How do you simplify #5 1/2 + 2 7/9#?

1 Answer
May 21, 2018

Answer:

See a solution process below:

Explanation:

First, convert each number from a mixed number into an improper fraction:

#5 1/2 = 5 + 1/2 = (2/2 xx 5) + 1/2 = 10/2 + 1/2 = (10 + 1)/2 = 11/2#

#2 7/9 = 2 + 7/9 = (9/9 xx 2) + 7/9 = 18/9 + 7/9 = (18 + 7)/9 = 25/9#

To add fractions they must be over a common denominator:

#11/2 = 11/2 xx 9/9 = (11 xx 9)/(2 xx 9) = 99/18#

#25/9 = 25/9 xx 2/2 = (25 xx 2)/(9 xx 2) = 50/18#

We can now rewrite and add the numerators over the common denominator as:

#99/18 + 50/18 = (99 + 50)/18 = 149/18#

If necessary, we can covert this to a mixed number as:

#149/18 = (144 + 5)/18 = 144/18 + 5/18 = 8 + 5/18 = 8 5/18#