What is #10 2/3- 5 9/10#?

1 Answer
Jan 13, 2017

Answer:

#143/30#

or

#4 23/30#

Explanation:

First, we need to convert these mixed numbers to improper fractions. To convert a mixed number to an improper fraction you multiply the integer portion by the correct form of #1# and then add it to the fraction portion:

#((10 xx 3/3) + 2/3) - ((5 xx 10/10) + 9/10)#

#(30/3 + 2/3) - (50/10 + 9/10)#

#(30 + 2)/3 - (50 + 9)/10#

#32/3 - 59/10#

Next, to add or subtract fractions they need to be over common denominators, in this case #30#. We need to multiple each fraction by the appropriate form of #1# to make the denominator #30#:

#(10/10 xx 32/3) - (3/3 xx 59/10)#

#(10 xx 32)/(10 xx 3) - (3 xx 59)/(3 xx 10)#

#320/30 - 177/30#

#(320 - 177)/30#

#143/30#

or

#143 -: 30 = 4 # with a remainder of #23 = #

#4 + 23/30 = 4 23/30#