Solve 52/5x-1/3(x+3/4y)-y+3/8y

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

Evaluate

$$\frac{76x}{15}-\frac{7y}{8}$$

Solution Steps

Multiply 5 and 5 to get 25.

$$\frac{25+2}{5}x-\frac{1}{3}\left(x+\frac{3}{4}y\right)-y+\frac{3}{8}y$$

Add 25 and 2 to get 27.

$$\frac{27}{5}x-\frac{1}{3}\left(x+\frac{3}{4}y\right)-y+\frac{3}{8}y$$

Use the distributive property to multiply -\frac{1}{3} by x+\frac{3}{4}y.

$$\frac{27}{5}x-\frac{1}{3}x-\frac{1}{3}\times \frac{3}{4}y-y+\frac{3}{8}y$$

Multiply -\frac{1}{3} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{27}{5}x-\frac{1}{3}x+\frac{-3}{3\times 4}y-y+\frac{3}{8}y$$

Cancel out 3 in both numerator and denominator.

$$\frac{27}{5}x-\frac{1}{3}x+\frac{-1}{4}y-y+\frac{3}{8}y$$

Fraction \frac{-1}{4} can be rewritten as -\frac{1}{4} by extracting the negative sign.

$$\frac{27}{5}x-\frac{1}{3}x-\frac{1}{4}y-y+\frac{3}{8}y$$

Combine \frac{27}{5}x and -\frac{1}{3}x to get \frac{76}{15}x.

$$\frac{76}{15}x-\frac{1}{4}y-y+\frac{3}{8}y$$

Combine -\frac{1}{4}y and -y to get -\frac{5}{4}y.

$$\frac{76}{15}x-\frac{5}{4}y+\frac{3}{8}y$$

Combine -\frac{5}{4}y and \frac{3}{8}y to get -\frac{7}{8}y.

$$\frac{76}{15}x-\frac{7}{8}y$$

Expand

$$\frac{76x}{15}-\frac{7y}{8}$$

Solution Steps

Multiply 5 and 5 to get 25.

$$\frac{25+2}{5}x-\frac{1}{3}\left(x+\frac{3}{4}y\right)-y+\frac{3}{8}y$$

Add 25 and 2 to get 27.

$$\frac{27}{5}x-\frac{1}{3}\left(x+\frac{3}{4}y\right)-y+\frac{3}{8}y$$

Use the distributive property to multiply -\frac{1}{3} by x+\frac{3}{4}y.

$$\frac{27}{5}x-\frac{1}{3}x-\frac{1}{3}\times \frac{3}{4}y-y+\frac{3}{8}y$$

Multiply -\frac{1}{3} times \frac{3}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{27}{5}x-\frac{1}{3}x+\frac{-3}{3\times 4}y-y+\frac{3}{8}y$$

Cancel out 3 in both numerator and denominator.

$$\frac{27}{5}x-\frac{1}{3}x+\frac{-1}{4}y-y+\frac{3}{8}y$$

Fraction \frac{-1}{4} can be rewritten as -\frac{1}{4} by extracting the negative sign.

$$\frac{27}{5}x-\frac{1}{3}x-\frac{1}{4}y-y+\frac{3}{8}y$$

Combine \frac{27}{5}x and -\frac{1}{3}x to get \frac{76}{15}x.

$$\frac{76}{15}x-\frac{1}{4}y-y+\frac{3}{8}y$$

Combine -\frac{1}{4}y and -y to get -\frac{5}{4}y.

$$\frac{76}{15}x-\frac{5}{4}y+\frac{3}{8}y$$

Combine -\frac{5}{4}y and \frac{3}{8}y to get -\frac{7}{8}y.

$$\frac{76}{15}x-\frac{7}{8}y$$