Question

Evaluate : (2/11 * -22/15 ) + (-1/6 * 3/4) + (-1/21 * -3/5)​

Answer 1

★ How to do :-

Here, we are given with three brackets and we are asked to multiply the numbers in each bracket. We are given with the addition sign outside the brackets of all the three of them. We are asked to simplify those fractions. The rule of BODMAS says that, in any sum first we should solve the brackets. So, in this question, we will solve each of the brackets first. The all three brackets should be solved separately. Then, we add all the answers of those brackets together by taking the LCM of the denominators and then convert them into like fractions and then, we can add the numerators. So, let's solve!!

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➤ Solution :-

${\sf \leadsto \bigg( \dfrac{2}{11} \times \dfrac{(-22)}{15} \bigg) + \bigg( \dfrac{(-1)}{6} \times \dfrac{3}{4} \bigg) + \bigg( \dfrac{(-1)}{21} \times \dfrac{(-3)}{5} \bigg)}$

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Let's solve the first bracket.

${\sf \leadsto \bigg( \dfrac{2}{11} \times \dfrac{(-22)}{15} \bigg)}$

Write both numerators and denominators in a common fraction.

$\sf \leadsto \dfrac{2 \times (-22)}{11 \times 15}$

Multiply the fractions.

${\sf \leadsto \dfrac{(-44)}{165}}$

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Now, let's solve the second bracket.

${\sf \leadsto \bigg( \dfrac{(-1)}{6} \times \dfrac{3}{4} \bigg)}$

Write both numerators and denominators in a common fraction.

${\sf \leadsto \dfrac{(-1) \times 3}{6 \times 4}}$

Multiply the fractions.

${\sf \leadsto \dfrac{(-3)}{24}}$

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Now, let's solve the third bracket.

${\sf \leadsto \bigg( \dfrac{(-1)}{21} \times \dfrac{(-3)}{5} \bigg)}$

Write both numerators and denominators in a common fraction.

${\sf \leadsto \dfrac{(-1) \times (-3)}{21 \times 5}}$

Multiply the fractions.

${\sf \leadsto \dfrac{3}{105}}$

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Now, let's write all the obtained answer in it's place.

${\sf \leadsto \dfrac{(-44)}{165} + \dfrac{(-3)}{24} + \dfrac{3}{105}}$

Write the fractions in lowest form.

${\sf \leadsto \dfrac{(-44)}{165} + \dfrac{(-1)}{8} + \dfrac{1}{35}}$

LCM of 165, 8 and 35 is 9240.

${\sf \leadsto \dfrac{(-44) \times 56}{165 \times 56} + \dfrac{(-1) \times 1155}{8 \times 1155} + \dfrac{1 \times 264}{35 \times 264}}$

Multiply the numerators and denominators of all fractions.

${\sf \leadsto \dfrac{(-2464)}{9240} + \dfrac{(-1155)}{9240} + \dfrac{264}{9240}}$

Write all numerators with a common denominator.

${\sf \leadsto \dfrac{(-2464) + (-1155) + 264}{9240}}$

Write the second number in numerator with one sign.

${\sf \leadsto \dfrac{(-2464) - 1155 + 264}{9240}}$

Simplify the numbers in numerator to get the answer.

${\sf \leadsto \dfrac{(-3355)}{9240}}$

Write the number in lowest form by cancellation method.

${\sf \leadsto \cancel \dfrac{(-3355)}{9240} = \dfrac{(-671)}{1848}}$

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${\red{\underline{\boxed{\bf So, \: the \: answer \: obtained \: is \: \dfrac{(-671)}{1848}.}}}}$