Question

simplify 79/6+5/24-32/3​

Answer 1

★ How to do :-

Here, we are given with three fractions in which we are asked to subtract two of them and to add two of them. We are asked to simplify and find out the answer in the lowest form. We can find the answer of this by a concept called as LCM which means least common multiple. This concept is very helpful in adding the fractions when they have different denominators. This helps us to convert the unlike fractions into like fractions. If we have like fractions, we can add those directly without taking the LCM. So, let's solve!!

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➤ Solution :-

${\tt \leadsto \dfrac{79}{6} + \dfrac{5}{24} - \dfrac{32}{3}}$

First, we should add the fractions.

${\tt \leadsto \dfrac{79}{6} + \dfrac{5}{24}}$

LCM of 6 and 24 is 24.

${\tt \leadsto \dfrac{79 \times 4}{6 \times 4} + \dfrac{5}{24}}$

Multiply the numerator and denominator of first fraction.

${\tt \leadsto \dfrac{316}{24} + \dfrac{5}{24}}$

Add both the fractions now.

${\tt \leadsto \dfrac{316 + 5}{24} = \dfrac{321}{24}}$

Write the obtained fraction in lowest form by cancellation method.

${\tt \leadsto \dfrac{321}{24} = \dfrac{107}{8}}$

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Now, insert the obtained answer in it's place like given at first.

${\tt \leadsto \dfrac{107}{8} - \dfrac{32}{3}}$

LCM of 8 and 3 is 24.

${\tt \leadsto \dfrac{107 \times 3}{8 \times 3} - \dfrac{32 \times 8}{3 \times 8}}$

Multiply the numerators and denominators of both fractions.

${\tt \leadsto \dfrac{321}{24} - \dfrac{256}{24}}$

Now, subtract both fractions.

${\tt \leadsto \dfrac{321 - 256}{24} = \dfrac{65}{24}}$

Write the obtained answer in the form of mixed fraction.

${\tt \leadsto \dfrac{65}{24} = 2 \dfrac{17}{24}}$

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${\red{\underline{\boxed{\bf So, \: the \: answer \: obtained \: is \: \: 2 \dfrac{17}{24}}}}}$