Find each of the following products - i 3-5-7-8 ii -9-2-5-4 iii -6-11-5-3 iv -2-3-6-7 v -12-5-10-3 vi 25-9-3-10 vii 5-18-9-20 viii -13-15-25-26 ix 16-21-14-5 x -7-6- 24 xi 7-24- -48 xii -13-5- -10

(i) 3/5× 7/8 = 3 × ( 7)/5 × 8 = 21/40 (ii) 9/2×5/4 = 9 × 5/2 × 4 = 45/8 (iii) 6/11× 5/3 = 6 × ( 5)/11 × 3 = 30/33 = 30 ÷ 3/33 ÷ 3 = 10/11 (iv) 2/3×6/7 = ...

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Byju's Answer

Standard VII

Mathematics

Multiplication and Division of Rational Numbers

Find each of ...

Question

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) $\frac{- 13}{5} \times (- 10)$

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Solution

(i) $\frac{3}{5} \times \frac{- 7}{8} = \frac{3 \times (- 7)}{5 \times 8} = \frac{- 21}{40}$

(ii) $\frac{- 9}{2} \times \frac{5}{4} = \frac{- 9 \times 5}{2 \times 4} = \frac{- 45}{8}$

(iii) $\frac{- 6}{11} \times \frac{- 5}{3} = \frac{- 6 \times (- 5)}{11 \times 3} = \frac{30}{33}$

$= \frac{30 \div 3}{33 \div 3} = \frac{10}{11}$

(iv) $\frac{- 2}{3} \times \frac{6}{7} = \frac{- 2 \times 6}{3 \times 7} = \frac{- 12}{21}$

$= \frac{- 12 \div 3}{21 \div 3} = \frac{- 4}{7}$

(v) $\frac{- 12}{5} \times \frac{10}{- 3}$

$= \frac{- 12 \times 10}{5 \times (- 3)} = \frac{- 120}{- 15} = \frac{- 120 \div 15}{- 15 \div 15}$

$= \frac{- 8}{- 1} = \frac{8}{1} = 8$

(vi) $\frac{25}{- 9} \times \frac{3}{- 10}$

$= \frac{25 \times 3}{(- 9) \times (- 10)} = \frac{75}{90} = \frac{75 \div 15}{90 \div 15} = \frac{5}{6}$

(vii) $\frac{5}{- 18} \times \frac{- 9}{20}$

$\frac{5 \times (- 9)}{- 18 \times 20} = \frac{- 45}{- 360} = \frac{- 45 \div 45}{- 360 \div 45}$

$= \frac{- 1}{- 8} = \frac{1}{8}$

(viii) $\frac{- 13}{15} \times \frac{- 25}{26} = \frac{- 13 \times (- 25)}{15 \times 26} = \frac{325}{390}$

$= \frac{325 \div 65}{390 \div 65} = \frac{5}{6}$

(ix) $\frac{16}{- 21} \times \frac{14}{5} = \frac{16 \times 14}{- 21 \times 5} = \frac{224}{- 105}$

$= \frac{224 \div 7}{- 105 \div 7} = \frac{32}{- 15} = \frac{- 32}{15}$

(x) $\frac{- 7}{6} \times 24 = \frac{- 7 \times 24}{6} = - 7 \times 4 = - 28$

(xi) $\frac{7}{24} \times (- 48) = \frac{7 \times (- 48)}{24}$

$= 7 \times (- 2) = - 14$

(xii) $\frac{- 13}{5} \times (- 10) = \frac{- 13 \times (- 10)}{5}$

$= - 13 \times (- 2) = 26$

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

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

Name the property of multiplication illustrated by each of the following statements :

(i) $\frac{- 15}{8} \times \frac{- 12}{7} = \frac{- 12}{7} \times \frac{- 15}{8}$

(ii) $(\frac{- 2}{3} \times \frac{7}{9}) \times \frac{- 9}{5} = \frac{- 2}{3} \times (\frac{7}{9} \times \frac{- 9}{5})$

(iii) $\frac{- 3}{4} \times (\frac{- 3}{4} \times \frac{- 5}{6}) + (\frac{- 3}{4} \times \frac{7}{8})$

(iv) $\frac{- 16}{9} \times 1 = 1 \times \frac{- 16}{9} = \frac{- 16}{9}$

(v) $\frac{- 11}{15} \times \frac{15}{- 11} = \frac{15}{- 11} \times \frac{- 11}{15} = 1$

(vi) $\frac{- 7}{5} \times 0 = 0$

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

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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Find each of the following products : (i) 35×−78 (ii) −92×54 (iii) −611×−53 (iv) −23×67 (v) −125×10−3 (vi) 25−9×3−10 (vii) 5−18×−920 (viii) −1315×−2526 (ix) 16−21×145 (x) −76×24 (xi) 724×(−48) (xii) −135×(−10)