Evaluate each of the following- i2-3-3-5- ii-4-7-2-3- iii4-7-5-7- iv-2-5-9- v-3-8-2-7- vi-4-13-5-26- vii-5-14-2-7- viii13-15-12-25- ix-6-13-7-13- x7-24-19-36- xi5-63-8-21

(i)2/3 3/5 =10 9/15 (LCM of 3,5 = 15) =1/15 (ii) 4/7 2/ 3= 4/7+2/3 12+14/21 (LCM of 7,3=21) 2/21 (iii) 4/7 5/ 7=4/7 5/7 =4 5/7= 1/7 (iv) 2 ...

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Standard VII

Mathematics

Subtraction of Rational Numbers

Evaluate each...

Question

Evaluate each of the following: $(i) \frac{2}{3} - \frac{3}{5} (i i) \frac{- 4}{7} - \frac{2}{- 3} (i i i) \frac{4}{7} - \frac{- 5}{- 7} (i v) - 2 - \frac{5}{9} (v) \frac{- 3}{- 8} - \frac{- 2}{7} (v i) \frac{- 4}{13} - \frac{- 5}{26} (v i i) \frac{- 5}{14} - \frac{- 2}{7} (v i i i) \frac{13}{15} - \frac{12}{25} (i x) \frac{- 6}{13} - \frac{- 7}{13} (x) \frac{7}{24} - \frac{19}{36} (x i) \frac{5}{63} - \frac{- 8}{21}$

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Solution

(i) $\frac{2}{3} - \frac{3}{5} = \frac{10 - 9}{15} (L C M o f 3, 5 = 15) = \frac{1}{15}$

(ii) $\frac{- 4}{7} - \frac{2}{- 3} = \frac{- 4}{7} + \frac{2}{3} \frac{- 12 + 14}{21} (L C M o f 7, 3 = 21) \frac{2}{21}$

(iii) $\frac{4}{7} - \frac{- 5}{- 7} = \frac{4}{7} - \frac{5}{7} = \frac{4 - 5}{7} = \frac{- 1}{7}$

(iv) $\frac{- 2}{1} - \frac{5}{9} = \frac{- 18 - 5}{9} = \frac{- 23}{9}$

(v) $\frac{- 3}{- 8} - \frac{- 2}{7} = \frac{3}{8} + \frac{2}{7} = \frac{21 + 16}{56} (L C M o f 8, 7 = 56) = \frac{37}{56}$

(vi) $\frac{- 4}{13} - \frac{- 5}{26} = \frac{- 4}{13} + \frac{5}{26} = \frac{- 8 + 5}{26} (L C M o f 13, 26 = 26) = \frac{- 3}{26}$

(vii) $\frac{- 5}{14} - \frac{- 2}{7} = \frac{- 5}{14} + \frac{2}{7} = \frac{- 5 + 4}{14} (L C M o f 14, 7 = 14) = \frac{- 1}{14}$

(viii) $\frac{13}{15} - \frac{12}{25} \frac{65 - 36}{75} (L C M o f 15, 25 = 75) = \frac{29}{75}$

(ix) $\frac{- 6}{13} - \frac{- 7}{13} = \frac{- 6}{13} + \frac{7}{13} = \frac{- 6 + 7}{13} = \frac{1}{13}$

(x) $\frac{7}{24} - \frac{19}{36} L C M o f 24, 36 = 72 = \frac{7}{24} - \frac{19}{36} = \frac{21 - 38}{72} = \frac{- 17}{72}$

(xi) $\frac{5}{63} - \frac{- 8}{21} = \frac{5}{63} + \frac{8}{21} = \frac{5 + 24}{63} (L C M o f 63, 21 = 63) = \frac{29}{63}$

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Similar questions

Find each of the following products :

(i) $\frac{3}{5} \times \frac{- 7}{8}$ (ii) $\frac{- 9}{2} \times \frac{5}{4}$ (iii) $\frac{- 6}{11} \times \frac{- 5}{3}$

(iv) $\frac{- 2}{3} \times \frac{6}{7}$ (v) $\frac{- 12}{5} \times \frac{10}{- 3}$ (vi) $\frac{25}{- 9} \times \frac{3}{- 10}$

(vii) $\frac{5}{- 18} \times \frac{- 9}{20}$ (viii) $\frac{- 13}{15} \times \frac{- 25}{26}$ (ix) $\frac{16}{- 21} \times \frac{14}{5}$

(x) $\frac{- 7}{6} \times 24$ (xi) $\frac{7}{24} \times (- 48)$ (xii) $\frac{- 13}{5} \times (- 10)$

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

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) $\frac{- 16}{7} \times (\frac{- 8}{9} + \frac{- 7}{6}) = (\frac{- 16}{7} \times \frac{- 8}{9}) + (\frac{- 16}{7} \times \frac{- 7}{6})$

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

Q. Find variance for following data:

Marks	$0 - 4$	$5 - 9$	$10 - 14$	$15 - 19$	$20 - 24$	$25 - 29$	$30 - 34$	$35 - 39$
Frquency	$2$	$5$	$7$	$13$	$21$	$16$	$8$	$3$

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