How do you evaluate #5\frac { 5} { 8}- 2\frac { 3} { 4}#?

1 Answer
smendyka
Sep 14, 2017

See a solution process below:

Explanation:

First, we need to convert both mixed numbers into improper fractions:

#5 5/8 - 2 3/4 =>#

#(5 + 5/8) - (2 + 3/4) =>#

#([8/8 xx 5] + 5/8) - ([4/4 xx 2] + 3/4) =>#

#(40/8 + 5/8) - (8/4 + 3/4) =>#

#(40 + 5)/8 - (8 + 3)/4 =>#

#45/8 - 11/4#

Next, we need to put the fraction on the right over a common denominator with the fraction on the left by multiplying the fraction on the right by the appropriate form of #1#:

#45/8 - (2/2 xx 11/4) =>#

#45/8 - (2 xx 11)/(2 xx 4) =>#

#45/8 - 22/8#

Then, we can subtract the numerators over the common denominator:

#(45 - 22)/8#

#23/8#

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

#23/8 => (16 + 7)/8 => 16/8 + 7/8 => 2 + 7/8 => 2 7/8#

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