Question

How do you determine the sum of `- 11\frac { 3} { 5} + 4\frac { 2} { 3}`?

Answer 1

See a solution process below:

Explanation:

First, convert each mixed number into an improper fraction:

`-11 3/5 = - (11 + 3/5) = -((5/5 xx 11) + 3/5) =`

`-(55/5 + 3/5) = -(55 + 3)/5 = -58/5`

`4 2/3 = 4 + 2/3 = (3/3 xx 4) + 2/3 = 12/3 + 2/3 = (12 + 2)/3 =`

`14/3`

Next, put each of the fractions over a common denominator by multiplying by the appropriate form of `1`:

`-58/5 xx 3/3 = -(58 xx 3)/(5 xx 3) = -174/15`

`14/3 xx 5/5 = (14 xx 5)/(3 xx 5) = 70/15`

We can then rewrite the expression as:

`-174/15 + 70/15`

Now, sum the numerators over the common denominator:

`(-174 + 70)/15 = -104/15`

If required we can convert the improper fraction into a mixed number:

`-104/15 = -(90 + 14)/15 = -(90/15 + 14/15) =`

`-(6 + 14/15) = -6 14/15`