Question

(-3/2×4/5)+(9/5×-10/3)-(5/13+6/15)​

Answer 1

is it + or × in 3rd bracket ?

Answer 2

★ How to do :-

Here, we are given with three brackets in which we are asked to multiply some of them, add some of them and also to subtract some of them. We are asked to simplify the full problem. To find the answer in correct and a simple way, we should solve all the three brackets separately and then, we can again insert all the obtained answers in it's place as given in the question and then, we can again simplify them by the appropriate signs provided to us. Taking of the LCM of denominators, we can convert the unlike fractions to like fractions and add or subtract them. So, let's solve!!

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➤ Solution :-

${\tt \leadsto \bigg( \dfrac{-3}{2} \times \dfrac{4}{5} \bigg) + \bigg( \dfrac{9}{5} \times \dfrac{-10}{3} \bigg) - \bigg( \dfrac{5}{13} + \dfrac{6}{15} \bigg)}$

Let's solve the first bracket.

${\tt \leadsto \dfrac{-3}{2} \times \dfrac{4}{5}}$

Multiply the numerator with numerator and denominator with denominator.

${\tt \leadsto \dfrac{(-3) \times 4}{2 \times 5} = \dfrac{(-12)}{10}}$

Write the fraction in lowest form by cancellation method.

${\tt \leadsto \cancel \dfrac{(-12)}{10} = \dfrac{(-6)}{5}}$

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Now, let's solve the second bracket.

${\tt \leadsto \dfrac{9}{5} \times \dfrac{-10}{3}}$

Multiply the numerator with numerator and denominator with denominator.

${\tt \leadsto \dfrac{9 \times (-10)}{5 \times 3} = \dfrac{(-90)}{15}}$

Write the fraction in lowest form by cancellation method

${\tt \leadsto \cancel \dfrac{(-90)}{15} = (-6)}$

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Now, let's solve the the third bracket.

${\tt \leadsto \dfrac{5}{13} + \dfrac{6}{15}}$

LCM of 13 and 15 is 195.

${\tt \leadsto \dfrac{5 \times 15}{13 \times 15} + \dfrac{6 \times 13}{15 \times 13}}$

Multiply the numerator and denominator of both fractions.

${\tt \leadsto \dfrac{75}{195} + \dfrac{78}{195}}$

Add the numerators.

${\tt \leadsto \dfrac{75 + 78}{195} = \dfrac{153}{195}}$

Write the fraction in lowest form by cancellation method.

${\tt \leadsto \cancel \dfrac{153}{195} = \dfrac{51}{65}}$

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Now, let's insert all the obtained answers in it's place.

${\tt \leadsto \dfrac{(-6)}{5} + (-6) - \dfrac{51}{65}}$

${\tt \leadsto \dfrac{(-6)}{5} + \dfrac{(-6)}{1} - \dfrac{51}{65}}$

LCM of 5, 1 and 65 is 65.

${\tt \leadsto \dfrac{(-6) \times 13}{5 \times 13} + \dfrac{(-6) \times 65}{1 \times 65} - \dfrac{51}{65}}$

Multiply the numerator and denominator of first two fractions.

${\tt \leadsto \dfrac{(-78)}{65} + \dfrac{(-390)}{65} - \dfrac{51}{65}}$

Now, write all numerators with one common denominator.

${\tt \leadsto \dfrac{(-78) + (-390) - 52}{65} = \dfrac{(-78) - 390 - 52}{65}}$

Now, subtract all the numerators to get the final answer.

${\tt \leadsto \dfrac{(-468) - 52}{65} = \dfrac{(-520)}{65}}$

Write the obtained answer in lowest form by cancellation method.

${\tt \leadsto \cancel \dfrac{(-520)}{65} = (-8})$

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${\red{\underline{\boxed{\bf So, \: the \: answer \: obtained \: is \: \: (-8)}}}}$