2-3-4-5-7-15-11-20- a -1-5 b -4-15 c -13-60 d -7-30

LCM of 3, 5, 15 and 20 = 60 ∴ 2/3+ 4/5+7/15+ 11/20 =40+( 48)+28+( 33)/60 =40 48+28 33/60=68 81/60= 13/60 ...

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Byju's Answer

Standard VII

Mathematics

Addition of Rational Numbers

2/3+-4/5+7/15...

Question

$\frac{2}{3} + \frac{- 4}{5} + \frac{7}{15} + \frac{- 11}{20} = ?$

(a) $- \frac{1}{5}$

(b) $- \frac{4}{15}$

(c) $- \frac{13}{60}$

(d) $- \frac{7}{30}$

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Solution

LCM of 3, 5, 15 and 20 = 60

$∴ \frac{2}{3} + \frac{- 4}{5} + \frac{7}{15} + \frac{- 11}{20} = \frac{40 + (- 48) + 28 + (- 33)}{60} = \frac{40 - 48 + 28 - 33}{60} = \frac{68 - 81}{60} = \frac{- 13}{60}$

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133

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:

(a)

{sin}^{- 1} \frac{4}{5} + 2 {tan}^{- 1} \frac{1}{3} = \frac{π}{2}

(b)

{tan}^{- 1} \frac{1}{7} + 2 {tan}^{- 1} \frac{1}{3} = \frac{π}{4}

(c)

{tan}^{- 1} \frac{1}{5} + {tan}^{- 1} \frac{1}{7} + {tan}^{- 1} \frac{1}{3} + {tan}^{- 1} \frac{1}{8} = \frac{π}{4}

Q. If

A = {2, 3, 5, 7, 11, 13}

B = {5, 7, 9, 11, 15}

are the subsets of

U = {2, 3, 5, 7, 9, 11, 13, 15}

, verify De Morgan's laws.

Multiply and reduce to lowest form and convert into a mixed fraction:

(i) $7 \times \frac{3}{5}$ (ii) $4 \times \frac{1}{3}$
(iii) $2 \times \frac{6}{7}$ (iv) $5 \times \frac{2}{9}$

(v) $\frac{2}{3} \times 4$ (vi) $\frac{5}{2} \times 6$
(vii) $11 \times \frac{4}{7}$ (viii) $20 \times \frac{4}{5}$
(ix) $13 \times \frac{1}{3}$ (x) $15 \times \frac{3}{5}$

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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23+−45+715+−1120=? (a) −15 (b) −415 (c) −1360 (d) −730

LCM of 3, 5, 15 and 20 = 60 ∴ 23+−45+715+−1120=40+(−48)+28+(−33)60=40−48+28−3360=68−8160=−1360

$\frac{2}{3} + \frac{- 4}{5} + \frac{7}{15} + \frac{- 11}{20} = ?$

(a) $- \frac{1}{5}$

(b) $- \frac{4}{15}$

(c) $- \frac{13}{60}$

(d) $- \frac{7}{30}$

LCM of 3, 5, 15 and 20 = 60

$∴ \frac{2}{3} + \frac{- 4}{5} + \frac{7}{15} + \frac{- 11}{20} = \frac{40 + (- 48) + 28 + (- 33)}{60} = \frac{40 - 48 + 28 - 33}{60} = \frac{68 - 81}{60} = \frac{- 13}{60}$