Question

divide the sum of -13/5 and - 12/7 by the product of -31/7 and -1/2

Answer 1

$\large\sf\underline{Given\::}$

• Divide the sum of -13/5 and - 12/7 by the product of -31/7 and -1/2 .

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$\large\sf\underline{To\::}$

• Calculate the sum of $\sf\:\frac{-13}{5}$ and $\sf\:\frac{-12}{7}$ .

• Calculate the product of $\sf\:\frac{-31}{7}$ and $\sf\:\frac{-1}{2}$ .

• Last step to divide the resultant sum and resultant product.

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$\large\sf\underline{Solution\::}$

${\sf{{\pink{1^{st}\:Step\::}}}}$

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Sum of $\sf\:\frac{-13}{5}$ and $\sf\:\frac{-12}{7}$ .

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$\sf\implies\:\frac{-13}{5} + \frac{-12}{7}$

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• LCM of 7 and 5 = 35 .

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$\sf\implies\:\frac{(-13 \times 7)+(-12 \times 5)}{35}$

$\sf\implies\:\frac{(-91 )+(-60)}{35}$

$\sf\implies\:\frac{-91 -60}{35}$

$\large{\mathfrak\red{\implies\:\frac{-151}{35}}}$ ★

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${\sf{{\pink{2^{nd}\:Step\::}}}}$

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Product of $\sf\:\frac{-31}{7}$ and $\sf\:\frac{-1}{2}$ .

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$\sf\implies\:\frac{-31}{7} \times \frac{-1}{2}$

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• Multiplying numerator and denominator

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$\large{\mathfrak\red{\implies\:\frac{31}{14}}}$ ★

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${\sf{{\pink{3^{rd}\:Step\::}}}}$

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Dividing the sum of $\sf\:\frac{-13}{5}$ and $\sf\:\frac{-12}{7}$ and product of $\sf\:\frac{-31}{7}$ and $\sf\:\frac{-1}{2}$ .

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$\sf\implies\:Sum \div Product$

$\sf\implies\:\frac{Sum}{Product}$

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• Substituiting the values we got

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$\sf\large\implies\:\frac{\frac{-151}{35}}{\frac{31}{14}}$

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• Let's simplify the expression , when we × the number in division form the sign changes to × and the denominator becomes numerator and vice - versa.

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$\sf\implies\:\frac{-151}{35} \times \frac{14}{31}$

$\sf\implies\:\frac{-2114}{1085}$

$\large{\mathfrak\red{\implies\:-1.948}}$ ★

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!! Hope it helps !!