Question

Evaluate and simplify the following complex fraction. 9 − 5 − 3 8 = 8 −3 ​ −5 9 ​ ​ =start fraction, space, start fraction, 9, divided by, minus, 5, end fraction, space, divided by, start fraction, minus, 3, divided by, 8, end fraction, end fraction, equals

Answer 1

`\displaystyle ((9)/(-5))/((-3)/(8))=(24)/(5)`

Explanation:

Operations With Fractions

The division of the fractions \frac{a}{b} and \frac{c}{d} can be calculated by multiplying the first by the reciprocal of the second fraction:

`\displaystyle ((a)/(b))/((c)/(d))=(a)/(b)*(d)/(c)`

We are given the following division of fractions:

`\displaystyle ((9)/(-5))/((-3)/(8))=(9)/(-5)*(8)/(-3)`

Multiplying and simplifying:

`\displaystyle ((9)/(-5))/((-3)/(8))=(9)/(5)*(8)/(3)`

`\displaystyle ((9)/(-5))/((-3)/(8))=(9*8)/(5*3)`

Simplifying by 3:

`\displaystyle ((9)/(-5))/((-3)/(8))=(3*8)/(5)`

`\mathbf{\displaystyle ((9)/(-5))/((-3)/(8))=(24)/(5)}`