Question

Simplify 2- 2 ⅚ + 2 ¼ - ⅔​

Answer 1

★ How to do :-

Here, we are given with some fractions in which we are asked to simplify it. We are given to add and also yo subtract the fractions. So, here we are going to use the BODMAS rule. This rule says that in the following statement, first we should add the fractions before subtracting the fractions. So, first we will add two fractions that have addition sign. Later, we will insert the obtained answer in the place of those two fractions and then subtract them. So, let's solve!!

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➤ Solution :-

${\tt \leadsto 2 - 2 \dfrac{5}{6} + 2 \dfrac{1}{4} - \dfrac{2}{3}}$

Let's add the fractions first.

${\tt \leadsto 2 \dfrac{5}{6} + 2 \dfrac{1}{4}}$

Convert them into improper fractions.

${\tt \leadsto \dfrac{17}{6} + \dfrac{9}{4}}$

LCM of 6 and 4 is 12.

${\tt \leadsto \dfrac{14 \times 2}{6 \times 2} + \dfrac{9 \times 3}{4 \times 3}}$

Multiply the numerators and denominators of both fractions.

${\tt \leadsto \dfrac{28}{12} + \dfrac{27}{12}}$

Add both the numerators of the fractions.

${\tt \leadsto \dfrac{28 + 27}{12} = \dfrac{55}{12}}$

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${\tt \leadsto 2 - \dfrac{55}{12} - \dfrac{2}{3}}$

Subtract first two fractions.

${\tt \leadsto \dfrac{2}{1} - \dfrac{55}{12}}$

LCM of 1 and 12 is 12.

${\tt \leadsto \dfrac{2 \times 12}{1 \times 12} - \dfrac{55}{12}}$

Multiply the numerator and denominator of first fraction.

${\tt \leadsto \dfrac{24}{12} - \dfrac{55}{12}}$

Subtract both numerators of the fraction.

${\tt \leadsto \dfrac{24 - 55}{12} = \dfrac{(-31)}{12}}$

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Now, subtract the remaining two fractions.

${\tt \leadsto \dfrac{(-31)}{12} - \dfrac{2}{3}}$

LCM of 12 and 3 is 12.

${\tt \leadsto \dfrac{(-31)}{12} - \dfrac{2 \times 4}{3 \times 4}}$

Multiply the numerator and denominator of second fraction.

${\tt \leadsto \dfrac{(-31)}{12} - \dfrac{8}{12}}$

Subtract both numerators of the fraction.

${\tt \leadsto \dfrac{(-31) - 8}{12} = \dfrac{(-39)}{12}}$

Write the answer in mixed fraction.

${\tt \leadsto \dfrac{(-39)}{12} = \pink{\underline{\boxed{\tt -3 \dfrac{3}{12}}}}}$

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Hence solved !!