Question

the product of two number is 1 whole 2/9 .If one of the number is 5 whole 7/9 find the other number ​

Answer 1

★ How to do :-

Here, we are given with a rational number that should be multiplied by an other number. We are also given with the answer obtained while multiplying those two fractions. But, we aren't given with the second number that the first number should be multiplied with. We are asked to find the same. To find the answer, we make use of some other concepts such as variables and the transition of numbers from one hand side to the other. While we are using this method, the sign of the appropriate number changes. We can also check out our answer by verification method. So, let's solve!!

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➤ Solution :-

Let the other number be y,

${\sf \leadsto 5 \dfrac{7}{9} \times y = 1 \dfrac{2}{9}}$

Convert the mixed fractions to improper fractions.

${\sf \leadsto \dfrac{52}{9} \times y = \dfrac{11}{9}}$

Shift the fraction on LHS to RHS.

${\sf \leadsto y = \dfrac{11}{9} \div \dfrac{52}{9}}$

Take the reciprocal of second fraction and multiply both fractions.

${\sf \leadsto y = \dfrac{11}{9} \times \dfrac{9}{52}}$

Write the numbers in lowest form by cancellation method.

${\sf \leadsto \cancel \dfrac{11 \times 9}{9 \times 52} = \dfrac{11}{52}}$

${\sf \leadsto y = \dfrac{11}{52}}$

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${\red{\underline{\boxed{\bf So, \: the \: other \: number \: is \: \dfrac{11}{52}.}}}}$

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Verification :-

${\sf \leadsto \dfrac{52}{9} \times y = \dfrac{11}{9}}$

Substitute the value of u.

${\sf \leadsto \dfrac{52}{9} \times \dfrac{11}{52} = \dfrac{11}{9}}$

Write both fractions on LHS with a common fraction.

${\sf \leadsto \dfrac{52 \times 11}{9 \times 52} = \dfrac{11}{9}}$

Write the fraction in lowest form by cancellation method.

${\sf \leadsto \dfrac{\cancel{52} \times 11}{9 \times \cancel{52}} = \dfrac{11}{9}}$

Write the resulting fraction.

${\sf \leadsto \dfrac{11}{9} = \dfrac{11}{9}}$

So,

${\sf \leadsto LHS = RHS}$

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Hence verified !!