Question

divide the sum of 2 whole1/4 and 5 whole1/5 by the product of 2 whole 1/4 and 5 whole 1/5

pls solve this​

Answer 1

★ How to do :-

Here, we are given with some of the fractions to add with and some of the fractions to multiply with. We are also said that we should divide the fractions that we obtain while we multiply the fractions and add some fractions. So, first we should find the sum of the two fractions given and then, we should find the product of the other two numbers given. Then, we divide the answers that are obtained to us at the begining while we added and multiplied some numbers. We can divide the fractions in different ways than the integers. We have some different ways to divide the fractions. So, let's solve!!

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➤ Solution :-

${\sf \leadsto \bigg( 2 \dfrac{1}{4} + 5 \dfrac{1}{5} \bigg) \div \bigg( 2 \dfrac{1}{4} \times 5 \dfrac{1}{5} \bigg)}$

Let's solve the both brackets together.

Convert the mixed fractions to improper fractions.

${\sf \leadsto \bigg( \dfrac{9}{4} + \dfrac{26}{5} \bigg) \div \bigg( \dfrac{9}{4} \times \dfrac{26}{5} \bigg)}$

LCM of 4 and 5 is 20.

${\sf \leadsto \bigg( \dfrac{9 \times 5}{4 \times 5} + \dfrac{26 \times 4}{5 \times 4} \bigg) \div \bigg( \dfrac{9 \times 26}{4 \times 5} \bigg)}$

Multiply the fractions on both brackets.

${\sf \leadsto \bigg( \dfrac{45}{20} + \dfrac{104}{20} \bigg) \div \dfrac{234}{20}}$

Write both numerators with a common denominator.

${\sf \leadsto \bigg( \dfrac{45 + 104}{20} \bigg) \div \dfrac{234}{20}}$

Add the numbers.

${\sf \leadsto \dfrac{149}{20} \div \dfrac{234}{20}}$

Take the reciprocal of second fraction and multiply both fractions.

${\sf \leadsto \dfrac{149}{20} \times \dfrac{20}{234}}$

Write the fraction in lowest form by cancellation method.

${\sf \leadsto \dfrac{149 \times \cancel{20}}{\cancel{20} \times 234} = \dfrac{149 \times 1}{1 \times 234}}$

Multiply the remaining numbers.

${\sf \leadsto \dfrac{149}{234}}$

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${\red{\underline{\boxed{\bf So, \: the \: answer \: obtained \: is \: \dfrac{149}{234}.}}}}$