Subtract - i 3-4 from 1-3 ii -5-6 from 1-3 iii -8-9 from -3-5 iv -9-7 from -1 v -18-11 from 1 vi -13-9 from 0 vii -32-13 from -6-5 viii -7 from -4-7

(i) 3/4 from 1/3 or 1/3 3/4 = 4 9/12 = 5/12 (ii) 5/6 from 1/3 or 1/3 5/6 = 2 ( 5)/6 = 2+5/6 = 7/6 (iii) 8/9 from 3/5 3/5 8/9 27 ( 40)/45 = 27+40/ ...

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Byju's Answer

Standard VII

Mathematics

Subtraction of Rational Numbers

Subtract : i ...

Question

Subtract :

(i) $\frac{3}{4}$ from $\frac{1}{3}$ (ii) $\frac{- 5}{6}$ from $\frac{1}{3}$ (iii) $\frac{- 8}{9}$ from $\frac{- 3}{5}$

(iv) $\frac{- 9}{7}$ from -1 (v) $\frac{- 18}{11}$ from 1 (vi) $\frac{- 13}{9}$ from 0

(vii) $\frac{- 32}{13}$ from $\frac{- 6}{5}$ (viii) -7 from $\frac{- 4}{7}$

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Solution

(i) $\frac{3}{4}$ from $\frac{1}{3}$ or $\frac{1}{3} - \frac{3}{4}$

$= \frac{4 - 9}{12} = \frac{- 5}{12}$

(ii) $\frac{- 5}{6}$ from $\frac{1}{3}$ or $\frac{1}{3} - \frac{- 5}{6}$

$= \frac{2 - (- 5)}{6} = \frac{2 + 5}{6} = \frac{7}{6}$

(iii) $\frac{- 8}{9}$ from $\frac{- 3}{5}$

$\frac{- 3}{5} - \frac{- 8}{9}$

$\frac{- 27 - (- 40)}{45} = \frac{- 27 + 40}{45} = \frac{13}{45}$

(iv) $\frac{- 9}{7}$ from -1

$\frac{- 1}{1} - \frac{- 9}{7}$

$= \frac{- 7 - (- 9)}{7} = \frac{- 7 + 9}{7} = \frac{2}{7}$

(v) $\frac{- 18}{11}$ from 1

$= \frac{1}{1} - \frac{- 18}{11}$

$= \frac{11 - (- 18)}{11} = \frac{11 + 18}{11} = \frac{29}{11}$

(vi) $\frac{- 13}{9}$ from 0

$= 0 - (\frac{- 13}{9})$

$= \frac{- 0 - (- 13)}{9} = \frac{13}{9}$

(vii) $\frac{- 32}{13}$ from $\frac{- 6}{5}$

$= \frac{- 6}{5} - \frac{- 32}{13}$

$= \frac{- 78 - (- 160)}{65} = \frac{- 78 + 160}{65}$

$= \frac{82}{65}$

(viii) -7 from $\frac{- 4}{7}$

$= \frac{- 4}{7} - (\frac{- 7}{1})$

$= \frac{- 4 - (- 49)}{7} = \frac{- 4 + 49}{7} = \frac{45}{7}$

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Similar questions

Subtract :
$(i) \frac{5}{8} ~ f r o m \frac{- 3}{8} (i i) \frac{- 8}{11} ~ f r o m \frac{4}{11} (i i i) \frac{4}{9} ~ f r o m \frac{- 5}{9} (i v) \frac{1}{4} ~ f r o m \frac{- 3}{8} (v) \frac{- 5}{8} ~ f r o m \frac{- 13}{16} (v i) \frac{- 9}{22} ~ f r o m \frac{- 9}{33}$

Subtract by using number line:

(1) 6 from 8

(2) 9 from 6

(3) +5 from −7

(4) −4 from +5

(5) −2 from −5

Verify the following :

(i) $\frac{3}{7} \times (\frac{5}{6} + \frac{12}{13}) = (\frac{3}{7} \times \frac{5}{6}) + (\frac{3}{7} \times \frac{12}{13})$
(ii) $\frac{- 15}{4} \times (\frac{3}{7} + \frac{- 12}{5}) = (\frac{- 15}{4} \times \frac{3}{7}) + (\frac{- 15}{4} \times \frac{- 12}{5})$
(iii) $(\frac{- 8}{3} + \frac{- 13}{12}) \times \frac{5}{6} = (\frac{- 8}{3} \times \frac{5}{6}) + (\frac{- 13}{12} \times \frac{5}{6})$
(iv) $\frac{- 16}{7} \times (\frac{- 8}{9} + \frac{- 7}{6}) = (\frac{- 16}{7} \times \frac{- 8}{9}) + (\frac{- 16}{7} \times \frac{- 7}{6})$

Subtract the first rational number from the second in each of the following:

(i) $\frac{3}{8}, \frac{5}{8}$

(ii) $\frac{- 7}{9}, \frac{4}{9}$

(iii) $\frac{- 2}{11}, \frac{- 9}{11}$

(iv) $\frac{11}{13}, \frac{- 4}{13}$

(v) $\frac{1}{4}, \frac{- 3}{8}$

(vi) $\frac{- 2}{3}, \frac{5}{6}$

(vii) $\frac{- 6}{7}, \frac{- 13}{14}$

(viii) $\frac{- 8}{33}, \frac{- 7}{22}$

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) $\frac{1}{1 + \sqrt{2}} + \frac{1}{\sqrt{2} + \sqrt{3}} + \frac{1}{\sqrt{3} + \sqrt{4}} + \frac{1}{\sqrt{4} + \sqrt{5}} + \frac{1}{\sqrt{5} + \sqrt{6}} + \frac{1}{\sqrt{6} + \sqrt{7}} + \frac{1}{\sqrt{7} + \sqrt{8}} + \frac{1}{\sqrt{8} + \sqrt{9}} = 2$

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Subtract : (i) 34 from 13 (ii) −56 from 13 (iii) −89 from −35 (iv) −97 from -1 (v) −1811 from 1 (vi) −139 from 0 (vii) −3213 from −65 (viii) -7 from −47

Subtract :

(i) $\frac{3}{4}$ from $\frac{1}{3}$ (ii) $\frac{- 5}{6}$ from $\frac{1}{3}$ (iii) $\frac{- 8}{9}$ from $\frac{- 3}{5}$

(iv) $\frac{- 9}{7}$ from -1 (v) $\frac{- 18}{11}$ from 1 (vi) $\frac{- 13}{9}$ from 0

(vii) $\frac{- 32}{13}$ from $\frac{- 6}{5}$ (viii) -7 from $\frac{- 4}{7}$