How do you subtract #9\frac { 4} { 5} - 5\frac { 3} { 10}#?

1 Answer
smendyka
Aug 1, 2017

See a solution process below:

Explanation:

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

#9 4/5 - 5 3/10 =>#

#(9 + 4/5) - (5 + 3/10) =>#

#([5/5 xx 9] + 4/5) - ([10/10 xx 5] + 3/10) =>#

#(45/5 + 4/5) - (50/10 + 3/10) =>#

#49/5 - 53/10#

Next, in order to be able to subtract the fractions, they must be over common denominators. We can give them common denominators by multiplying the fraction on the left by the appropriate form of #1#:

#(2/2 xx 49/5) - 53/10 =>#

#(2 xx 49)/(2 xx 5) - 53/10 =>#

#98/10 - 53/10#

We can now subtract the numerators over the common denominator:

#(98 - 53)/10 =>#

#45/10#

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

#45/10 =>#

#(40 + 5)/10 =>#

#40/10 + 5/10 =>#

#4 + 5/10 =>#

#4 + 1/2 =>#

#4 1/2#

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