Question

How do you evaluate `\frac { 8} { 5} + \frac { 2} { 9} =`?

Answer 1

See a solution process below:

Explanation:

To evaluate this expression the fractions must be over common denominators. We can multiply each fraction by the appropriate form of `1` so we can add the fractions:

`8/5 + 2/9 =>`

`(9/9 xx 8/5) + (5/5 xx 2/9) =>`

`(9 xx 8)/(9 xx 5) + (5 xx 2)/(5 xx 9) =>`

`72/45 + 10/45`

We can now add the numerators of the two fractions over the common denominator:

`(72 + 10)/45 =>`

`82/45`

If necessary, we can convert this improper fraction into a mixed number:

`82/45 = (45 + 37)/45 = 45/45 + 37/45 = 1 + 37/45 = 1 37/45`

`8/5 + 2/9 = 82/45`

Or

`8/5 + 2/9 = 1 37/45`

Answer 2

`82/45`

Explanation:

It's easier to evaluate fractions when you have the same denominator for each, so let's do that first.

The common base between 5 and 9 is 45

`8/5*9+2/9*5`

`= 72/45 +10/45`

Note: When multiplying with fractions, make sure to multiply both numerator and denominator.

So now we see `72/45 +10/45` , we can add 72 and 10 together to get:

`82/45`

Since there is no common factor that can be used to reduce the fraction, the answer is `82/45`