 14/24=1/24 (LCM of 8, 12=24) (iii) 8/9 + 11/6 16+33/18= 17/1 ...

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Byju's Answer

Standard VII

Mathematics

Addition of Rational Numbers

Add the follo...

Question

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 $\frac{- 2}{5}$

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Solution

(i) $\frac{3}{4} + (\frac{- 3}{5})$
$\frac{15 + (- 12)}{20} = \frac{15 - 12}{20} = \frac{3}{20}$
(LCM of 4, 5 = 20)

(ii) $\frac{5}{8} + \frac{- 7}{12} = \frac{15 + (- 14)}{24} = \frac{15 - 14}{24} = \frac{1}{24}$
(LCM of 8, 12=24)

(iii) $\frac{- 8}{9} + \frac{11}{6} \frac{- 16 + 33}{18} = \frac{- 17}{18}$
(LCM of 9, 6=18)

(iv) $\frac{- 5}{16} + \frac{7}{24} \frac{- 15 + 14}{48} = \frac{1}{48}$
(LCM of 16, 24 = 48)

(v) $\frac{7}{- 18} + \frac{8}{27} = \frac{- 7}{18} + \frac{8}{27} \frac{- 21 + 16}{54} = \frac{- 5}{54}$
(LCM of 18, 27 = 54)

(vi) $\frac{1}{- 12} + \frac{2}{- 15} = \frac{- 1}{12} + \frac{- 2}{15} = \frac{- 5 + (- 8)}{60}$
(LCM of 12, 15 = 60)
$= \frac{- 5 - 8}{60} = \frac{- 13}{60}$

(vii) $- 1 + \frac{3}{4} \frac{- 4 + 3}{4} = \frac{- 1}{4}$

(viii) $2 + \frac{- 5}{4} \frac{8 + (- 5)}{4} = \frac{8 - 5}{4} = \frac{3}{4}$

(ix) $0 + \frac{- 2}{5} \frac{0 - 2}{5} = \frac{- 2}{5}$

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Similar questions

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 $\frac{- 1}{15}$

Q. 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} a n d \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}

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 using number line:

(1) 5 and 3

(2) 6 and 2

(3) (−3) and (+5)

(4) 8 and (−12)

(5) (−7) and 5

(6) 10 and (−14)

(7) (−5) and (−2)

(8) (+6) and (−9)

(9) (−4) and (−1)

(10) 1 and (−5)

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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Add the following rational numbers: (i) 34 and −35 (ii) 58 and −712 (iii) −89 and 116 (iv) −516 and 724 (v) 7−18 and 827 (vi) 1−12 and 2−15 (vii) −1 and 34 (viii) 2 and −54 (ix) 0 and −25