Question

How do you evaluate `3\frac { 5} { 9} - 2\frac { 2} { 5}`?

Answer 1

See a solution process below:

Explanation:

First, convert each mixed number to an improper fraction:

`3 5/9 = 3 + 5/9 = (9/9 xx 3) + 5/9 = 27/9 + 5/9 = (27 + 5)/9 = 32/9`

`2 2/5 = 2 + 2/5 = (5/5 xx 2) + 2/5 = 10/5 + 2/5 = (10 + 2)/5 = 12/5`

Next, put each fraction over a common denominator:

`32/9 = 5/5 xx 32/9 = (5 xx 32)/(5 xx 9) = 160/45`

`12/5 = 9/9 xx 12/5 = (9 xx 12)/(9 xx 5) = 108/45`

Then, rewrite the expression and subtract the numerators over the common denominator:

`160/45 - 108/45 = (160 - 108)/45 = 52/45`

Now, convert the improper fraction into a mixed number:

`52/45= (45 + 7)/45 = 45/45 + 7/45 = 1 + 7/45 = 1 7/45`