How do you evaluate #5\frac { 2} { 3} - 1\frac { 3} { 5}#?

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Answer 1 · 2017-11-06T15:29:18

See a solution process below:

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

#5 2/3 = 5 + 2/3 = (3/3 xx 5) + 2/3 = 15/3 + 2/3 = (15 + 2)/3 = 17/3#

#1 3/5 = 1 + 3/5 = (5/5 xx 1) + 3/5 = 5/5 + 3/5 = (5 + 3)/5 = 8/5#

Now, we can rewrite the expression as:

#17/3 - 8/5#

Next, we need to multiply each term by the appropriate form of #1# to put each fraction over a common denominator:

#(5/5 xx 17/3) - (3/3 xx 8/5) => (5 xx 17)/(5 xx 3) - (3 xx 8)/(3 xx 5) =>#

#85/5 - 24/15#

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

#(85 - 24)/15 => 61/15#

Now, we can convert the improper fraction into a mixed number:

#61/15 = (60 + 1)/15 60/15 + 1/15 = 4 + 1/15 = 4 1/15#