Question

simpilify {13/9× -15/2}+{7/3 × 8/5}+{3/5 × 1/2}

Answer 1

★ How to do :-

Here, we are given with some of the fractions to simplify with. We are given with different mathematical signs such as multiplication and addition. We are also given with three brackets and two numbers in each of those brackets. According to the rule of maths, always in the simplification we should solve the numbers given in the brackets first. Then, we can add the obtained answers with each other. The obtained answers refers to the answers obtained while solving the brackets. The rule used here is the LCM method in which we take the LCM of all the denominators and convert them into like fractions. This should only be done while addition or subtraction of fractions. So, let's solve!!

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➤ Solution :-

${\sf \leadsto \bigg( \dfrac{13}{9} \times \dfrac{(-15)}{2} \bigg) + \bigg( \dfrac{7}{3} \times \dfrac{8}{5} \bigg) + \bigg( \dfrac{3}{5} \times \dfrac{1}{2} \bigg)}$

Let's solve the first bracket.

${\sf \leadsto \bigg( \dfrac{13}{9} \times \dfrac{(-15)}{2} \bigg)}$

Write both numerators and denominators with a common fraction.

${\sf \leadsto \dfrac{13 \times (-15)}{9 \times 2}}$

Multiply the numerators and denominators.

${\sf \leadsto \cancel \dfrac{(-195)}{18} = \dfrac{(-65)}{6}}$

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Now, let's solve the second bracket.

${\sf \leadsto \bigg( \dfrac{7}{3} \times \dfrac{8}{5} \bigg)}$

Write both numerators and denominators with a common fraction.

${\sf \leadsto \dfrac{7 \times 8}{3 \times 5}}$

Multiply the numerators and denominators.

${\sf \leadsto \dfrac{56}{15}}$

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Now, let's solve the third bracket.

${\sf \leadsto \bigg( \dfrac{3}{5} \times \dfrac{1}{2} \bigg)}$

Write both numerators and denominators with a common fraction.

${\sf \leadsto \dfrac{3 \times 1}{5 \times 2}}$

Multiply the numerators and denominators.

${\sf \leadsto \dfrac{3}{10}}$

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Insert all the obtained answers in it's places.

${\sf \leadsto \dfrac{(-65)}{6} + \dfrac{56}{15} + \dfrac{3}{10}}$

LCM of 6, 15 and 10 is 60.

${\sf \leadsto \dfrac{(-65) \times 10}{6 \times 10} + \dfrac{56 \times 4}{15 \times 4} + \dfrac{3 \times 6}{10 \times 6}}$

Multiply the numerators and denominators of all fractions.

${\sf \leadsto \dfrac{(-650)}{60} + \dfrac{224}{60} + \dfrac{18}{60}}$

Add the fractions.

${\sf \leadsto \dfrac{(-650) + 224 + 18}{60} = \dfrac{(-408)}{60}}$

Write the obtained answer in lowest form by cancellation method.

${\sf \leadsto \cancel \dfrac{(-408)}{60} = \dfrac{(-34)}{5}}$

Write the obtained answer in the form of mixed fraction.

${\sf \leadsto \dfrac{(-34)}{5} = -6 \dfrac{4}{5}}$

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${\red{\underline{\boxed{\bf So, \: the \: answer \: obtained \: is \: \bigg( -6 \dfrac{4}{5} \bigg).}}}}$