4-9-8-15- a -32-45 b -8-5 c -9-10 d -5-6

Let x is required rational ∴ 4/9÷ x= 8/15⇒ 4/9×1/x= 8/15 1/x= 8/15×9/4= 72/60= 72÷12/60÷12= 6/5 ∴ x= 5/6 ...

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Byju's Answer

Standard VII

Mathematics

Multiplication and Division of Rational Numbers

4/9÷ ?=-8/...

Question

$\frac{4}{9} \div ? = \frac{- 8}{15} .$

(a) $\frac{- 32}{45}$

(b) $\frac{- 8}{5}$

(c) $\frac{- 9}{10}$

(d) $\frac{- 5}{6}$

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Solution

Let x is required rational

$∴ \frac{4}{9} \div x = \frac{- 8}{15} \Rightarrow \frac{4}{9} \times \frac{1}{x} = \frac{- 8}{15} \frac{1}{x} = \frac{- 8}{15} \times \frac{9}{4} = \frac{- 72}{60} = \frac{- 72 \div 12}{60 \div 12} = \frac{- 6}{5} ∴ x = \frac{- 5}{6}$

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Q. Express

{[(2^{1 / 2} . 4^{3 / 4} . 8^{5 / 6} . 16^{7 / 8} . 32^{9 / 10})^{4}]}^{8 / 25}

as an integer.

Q. Which of the following will come next in the following series?

919829873987649876559876546987654

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

Evaluate:

$(i) (\frac{5}{3})^{2} \times (\frac{5}{3})^{2}$

$(i i) (\frac{5}{6})^{6} \times (\frac{5}{6})^{- 4}$

$(i i i) (\frac{2}{3})^{- 3} \times (\frac{2}{3})^{- 2}$

$(i v) (\frac{9}{8})^{- 3} \times (\frac{9}{8})^{2}$

find the number of zeroes at the end of 10*9*8*7*5*6*4*3*32*1

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49÷ ?=−815. (a) −3245 (b) −85 (c) −910 (d) −56

Let x is required rational ∴ 49÷x=−815⇒ 49×1x=−8151x=−815×94=−7260=−72÷1260÷12=−65∴ x=−56

$\frac{4}{9} \div ? = \frac{- 8}{15} .$

(a) $\frac{- 32}{45}$

(b) $\frac{- 8}{5}$

(c) $\frac{- 9}{10}$

(d) $\frac{- 5}{6}$

Let x is required rational

$∴ \frac{4}{9} \div x = \frac{- 8}{15} \Rightarrow \frac{4}{9} \times \frac{1}{x} = \frac{- 8}{15} \frac{1}{x} = \frac{- 8}{15} \times \frac{9}{4} = \frac{- 72}{60} = \frac{- 72 \div 12}{60 \div 12} = \frac{- 6}{5} ∴ x = \frac{- 5}{6}$