Question

By what no should we multiply -3/14 , so that the product may be 5/12 *​

Answer 1

★ How to do :-

Here, we are given with a number in which it should be multiplied with an other number. The second number to be multiplied with isn't given to us. But, the product that occurs while multiplying those two fractions is given. We are asked to find the second number that to be multiplied with the first number. So, here we are going to use the concept called transportation of numbers from one hand side to the other. While doing this, the sign of the appropriate number will change. So, let's solve!!

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➤ Solution :-

Let, the second number be x.

${\tt \leadsto \dfrac{(-3)}{14} \times (x) = \dfrac{5}{12}}$

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

${\tt \leadsto (x) = \dfrac{5}{12} \div \dfrac{(-3)}{14}}$

Take the reciprocal of second fraction and multiply both the fractions.

${\tt \leadsto (x) = \dfrac{5}{12} \times \dfrac{14}{(-3)}}$

Multiply the numerator with numerator and the denominator with denominator.

${\tt \leadsto \dfrac{5 \times 14}{12 \times (-3)} = \dfrac{70}{(-36)}}$

Write the fraction in lowest form by cancellation method to get the answer.

${\tt \leadsto x = \cancel \dfrac{70}{(-36)} = \pink{\underline{\boxed{\tt \dfrac{35}{(-18)}}}}}$

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Verification :-

${\tt \leadsto \dfrac{(-3}{14} \times (x) = \dfrac{5}{12}}$

Substitute the value of x.

${\tt \leadsto \dfrac{(-3)}{14} \times \dfrac{35}{(-18)} = \dfrac{5}{12}}$

Multiply the numerator with numerator and denominator with denominator.

${\tt \leadsto \dfrac{(-3) \times 35}{14 \times (-18)} = \dfrac{5}{12}}$

Multiply the numbers on LHS.

${\tt \leadsto \dfrac{(-105)}{(-252)} = \dfrac{5}{12}}$

Write the fraction on LHS in simplest form.

${\tt \leadsto \dfrac{5}{12} = \dfrac{5}{12}}$

So,

${\sf \leadsto LHS = RHS}$

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Hence solved !!