Question

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Answer 1

`-(3)/(2)`

Explanation:

Given expression:

`((1)/(2))/(-(2)/(5))+\left(-(1)/(4)\right)`

To divide fractions, flip the second fraction (make the numerator the denominator, and the denominator the numerator) then multiply it by the first fraction:

`\implies (1)/(2) * -(5)/(2)+\left(-(1)/(4)\right)`

To multiply the fractions, multiply the numerators and multiply the denominators:

`\implies (1 * (-5))/(2 * 2) +\left(-(1)/(4)\right)`

`\implies -(5)/(4) +\left(-(1)/(4)\right)`

Apply the rule -a + (-b) = -a - b :

`\implies -(5)/(4) -(1)/(4)`

As the denominators are the same, subtract the numerators and put the answer over the same denominator:

`\implies (-5-1)/(4)`

`\implies -(6)/(4)`

Simplify by dividing the numerator and denominator by the highest common factor:

`\implies -(6 / 2)/(4 / 2)`

`\implies -(3)/(2)`

Answer 2

-3/2

Explanation:

First, you divide by taking the reciprocal of -2/5 which is -5/2.

Second, you get the answer which is -5/4.

Add that with -1/4 and you will get -6/4.

Simplify to get the answer which is -3/2.