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

2 Answers
Mar 4, 2018

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#

Mar 4, 2018

#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#