Please solve # 15 1/2 + 16 1/4 - 12 5/8 - 14 1/6 ?#

4 Answers

#4 23/24#

Explanation:

There are a couple of ways to approach this - we can convert the mixed numbers to improper fractions (which will result in big numerators when we get a common denominator) or we can rewrite the expression this way:

#15+1/2+16+1/4-(12+5/8)-(14+1/6)#

Let's distribute the negative signs:

#15+1/2+16+1/4-12-5/8-14-1/6#

and now regroup the expression with whole numbers grouped together and fractions grouped together:

#(15+16-12-14)+(1/2+1/4-5/8-1/6)#

We can simplify the whole number part of the expression:

#5+(1/2+1/4-5/8-1/6)#

And now let's focus on the fractions. We need the Lowest Common Denominator, which is 24 and can be found by using prime factorizations:

#2=2#
#4=2xx2#
#8=2xx2xx2#
#6=2xx3#

And now we grab the largest grouping of each prime. There are three 2s (in the 8) and a single 3 (in the 6), so we have:

#LCD=2xx2xx2xx3=24#

#5+(1/2(1)+1/4(1)-5/8(1)-1/6(1))#

#5+(1/2(12/12)+1/4(6/6)-5/8(3/3)-1/6(4/4))#

#5+(12/24+6/24-15/24-4/24)#

#5+(-1/24)#

Let's now see that we can express the number 5 as #4+1#:

#4+1-1/24#

and we can express 1 as #24/24#:

#4+24/24-1/24#

#4+23/24=>4 23/24#

Deal with the whole numbers first

#15 - 14 = 1#
#16 - 12 = 4#
#4 + 1 = 5#

Then the fractions

#1/2+1/4=2/4+1/4=3/4#

#3/4-5/8=6/8-5/8=1/8#

#1/8-1/6=3/24-4/24=-1/24#

Putting these together

#5+ -1/24#

#4 24/24-1/24= 4 23/24#

Jul 20, 2018

#=4 23/24#

Explanation:

#color(blue)(15) 1/2 +color(blue)(16) 1/4 -color(red)(12) 5/8 -color(red)(14) 1/6#

#=color(blue)(31) 1/2 + 1/4 -color(red)(26) 5/8 - 1/6#

#=5 (12+6-15-4)/24" "larr# find the common denominator

#=5 (18-19)/24 = 4+color(magenta)(1) (18-19)/24" "# (convert #color(magenta)(1 = 24/24)#)

#= 4 (color(magenta)(24)+18-19)/24#

#=4 23/24#

Aug 10, 2018

#4 23/24#

Explanation:

#15 1/2+16 1/4-12 5/8-14 1/6#

#:.=31/2+65/4-101/8-85/6#

#:.=(372+390+303-340)/24#

#:.=119/24#

#:.=4 23/24#