Solve 15/6+(51/6-33/4)=31/4

$$1 \frac { 5 } { 6 } + ( 5 \frac { 1 } { 6 } - 3 \frac { 3 } { 4 } ) = 3 \frac { 1 } { 4 }$$

Verify

Solution Steps

Multiply both sides of the equation by 12, the least common multiple of 6,4.

$$2\left(1\times 6+5\right)+2\left(5\times 6+1\right)-3\left(3\times 4+3\right)=3\left(3\times 4+1\right)$$

Multiply 1 and 6 to get 6.

$$2\left(6+5\right)+2\left(5\times 6+1\right)-3\left(3\times 4+3\right)=3\left(3\times 4+1\right)$$

Add 6 and 5 to get 11.

$$2\times 11+2\left(5\times 6+1\right)-3\left(3\times 4+3\right)=3\left(3\times 4+1\right)$$

Multiply 2 and 11 to get 22.

$$22+2\left(5\times 6+1\right)-3\left(3\times 4+3\right)=3\left(3\times 4+1\right)$$

Multiply 5 and 6 to get 30.

$$22+2\left(30+1\right)-3\left(3\times 4+3\right)=3\left(3\times 4+1\right)$$

Add 30 and 1 to get 31.

$$22+2\times 31-3\left(3\times 4+3\right)=3\left(3\times 4+1\right)$$

Multiply 2 and 31 to get 62.

$$22+62-3\left(3\times 4+3\right)=3\left(3\times 4+1\right)$$

Add 22 and 62 to get 84.

$$84-3\left(3\times 4+3\right)=3\left(3\times 4+1\right)$$

Multiply 3 and 4 to get 12.

$$84-3\left(12+3\right)=3\left(3\times 4+1\right)$$

Add 12 and 3 to get 15.

$$84-3\times 15=3\left(3\times 4+1\right)$$

Multiply -3 and 15 to get -45.

$$84-45=3\left(3\times 4+1\right)$$

Subtract 45 from 84 to get 39.

$$39=3\left(3\times 4+1\right)$$

Multiply 3 and 4 to get 12.

$$39=3\left(12+1\right)$$

Add 12 and 1 to get 13.

$$39=3\times 13$$

Multiply 3 and 13 to get 39.

$$39=39$$

Compare 39 and 39.

$$\text{true}$$