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

Question

Mila Anderson · Accepted Answer

Prioritize handling the entire number. #15 - 14 = 1#
#16 - 12 = 4#
#4 + 1 = 5# Next, 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# Combining these #5+ -1/24# #4 24/24-1/24= 4 23/24#

Cameron Arnold · Answer

#4 23/24#

There are two ways to go about this: either we rewrite the expression as follows, or we convert the mixed numbers to improper fractions, which will lead to large numerators when we find a common denominator:

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

Let's disperse the warning signs:

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

and now rearrange the expression so that fractions and whole numbers are grouped together:

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

The expression's entire numerical portion can be made simpler:

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

Let's turn our attention to the fractions now. To find the Lowest Common Denominator, which is 24, prime factorizations can be utilized:

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

We now take the largest grouping of each prime, and we have the following: three 2s (in the 8) and one 3 (in the 6).

#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#

Gabriel Agustin · Answer

#=4 23/24# #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#

Gianna Caruso · Answer

#4 23/24# #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#