Solve 1/2(231/3+42/3)(123/4)

$$\frac { 1 } { 2 } ( 23 \frac { 1 } { 3 } + 4 \frac { 2 } { 3 } ) ( 12 \frac { 3 } { 4 } )$$

Evaluate

$$\frac{357}{2}=178.5$$

Solution Steps

Multiply 23 and 3 to get 69.

$$\frac{1}{2}\left(\frac{69+1}{3}+\frac{4\times 3+2}{3}\right)\times \frac{12\times 4+3}{4}$$

Add 69 and 1 to get 70.

$$\frac{1}{2}\left(\frac{70}{3}+\frac{4\times 3+2}{3}\right)\times \frac{12\times 4+3}{4}$$

Multiply 4 and 3 to get 12.

$$\frac{1}{2}\left(\frac{70}{3}+\frac{12+2}{3}\right)\times \frac{12\times 4+3}{4}$$

Add 12 and 2 to get 14.

$$\frac{1}{2}\left(\frac{70}{3}+\frac{14}{3}\right)\times \frac{12\times 4+3}{4}$$

Since \frac{70}{3} and \frac{14}{3} have the same denominator, add them by adding their numerators.

$$\frac{1}{2}\times \frac{70+14}{3}\times \frac{12\times 4+3}{4}$$

Add 70 and 14 to get 84.

$$\frac{1}{2}\times \frac{84}{3}\times \frac{12\times 4+3}{4}$$

Divide 84 by 3 to get 28.

$$\frac{1}{2}\times 28\times \frac{12\times 4+3}{4}$$

Multiply \frac{1}{2} and 28 to get \frac{28}{2}.

$$\frac{28}{2}\times \frac{12\times 4+3}{4}$$

Divide 28 by 2 to get 14.

$$14\times \frac{12\times 4+3}{4}$$

Multiply 12 and 4 to get 48.

$$14\times \frac{48+3}{4}$$

Add 48 and 3 to get 51.

$$14\times \frac{51}{4}$$

Express 14\times \frac{51}{4} as a single fraction.

$$\frac{14\times 51}{4}$$

Multiply 14 and 51 to get 714.

$$\frac{714}{4}$$

Reduce the fraction \frac{714}{4} to lowest terms by extracting and canceling out 2.

$$\frac{357}{2}$$

Factor

$$\frac{3 \cdot 7 \cdot 17}{2} = 178\frac{1}{2} = 178.5$$