Question

Divide the sum of -7/8 and 11/24 by there difference.

Answer 1

Answer:

5/16

Step-by-step explanation:

Sum of -7/8 and 11/24

$\frac{-7}{8} +\frac{11}{24} \\\\=\frac{-21+11}{24} \\\\=\frac{-10}{24}$

Difference of -7/8 and 11/24

$\frac{-7}{8} -\frac{11}{24} \\\\=\frac{-21-11}{24} \\\\=\frac{-32}{24}$

Dividing the sum of -7/8 and 11/24 by there difference.

$\frac{\frac{-10}{24}}{\frac{-32}{24} } \\\\=\frac{-10}{24} *\frac{24}{-32} \\\\=\frac{5}{16}$

Answer 2

★ How to do :-

Here, we are given with two fractions in which we are asked to divide them. But, we aren't given with the appropriate numbers by which we are supposed to divide the numbers. But, we are given with two fractions by which we can obtain our two numbers to divide. We are said that the sum of the given fraction. become the first number of the division. We are also said that the the difference of those both fractions becomes the second fraction of the division. So, first we should find the value of the fractions by which we are required. To find the that, we must add and subtract the given fractions. So, first we'll add the fractions, then we can subtract them. Finally, we can divide the results of those both. As we know that, we cannot add or subtract the fractions directly. So, we use a method called LCM. So, let's solve!!

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➤ Solution :-

${\sf \leadsto \bigg( \dfrac{(-7)}{8} + \dfrac{11}{24} \bigg) \div \bigg( \dfrac{(-7)}{8} - \dfrac{11}{24} \bigg)}$

LCM of 8 and 24 is 24.

${\sf \leadsto \bigg( \dfrac{(-7) \times 3}{8 \times 3} + \dfrac{11}{24} \bigg) \div \bigg( \dfrac{(-7) \times 3}{8 \times 3} - \dfrac{11}{24} \bigg)}$

Multiply the numerators and denominators of all fractions.

${\sf \leadsto \bigg( \dfrac{(-21)}{24} + \dfrac{11}{24} \bigg) \div \bigg( \dfrac{(-21)}{24} - \dfrac{11}{24} \bigg)}$

Write both numerators with a common denominator in both brackets.

${\sf \leadsto \bigg( \dfrac{(-21) + 11}{24} \bigg) \div \bigg( \dfrac{(-21) - 11}{24} \bigg)}$

Add and subtract the numbers.

${\sf \leadsto \dfrac{(-10)}{24} \div \dfrac{(-32)}{24}}$

Take the reciprocal of second fraction and multiply both fractions.

${\sf \leadsto \dfrac{(-10)}{24} \times \dfrac{24}{(-32)}}$

Write the fraction in lowest form by cancellation method.

${\sf \leadsto \dfrac{(-10) \times \cancel{24}}{\cancel{24} \times (-32)} = \dfrac{(-10) \times 1}{1 \times (-32)}}$

Multiply the fractions and write the fraction in lowest form by cancellation method.

${\sf \leadsto \dfrac{(-10)}{(-32)} = \dfrac{5}{16}}$

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${\red{\underline{\boxed{\bf So, \: the \: answer \: obtained \: is \: \dfrac{5}{16}.}}}}$