Solve (21/3-11/6)div(31/4+21/8)divfrac{28}{129}

$$( 2 \frac { 1 } { 3 } - 1 \frac { 1 } { 6 } ) \div ( 3 \frac { 1 } { 4 } + 2 \frac { 1 } { 8 } ) \div \frac { 28 } { 129 }$$

Evaluate

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Solution Steps

Divide \frac{\frac{2\times 3+1}{3}-\frac{1\times 6+1}{6}}{\frac{3\times 4+1}{4}+\frac{2\times 8+1}{8}} by \frac{28}{129} by multiplying \frac{\frac{2\times 3+1}{3}-\frac{1\times 6+1}{6}}{\frac{3\times 4+1}{4}+\frac{2\times 8+1}{8}} by the reciprocal of \frac{28}{129}.

$$\frac{\left(\frac{2\times 3+1}{3}-\frac{1\times 6+1}{6}\right)\times 129}{\left(\frac{3\times 4+1}{4}+\frac{2\times 8+1}{8}\right)\times 28}$$

Multiply 2 and 3 to get 6.

$$\frac{\left(\frac{6+1}{3}-\frac{1\times 6+1}{6}\right)\times 129}{\left(\frac{3\times 4+1}{4}+\frac{2\times 8+1}{8}\right)\times 28}$$

Add 6 and 1 to get 7.

$$\frac{\left(\frac{7}{3}-\frac{1\times 6+1}{6}\right)\times 129}{\left(\frac{3\times 4+1}{4}+\frac{2\times 8+1}{8}\right)\times 28}$$

Multiply 1 and 6 to get 6.

$$\frac{\left(\frac{7}{3}-\frac{6+1}{6}\right)\times 129}{\left(\frac{3\times 4+1}{4}+\frac{2\times 8+1}{8}\right)\times 28}$$

Add 6 and 1 to get 7.

$$\frac{\left(\frac{7}{3}-\frac{7}{6}\right)\times 129}{\left(\frac{3\times 4+1}{4}+\frac{2\times 8+1}{8}\right)\times 28}$$

Least common multiple of 3 and 6 is 6. Convert \frac{7}{3} and \frac{7}{6} to fractions with denominator 6.

$$\frac{\left(\frac{14}{6}-\frac{7}{6}\right)\times 129}{\left(\frac{3\times 4+1}{4}+\frac{2\times 8+1}{8}\right)\times 28}$$

Since \frac{14}{6} and \frac{7}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{14-7}{6}\times 129}{\left(\frac{3\times 4+1}{4}+\frac{2\times 8+1}{8}\right)\times 28}$$

Subtract 7 from 14 to get 7.

$$\frac{\frac{7}{6}\times 129}{\left(\frac{3\times 4+1}{4}+\frac{2\times 8+1}{8}\right)\times 28}$$

Express \frac{7}{6}\times 129 as a single fraction.

$$\frac{\frac{7\times 129}{6}}{\left(\frac{3\times 4+1}{4}+\frac{2\times 8+1}{8}\right)\times 28}$$

Multiply 7 and 129 to get 903.

$$\frac{\frac{903}{6}}{\left(\frac{3\times 4+1}{4}+\frac{2\times 8+1}{8}\right)\times 28}$$

Reduce the fraction \frac{903}{6} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{301}{2}}{\left(\frac{3\times 4+1}{4}+\frac{2\times 8+1}{8}\right)\times 28}$$

Multiply 3 and 4 to get 12.

$$\frac{\frac{301}{2}}{\left(\frac{12+1}{4}+\frac{2\times 8+1}{8}\right)\times 28}$$

Add 12 and 1 to get 13.

$$\frac{\frac{301}{2}}{\left(\frac{13}{4}+\frac{2\times 8+1}{8}\right)\times 28}$$

Multiply 2 and 8 to get 16.

$$\frac{\frac{301}{2}}{\left(\frac{13}{4}+\frac{16+1}{8}\right)\times 28}$$

Add 16 and 1 to get 17.

$$\frac{\frac{301}{2}}{\left(\frac{13}{4}+\frac{17}{8}\right)\times 28}$$

Least common multiple of 4 and 8 is 8. Convert \frac{13}{4} and \frac{17}{8} to fractions with denominator 8.

$$\frac{\frac{301}{2}}{\left(\frac{26}{8}+\frac{17}{8}\right)\times 28}$$

Since \frac{26}{8} and \frac{17}{8} have the same denominator, add them by adding their numerators.

$$\frac{\frac{301}{2}}{\frac{26+17}{8}\times 28}$$

Add 26 and 17 to get 43.

$$\frac{\frac{301}{2}}{\frac{43}{8}\times 28}$$

Express \frac{43}{8}\times 28 as a single fraction.

$$\frac{\frac{301}{2}}{\frac{43\times 28}{8}}$$

Multiply 43 and 28 to get 1204.

$$\frac{\frac{301}{2}}{\frac{1204}{8}}$$

Reduce the fraction \frac{1204}{8} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{301}{2}}{\frac{301}{2}}$$

Divide \frac{301}{2} by \frac{301}{2} to get 1.

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Factor

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