Question

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Answer 1

Question :

Subtract the sum of -3/4 and 1/3 from the sum of 2/3 and -1/2.

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To :

• Subtract the sum of -3/4 and 1/3 from the sum of 2/3 and -1/2.

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Concept :

First we would calculate the sum of -3/4 and 1/3 . Then the sum of 2/3 and -1/2. Finally we would subtract both the sums and then acquire our final answer.

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Solution :

$\tt\color{fushsia}{⋆}$ Calculating the sum of -3/4 and 1/3 -

$\sf\:\frac{-3}{4}+\frac{1}{3}$

LCM of 4 and 3 = 12

$\sf\twoheadrightarrow\:\frac{(-3 \times 3) + (4 \times 1)}{12}$

$\sf\twoheadrightarrow\:\frac{-9+4}{12}$

$\bf\color{pink}{\twoheadrightarrow\:\frac{-5}{12}}$

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$\tt\color{fushsia}{⋆}$ Calculating the sum of 2/3 and -1/2 -

$\sf\:\frac{2}{3}+(-\frac{1}{2})$

$\sf\twoheadrightarrow\:\frac{2}{3}-\frac{1}{2}$

LCM of 3 and 2 = 6

$\sf\twoheadrightarrow\:\frac{(2 \times 2) - (3 \times 1)}{6}$

$\sf\twoheadrightarrow\:\frac{4-3}{6}$

$\bf\color{pink}{\twoheadrightarrow\:\frac{-1}{6}}$

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$\tt\color{fushsia}{⋆}$ Now subtracting both the sums -

$\sf\:(\frac{2}{3}+\frac{-1}{2})-(\frac{-3}{4}+\frac{1}{3})$

Substituting the values we got

$\sf\twoheadrightarrow\:\frac{1}{6}-(-\frac{5}{12})$

$\sf\twoheadrightarrow\:\frac{1}{6}+\frac{5}{12}$

LCM of 6 and 12 = 12

$\sf\twoheadrightarrow\:\frac{(2 \times 1) +(1 \times 5)}{12}$

$\sf\twoheadrightarrow\:\frac{2+5}{12}$

$\small{\underline{\boxed{\mathrm{\twoheadrightarrow\:\frac{7}{12}}}}}$ ★

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