By what number should 1-2 -1 multiplied so that the product may equal to -4-7 -1-

Let x be multiplied,then x × ( 1/2 )^ 1= ( 4/7 )^ 1 x= ( 4/7 )^ 1÷ ( 1/2 )^ 1 = ( 7/ 4 )^1 ÷ ( 2/1 )^1=7/ 4÷ 2 =7/ 4×1/2=7/ 8= 7/8 ∴ Required number= 7/8 ...

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Byju's Answer

Standard VIII

Mathematics

Power of a Power

By what numbe...

Question

By what number should ${(\frac{1}{2})}^{- 1}$ multiplied so that the product may equal to ${(\frac{- 4}{7})}^{- 1} ?$

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Solution

$L e t x b e m u l t i p l i e d, t h e n x \times {(\frac{1}{2})}^{- 1} = {(\frac{- 4}{7})}^{- 1} x = {(\frac{- 4}{7})}^{- 1} \div {(\frac{1}{2})}^{- 1} = {(\frac{7}{- 4})}^{1} \div {(\frac{2}{1})}^{1} = \frac{7}{- 4} \div 2 = \frac{7}{- 4} \times \frac{1}{2} = \frac{7}{- 8} = \frac{- 7}{8} ∴ R e q u i r e d n u m b e r = \frac{- 7}{8}$

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By what number should (12)−1 multiplied so that the product may equal to (−47)−1 ?

Let x be multiplied,thenx×(12)−1=(−47)−1x=(−47)−1÷(12)−1=(7−4)1÷(21)1=7−4÷2=7−4×12=7−8=−78∴ Required number=−78

By what number should ${(\frac{1}{2})}^{- 1}$ multiplied so that the product may equal to ${(\frac{- 4}{7})}^{- 1} ?$