Solve 3y-1/2+2y+3/4+y+5/8

$$\frac { 3 y - 1 } { 2 } + \frac { 2 y + 3 } { 4 } + \frac { y + 5 } { 8 }$$

Evaluate

$$\frac{17y+7}{8}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 4 is 4. Multiply \frac{3y-1}{2} times \frac{2}{2}.

$$\frac{2\left(3y-1\right)}{4}+\frac{2y+3}{4}+\frac{y+5}{8}$$

Since \frac{2\left(3y-1\right)}{4} and \frac{2y+3}{4} have the same denominator, add them by adding their numerators.

$$\frac{2\left(3y-1\right)+2y+3}{4}+\frac{y+5}{8}$$

Do the multiplications in 2\left(3y-1\right)+2y+3.

$$\frac{6y-2+2y+3}{4}+\frac{y+5}{8}$$

Combine like terms in 6y-2+2y+3.

$$\frac{8y+1}{4}+\frac{y+5}{8}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 8 is 8. Multiply \frac{8y+1}{4} times \frac{2}{2}.

$$\frac{2\left(8y+1\right)}{8}+\frac{y+5}{8}$$

Since \frac{2\left(8y+1\right)}{8} and \frac{y+5}{8} have the same denominator, add them by adding their numerators.

$$\frac{2\left(8y+1\right)+y+5}{8}$$

Do the multiplications in 2\left(8y+1\right)+y+5.

$$\frac{16y+2+y+5}{8}$$

Combine like terms in 16y+2+y+5.

$$\frac{17y+7}{8}$$

Expand

$$\frac{17y+7}{8}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 4 is 4. Multiply \frac{3y-1}{2} times \frac{2}{2}.

$$\frac{2\left(3y-1\right)}{4}+\frac{2y+3}{4}+\frac{y+5}{8}$$

Since \frac{2\left(3y-1\right)}{4} and \frac{2y+3}{4} have the same denominator, add them by adding their numerators.

$$\frac{2\left(3y-1\right)+2y+3}{4}+\frac{y+5}{8}$$

Do the multiplications in 2\left(3y-1\right)+2y+3.

$$\frac{6y-2+2y+3}{4}+\frac{y+5}{8}$$

Combine like terms in 6y-2+2y+3.

$$\frac{8y+1}{4}+\frac{y+5}{8}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 8 is 8. Multiply \frac{8y+1}{4} times \frac{2}{2}.

$$\frac{2\left(8y+1\right)}{8}+\frac{y+5}{8}$$

Since \frac{2\left(8y+1\right)}{8} and \frac{y+5}{8} have the same denominator, add them by adding their numerators.

$$\frac{2\left(8y+1\right)+y+5}{8}$$

Do the multiplications in 2\left(8y+1\right)+y+5.

$$\frac{16y+2+y+5}{8}$$

Combine like terms in 16y+2+y+5.

$$\frac{17y+7}{8}$$