Solve 12*(7/24+5/6+3/4)

$$12 \times ( \frac { 7 } { 24 } + \frac { 5 } { 6 } + \frac { 3 } { 4 } )$$

Evaluate

$$\frac{45}{2}=22.5$$

Solution Steps

Least common multiple of 24 and 6 is 24. Convert \frac{7}{24} and \frac{5}{6} to fractions with denominator 24.

$$12\left(\frac{7}{24}+\frac{20}{24}+\frac{3}{4}\right)$$

Since \frac{7}{24} and \frac{20}{24} have the same denominator, add them by adding their numerators.

$$12\left(\frac{7+20}{24}+\frac{3}{4}\right)$$

Add 7 and 20 to get 27.

$$12\left(\frac{27}{24}+\frac{3}{4}\right)$$

Reduce the fraction \frac{27}{24} to lowest terms by extracting and canceling out 3.

$$12\left(\frac{9}{8}+\frac{3}{4}\right)$$

Least common multiple of 8 and 4 is 8. Convert \frac{9}{8} and \frac{3}{4} to fractions with denominator 8.

$$12\left(\frac{9}{8}+\frac{6}{8}\right)$$

Since \frac{9}{8} and \frac{6}{8} have the same denominator, add them by adding their numerators.

$$12\times \frac{9+6}{8}$$

Add 9 and 6 to get 15.

$$12\times \frac{15}{8}$$

Express 12\times \frac{15}{8} as a single fraction.

$$\frac{12\times 15}{8}$$

Multiply 12 and 15 to get 180.

$$\frac{180}{8}$$

Reduce the fraction \frac{180}{8} to lowest terms by extracting and canceling out 4.

$$\frac{45}{2}$$

Factor

$$\frac{3 ^ {2} \cdot 5}{2} = 22\frac{1}{2} = 22.5$$