Question

Use distributive property to solve the following:4/5× -7/8+ -8/15 × 7/8

Answer 1

★ How to do :-

Here, we are given with some of the fractions in which we are asked to find the answer by using the distributive property. So, first we should take a common fraction in which it should be multiplied with the sum of other two remaining fractions. Here, we can see that we don't have any common fractions. But, we can shift the negative symbol of second fraction to the first fraction by which it's value doesn't changes. After that, we can get a common fraction by which we can solve this question. So, let's solve!!

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➤ Solution :-

${\tt \leadsto \dfrac{4}{5} \times \dfrac{(-7)}{8} + \dfrac{(-8)}{15} \times \dfrac{7}{8}}$

The negative sign on second fraction can be shifted to first fraction by which it's value doesn't changes.

${\tt \leadsto \dfrac{(-4)}{5} \times \dfrac{7}{8} + \dfrac{(-8)}{15} \times \dfrac{7}{8}}$

Now, apply the distributive property here.

${\tt \leadsto \dfrac{7}{8} \times \bigg( \dfrac{(-4)}{5} + \dfrac{(-8)}{15} \bigg)}$

Solve the fractions in the bracket.

LCM of 5 and 15 is 15.

${\tt \leadsto \dfrac{7}{8} \times \bigg( \dfrac{(-4) \times 3}{5 \times 3} + \dfrac{(-8)}{15} \bigg)}$

Multiply the numerator and denominator of first fraction in bracket.

${\tt \leadsto \dfrac{7}{8} \times \bigg( \dfrac{(-12)}{12} + \dfrac{(-8)}{15} \bigg)}$

Add the fractions in the bracket.

${\tt \leadsto \dfrac{7}{8} \times \bigg( \dfrac{(-12) + (-8)}{5} = \dfrac{(-12) - 8}{15} \bigg)}$

Subtract them now.

${\tt \leadsto \dfrac{7}{8} \times \dfrac{(-20)}{5}}$

Multiply the fraction by obtained answer.

${\tt \leadsto \dfrac{7}{8} \times \dfrac{(-20)}{5}}$

Multiply the numerator with numerator and denominator with denominator.

${\tt \leadsto \dfrac{7 \times (-20)}{8 \times 5} = \dfrac{(-140)}{40}}$

Write the fraction in lowest form by cancellation method.

${\tt \leadsto \cancel \dfrac{(-140)}{40} = \dfrac{(-7)}{2}}$

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${\red{\underline{\boxed{\bf So, \: the \: answer \: obtained \: is \: \dfrac{(-7)}{2}}}}}$