Question

How do you evaluate `(3\frac { 1} { 4} - 5\frac { 2} { 5} ) \div - 1.5`?

Answer 1

43/30

Explanation:

First we should rewrite all mixed numbers and decimal numbers as fractions.

`(3 1/4 - 5 2/5) divide -1.5 = (13/4 - 27/5)divide (- 3)/2`

Now to subtract the two fractions in the brackets, we need to give them a common denominator by multiplying both the numerator and denominator by the other fraction's denominator.

`(13/4 * 5/5 - 27/5 * 4/4) divide -3/2 = (65/20 - 108/20) divide (-3)/2`

Now we can subtract the two fractions.

`(65/20 - 108/20) divide (-3)/2 = (-43)/20 divide (-3)/2`

When dividing by a fraction it is the same as multiplying by its reciprocal.

`(-43)/20 * 2/(-3) = (-86)/(-60)`

Now we can simplify by dividing the numerator and the denominator by `2` because 2 is the greatest common factor of both the numerator and the denominator.

`(-86divide2)/(-60divide2) = (-43)/(-30)`

When dividing two negative numbers by each other they will yield a positive quotient this is because out of two negative numbers you can factor out `-1`.

`(-1*43)/(-1*30) = (cancel(-1)*43)/(cancel(-1)*30) = 43/30`