Question

By what rational number should the sum of 18/5 and -7/15 be devided to get 47/6 ?

Answer 1

★ How to do :-

Here, we are given with a rational number that will be answer when we divide two fractions. We are given that if we add two fractions, we get the first fraction that the second fraction should be divided with. We are asked to find the second fraction that the first fraction should be divided with. To find the answer of this question, we use an other concept called as the transposition method. We use this method to find the values of the variables. We can consider any variable say y and then we can find the value of that variable y by this concept. We can also verify our answer which will also be done here. In this method we can see that the answer obtained to us is correct or not. So, let's solve!!

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➤ Solution :-

${\sf \leadsto \bigg( \dfrac{18}{5} + \dfrac{(-7)}{15} \bigg) \div y = \dfrac{47}{6}}$

Firstly, solve the fractions in bracket

LCM of 5 and 15 is 15.

${\sf \leadsto \bigg( \dfrac{18 \times 3}{5 \times 3} + \dfrac{(-7)}{15} \bigg) \div y = \dfrac{47}{6}}$

Multiply the numerators and denominators of first fraction.

${\sf \leadsto \bigg( \dfrac{54}{15} + \dfrac{(-7)}{15} \bigg) \div y = \dfrac{47}{6}}$

Write the second number with one sign.

${\sf \leadsto \bigg( \dfrac{54 - 7}{15} \bigg) \div y = \dfrac{47}{6}}$

Subtract the numerators.

${\sf \leadsto \dfrac{47}{15} \div y = \dfrac{47}{6}}$

Shift the fraction on LHS to RHS, changing it's sign.

${\sf \leadsto y = \dfrac{47}{15} \div \dfrac{47}{6}}$

Take the reciprocal of second fraction and multiply both fractions.

${\sf \leadsto y = \dfrac{47}{15} \times \dfrac{6}{47}}$

Write the fraction in lowest form by cancellation method.

${\sf \leadsto y = \dfrac{\cancel{47} \times 6}{15 \times \cancel{47}} = \dfrac{1 \times 6}{15 \times 1}}$

Multiply the numbers on numerator and denominator.

${\sf \leadsto y = \dfrac{6}{15}}$

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${\red{\underline{\boxed{\bf So, \: the \: other \: number \: is \: \dfrac{6}{15}.}}}}$

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Verification :-

${\sf \leadsto \dfrac{47}{15} \div y = \dfrac{47}{6}}$

Substitute the value of y.

${\sf \leadsto \dfrac{47}{15} \div \dfrac{6}{15} = \dfrac{47}{6}}$

Take the reciprocal of second fraction and multiply both fractions.

${\sf \leadsto \dfrac{47}{15} \times \dfrac{15}{6} = \dfrac{47}{6}}$

Write both numerators and denominators with common fraction.

${\sf \leadsto \dfrac{47 \times \cancel{15}}{\cancel{15} \times 6} = \dfrac{47}{6}}$

Write the fraction in lowest form.

${\sf \leadsto \dfrac{47}{6} = \dfrac{47}{6}}$

So,

${\sf \leadsto LHS = RHS}$

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Hence verified !!