Problem Solving

What is the value of 12 1/6 - 2 3/8 -7 2/3 + 19 3/4?

A)21
B)21 7/8
C)21 1/8
D)22
E)22 7/8

Thanks in advance.

There are two ways to do this: convert to fractions with a common denominator or convert to approximate decimals. For me, decimals were easier:

12 1/6 = 12.16
2 3/8 = 2.38
7 2/3 = 7.66
19 3/4 = 19.75

12.16 - 2.38 - 7.66 + 19.75

9.78 - 7.66 + 19.75

2.12 + 19.75

21.87

21 7/8

For fractions:

12 1/6 = 73/6 = 292/24
2 3/8 = 19/8 = 57/24
7 2/3 = 23/3 = 184/24
19 3/4 = 79/4 = 474/24

292/24 - 57/24 - 184/24 + 474/24

235/24 - 184/24 + 474/24

51/25 + 474/24

525/24

175/8

21 7/8

Add the whole numbers and fractions separately
12-2-7+19 = 22
1/6-3/8-2/3+3/4 = -3/24 = -1/8
Sum = 21 7/8