Question

subtract the sum of 1/2,1/3 and 1/5 from the sum of 3/2 , 1/2 and 1.​

Answer 1

Answer:

answer is in the attachment

Answer 2

★ How to do :-

Here, we are given with some fractions to subtract them. But, we are not given with the actual fractions to subtract them. The sum of three fractions should be subtracted from the sum of other three fractions. So, first we should find the sum of those three fractions and the other three fractions separately. We go under many process while solving this problem. Here, we are going to use the concepts of taking the LCM. Also, the rule is that we should add only numerators. So, let's solve!!

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➤ Solution :-

${\tt \leadsto \bigg(\dfrac{3}{2} + \dfrac{1}{2} + 1 \bigg) - \bigg(\dfrac{1}{2} + \dfrac{1}{3} + \dfrac{1}{5} \bigg)}$

Solve the first bracket first.

${\tt \leadsto \dfrac{3}{2} + \dfrac{1}{2} + \dfrac{1}{1}}$

Convert them into like fractions by taking the LCM of denominators.

LCM of 2 and 1 is 2.

${\tt \leadsto \dfrac{3}{2} + \dfrac{1}{2} + \dfrac{1 \times 2}{1 \times 2}}$

Write the resulting fraction and write all the numerators in one fraction.

${\tt \leadsto \dfrac{3}{2} + \dfrac{1}{2} + \dfrac{2}{2} = \dfrac{3 + 1 + 2}{2}}$

Add the numerators to get the first fraction.

${\tt \leadsto \cancel \dfrac{6}{2} = 3}$

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Now, solve the second bracket.

${\tt \leadsto \dfrac{1}{2} + \dfrac{1}{3} + \dfrac{1}{5}}$

Convert them into like fractions by taking the LCM of the denominators.

LCM of 2, 3 and 5 is 30.

${\tt \leadsto \dfrac{1 \times 15}{2 \times 15} + \dfrac{1 \times 10}{3 \times 10} + \dfrac{1 \times 6}{5 \times 6}}$

Write the resulting fraction and write all the numerators in one fraction.

${\tt \leadsto \dfrac{15}{30} + \dfrac{10}{30} + \dfrac{6}{30} = \dfrac{15 + 10 + 6}{30}}$

Add the numerators to get the second fraction.

${\tt \leadsto \dfrac{31}{30}}$

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Now, subtract the sum of both the fractions obtained.

${\tt \leadsto \dfrac{3}{1} - \dfrac{31}{30}}$

Convert them into like fractions by taking the LCM of the denominators.

LCM of 1 and 30 is 30.

${\tt \leadsto \dfrac{3 \times 30}{1 \times 30} - \dfrac{31}{30}}$

Write the resulting fraction and write both numerators in one fraction.

${\tt \leadsto \dfrac{90 - 31}{30} = \dfrac{59}{30}}$

Write the improper fraction as mixed fraction.

${\tt \leadsto \dfrac{59}{30} = \pink{\underline{\boxed{\tt 1 \dfrac{29}{30}}}}}$

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Hence solved !!