Solve 1/3[27x+3/4(4x+16y)]

$$\frac { 1 } { 3 } [ 27 x + \frac { 3 } { 4 } ( 4 x + 16 y ) ]$$

Evaluate

$$10x+4y$$

Solution Steps

Use the distributive property to multiply \frac{3}{4} by 4x+16y.

$$\frac{1}{3}\left(27x+\frac{3}{4}\times 4x+\frac{3}{4}\times 16y\right)$$

Cancel out 4 and 4.

$$\frac{1}{3}\left(27x+3x+\frac{3}{4}\times 16y\right)$$

Express \frac{3}{4}\times 16 as a single fraction.

$$\frac{1}{3}\left(27x+3x+\frac{3\times 16}{4}y\right)$$

Multiply 3 and 16 to get 48.

$$\frac{1}{3}\left(27x+3x+\frac{48}{4}y\right)$$

Divide 48 by 4 to get 12.

$$\frac{1}{3}\left(27x+3x+12y\right)$$

Combine 27x and 3x to get 30x.

$$\frac{1}{3}\left(30x+12y\right)$$

Use the distributive property to multiply \frac{1}{3} by 30x+12y.

$$\frac{1}{3}\times 30x+\frac{1}{3}\times 12y$$

Multiply \frac{1}{3} and 30 to get \frac{30}{3}.

$$\frac{30}{3}x+\frac{1}{3}\times 12y$$

Divide 30 by 3 to get 10.

$$10x+\frac{1}{3}\times 12y$$

Multiply \frac{1}{3} and 12 to get \frac{12}{3}.

$$10x+\frac{12}{3}y$$

Divide 12 by 3 to get 4.

$$10x+4y$$

Expand

$$10x+4y$$

Solution Steps

Use the distributive property to multiply \frac{3}{4} by 4x+16y.

$$\frac{1}{3}\left(27x+\frac{3}{4}\times 4x+\frac{3}{4}\times 16y\right)$$

Cancel out 4 and 4.

$$\frac{1}{3}\left(27x+3x+\frac{3}{4}\times 16y\right)$$

Express \frac{3}{4}\times 16 as a single fraction.

$$\frac{1}{3}\left(27x+3x+\frac{3\times 16}{4}y\right)$$

Multiply 3 and 16 to get 48.

$$\frac{1}{3}\left(27x+3x+\frac{48}{4}y\right)$$

Divide 48 by 4 to get 12.

$$\frac{1}{3}\left(27x+3x+12y\right)$$

Combine 27x and 3x to get 30x.

$$\frac{1}{3}\left(30x+12y\right)$$

Use the distributive property to multiply \frac{1}{3} by 30x+12y.

$$\frac{1}{3}\times 30x+\frac{1}{3}\times 12y$$

Multiply \frac{1}{3} and 30 to get \frac{30}{3}.

$$\frac{30}{3}x+\frac{1}{3}\times 12y$$

Divide 30 by 3 to get 10.

$$10x+\frac{1}{3}\times 12y$$

Multiply \frac{1}{3} and 12 to get \frac{12}{3}.

$$10x+\frac{12}{3}y$$

Divide 12 by 3 to get 4.

$$10x+4y$$