Question

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

Answer 1

`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`

Answer 2

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`

Answer 3

`=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`

Answer 4

`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`