What is the best estimate of the sum of the fractions? StartFraction 31 over 4 EndFraction + StartFraction 17 over 3 EndFraction + StartFraction 8 over 18 EndFraction 12 and one-half 13 14 and one-half 15

8767/252 or 34.78968253968253968253968253968253968253968253968253968253 decmial

Step-by-step explanation:

Simplify the following:

31/4 + 17/3 + 8/18 + 12 + 1/2 + 13/14 + 15/2

The gcd of 8 and 18 is 2, so 8/18 = (2×4)/(2×9) = 2/2×4/9 = 4/9:

31/4 + 17/3 + 4/9 + 12 + 1/2 + 13/14 + 15/2

Put 31/4 + 17/3 + 4/9 + 12 + 1/2 + 13/14 + 15/2 over the common denominator 252. 31/4 + 17/3 + 4/9 + 12 + 1/2 + 13/14 + 15/2 = (63×31)/252 + (84×17)/252 + (28×4)/252 + (252×12)/252 + 126/252 + (18×13)/252 + (126×15)/252:

(63×31)/252 + (84×17)/252 + (28×4)/252 + (252×12)/252 + 126/252 + (18×13)/252 + (126×15)/252

| | 6 | 3

× | | 3 | 1

| | 6 | 3

1 | 8 | 9 | 0

1 | 9 | 5 | 3:

1953/252 + (84×17)/252 + (28×4)/252 + (252×12)/252 + 126/252 + (18×13)/252 + (126×15)/252

| | 8 | 4

× | | 1 | 7

| 5 | 8 | 8

| 8 | 4 | 0

1 | 4 | 2 | 8:

1953/252 + 1428/252 + (28×4)/252 + (252×12)/252 + 126/252 + (18×13)/252 + (126×15)/252

28×4 = 112:

1953/252 + 1428/252 + 112/252 + (252×12)/252 + 126/252 + (18×13)/252 + (126×15)/252

| 2 | 5 | 2

× | | 1 | 2

| 5 | 0 | 4

2 | 5 | 2 | 0

3 | 0 | 2 | 4:

1953/252 + 1428/252 + 112/252 + 3024/252 + 126/252 + (18×13)/252 + (126×15)/252

| 1 | 8

× | 1 | 3

| 5 | 4

1 | 8 | 0

2 | 3 | 4:

1953/252 + 1428/252 + 112/252 + 3024/252 + 126/252 + 234/252 + (126×15)/252

| 1 | 2 | 6

× | | 1 | 5

| 6 | 3 | 0

1 | 2 | 6 | 0

1 | 8 | 9 | 0:

1953/252 + 1428/252 + 112/252 + 3024/252 + 126/252 + 234/252 + 1890/252

1953/252 + 1428/252 + 112/252 + 3024/252 + 126/252 + 234/252 + 1890/252 = (1953 + 1428 + 112 + 3024 + 126 + 234 + 1890)/252:

(1953 + 1428 + 112 + 3024 + 126 + 234 + 1890)/252

| 2 | 2 | 2 |  

| 3 | 0 | 2 | 4

| 1 | 9 | 5 | 3

| 1 | 8 | 9 | 0

| 1 | 4 | 2 | 8

| | 2 | 3 | 4

| | 1 | 2 | 6

+ | | 1 | 1 | 2

| 8 | 7 | 6 | 7:

8767/252

A.

Step-by-step explanation: