Solve (3/4-1/6+3/8)div1/44

$$( \frac { 3 } { 4 } - \frac { 1 } { 6 } + \frac { 3 } { 8 } ) \div \frac { 1 } { 44 }$$

Evaluate

$$\frac{253}{6}\approx 42.166666667$$

Solution Steps

Least common multiple of 4 and 6 is 12. Convert \frac{3}{4} and \frac{1}{6} to fractions with denominator 12.

$$\frac{\frac{9}{12}-\frac{2}{12}+\frac{3}{8}}{\frac{1}{44}}$$

Since \frac{9}{12} and \frac{2}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{9-2}{12}+\frac{3}{8}}{\frac{1}{44}}$$

Subtract 2 from 9 to get 7.

$$\frac{\frac{7}{12}+\frac{3}{8}}{\frac{1}{44}}$$

Least common multiple of 12 and 8 is 24. Convert \frac{7}{12} and \frac{3}{8} to fractions with denominator 24.

$$\frac{\frac{14}{24}+\frac{9}{24}}{\frac{1}{44}}$$

Since \frac{14}{24} and \frac{9}{24} have the same denominator, add them by adding their numerators.

$$\frac{\frac{14+9}{24}}{\frac{1}{44}}$$

Add 14 and 9 to get 23.

$$\frac{\frac{23}{24}}{\frac{1}{44}}$$

Divide \frac{23}{24} by \frac{1}{44} by multiplying \frac{23}{24} by the reciprocal of \frac{1}{44}.

$$\frac{23}{24}\times 44$$

Express \frac{23}{24}\times 44 as a single fraction.

$$\frac{23\times 44}{24}$$

Multiply 23 and 44 to get 1012.

$$\frac{1012}{24}$$

Reduce the fraction \frac{1012}{24} to lowest terms by extracting and canceling out 4.

$$\frac{253}{6}$$

Factor

$$\frac{11 \cdot 23}{2 \cdot 3} = 42\frac{1}{6} = 42.166666666666664$$