Solve 3/4div11/2*21/3-1/2=frac{1}{3}

$$\frac { 3 } { 4 } \div 1 \frac { 1 } { 2 } \times 2 \frac { 1 } { 3 } - \frac { 1 } { 2 } = \frac { 1 } { 3 }$$

Verify

Solution Steps

Multiply both sides of the equation by 6, the least common multiple of 3,2.

$$2\times \frac{\frac{3}{4}}{\frac{1\times 2+1}{2}}\left(2\times 3+1\right)-3=2$$

Divide \frac{3}{4} by \frac{1\times 2+1}{2} by multiplying \frac{3}{4} by the reciprocal of \frac{1\times 2+1}{2}.

$$2\times \frac{3\times 2}{4\left(1\times 2+1\right)}\left(2\times 3+1\right)-3=2$$

Cancel out 2 in both numerator and denominator.

$$2\times \frac{3}{2\left(1+2\right)}\left(2\times 3+1\right)-3=2$$

Add 1 and 2 to get 3.

$$2\times \frac{3}{2\times 3}\left(2\times 3+1\right)-3=2$$

Multiply 2 and 3 to get 6.

$$2\times \frac{3}{6}\left(2\times 3+1\right)-3=2$$

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

$$2\times \frac{1}{2}\left(2\times 3+1\right)-3=2$$

Cancel out 2 and 2.

$$2\times 3+1-3=2$$

Multiply 2 and 3 to get 6.

$$6+1-3=2$$

Add 6 and 1 to get 7.

$$7-3=2$$

Subtract 3 from 7 to get 4.

$$4=2$$

Compare 4 and 2.

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