How do you evaluate #8\frac{1}{2}-5\frac{3}{10}#?

2 Answers
MysticSmile
Oct 5, 2017

#3.2# or #3 1/5#

Explanation:

First, I would normally change mixed numbers to improper fractions:

#8 1/2-5 3/10# to #17/2-53/10#

Now we find the LCD for these two fractions. The LCD (least common denominator) would be #10#

So we would adjust the fraction #17/2# to match the denominator with #10#:

#(17*5)/10-53/10#

As the denominators are equal, we can combine the fractions.
#(5*17-53)/10->#

#(85-53)/10->#

#32/10->#

#3 2/10# or #3.2# as a decimal or #3 1/10# (simplified)

Jim G.
Oct 5, 2017

#3 1/5#

Explanation:

#"note that "8 1/2 =8+1/2#

#"and "5 3/10=5+3/10#

#"we can express the calculation in terms of whole"#
#"numbers and fractions"#

#rArr8 1/2-5 3/10#

#=8+1/2-(5+3/10)#

#=8+1/2-5-3/10#

#=(8-5)+1/2-3/10#

#=3+5/10-3/10larrcolor(blue)" common denominator of 10"#

#=3+2/10#

#=3+cancel(2)^1/cancel(10)^5#

#=3+1/5=3 1/5#

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