Question

Simplify:
7/12-(3/4÷7/12)×3/4
Please tell ​

Answer 1

★ How to do :-

Here, we are given with four fractions in which we are asked to divide, multiply and subtract some of them. We are also given with a bracket containing two fractions in it. So, here we use the BODMAS rule. This rule says that, we should solve the fractions given in brackets first. Then, we multiply the fractions and then we subtract the fractions. While adding or subtracting the fractions, we should convert them to like fractions by taking the LCM of the denominators. So, let's solve!!

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➤ Solution :-

${\tt \leadsto \dfrac{7}{12} - \bigg( \dfrac{3}{4} \div \dfrac{7}{12} \bigg) \times \dfrac{3}{4}}$

Take the reciprocal of second fraction and multiply both the fractions in the bracket.

${\tt \leadsto \dfrac{7}{12} - \bigg( \dfrac{3}{4} \times \dfrac{12}{7} \bigg) \times \dfrac{3}{4}}$

Multiply them now.

${\tt \leadsto \dfrac{7}{12} - \dfrac{36}{28} \times \dfrac{3}{4}}$

Write the fractions in lowest form by cancellation method.

${\tt \leadsto \dfrac{7}{12} - \dfrac{\cancel{36} \times 3}{28 \times \cancel{4}}}$

Write the resulting fraction now.

${\tt \leadsto \dfrac{7}{12} - \dfrac{9 \times 3}{28 \times 1}}$

Multiply the fractions now.

${\tt \leadsto \dfrac{7}{12} - \dfrac{27}{28}}$

LCM of 12 and 28 is 84.

${\tt \leadsto \dfrac{7 \times 7}{12 \times 7} - \dfrac{27 \times 3}{28 \times 3}}$

Multiply the numerator and denominator of each fraction.

${\tt \leadsto \dfrac{49}{84} - \dfrac{81}{84}}$

Subtract the fractions now.

${\tt \leadsto \dfrac{49 - 81}{84} = \dfrac{(-32)}{84}}$

Write the fraction in lowest form by cancellation method.

${\tt \leadsto \cancel \dfrac{(-32)}{84} = \pink{\underline{\boxed{\tt \dfrac{(-8)}{21}}}}}$

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Hence solved !!