How do you evaluate #7\frac { 9} { 10} - - 9\frac { 1} { 2}#?

1 Answer
smendyka
Jan 30, 2018

See a solution process below:

Explanation:

First rewrite the expression remembering "minus a minus is a plus":

#7 9/10 + 9 1/2#

Next, convert each mixed number into an improper fraction:

#7 9/10 = (10/10 xx 7) + 9/10 = 70/10 + 9/10 = (70 + 9)/10 = 79/10#

#9 1/2 = 9 + 1/2 = (2/2 xx 9) + 1/2 = 18/2 + 1/2 = (18 + 1)/2 = 19/2#

Then, to add fractions they must be over a common denominator. We can convert the second fraction to a common denominator by multiplying it by the appropriate form of #1# which will not change its value:

#19/2 = 5/5 xx 19/2 = (5 xx 19)/(5 xx 2) = 95/10#

Now we cam rewrite the expression and evaluate it as:

#79/10 + 95/10 = (79 + 95)/10 = 174/10#

If necessary, we can then convert this to a mixed number:

#174/10 = (170 + 4)/10 = 170/10 + 4/10 = 17 + 2/5 = 17 2/5#

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