Solve 2016div(135/7-88/11)*(5/7-5/11)

$$2016 \div ( 13 \frac { 5 } { 7 } - 8 \frac { 8 } { 11 } ) \times ( \frac { 5 } { 7 } - \frac { 5 } { 11 } )$$

Evaluate

$$105$$

Solution Steps

Multiply 13 and 7 to get 91.

$$\frac{2016}{\frac{91+5}{7}-\frac{8\times 11+8}{11}}\left(\frac{5}{7}-\frac{5}{11}\right)$$

Add 91 and 5 to get 96.

$$\frac{2016}{\frac{96}{7}-\frac{8\times 11+8}{11}}\left(\frac{5}{7}-\frac{5}{11}\right)$$

Multiply 8 and 11 to get 88.

$$\frac{2016}{\frac{96}{7}-\frac{88+8}{11}}\left(\frac{5}{7}-\frac{5}{11}\right)$$

Add 88 and 8 to get 96.

$$\frac{2016}{\frac{96}{7}-\frac{96}{11}}\left(\frac{5}{7}-\frac{5}{11}\right)$$

Least common multiple of 7 and 11 is 77. Convert \frac{96}{7} and \frac{96}{11} to fractions with denominator 77.

$$\frac{2016}{\frac{1056}{77}-\frac{672}{77}}\left(\frac{5}{7}-\frac{5}{11}\right)$$

Since \frac{1056}{77} and \frac{672}{77} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2016}{\frac{1056-672}{77}}\left(\frac{5}{7}-\frac{5}{11}\right)$$

Subtract 672 from 1056 to get 384.

$$\frac{2016}{\frac{384}{77}}\left(\frac{5}{7}-\frac{5}{11}\right)$$

Divide 2016 by \frac{384}{77} by multiplying 2016 by the reciprocal of \frac{384}{77}.

$$2016\times \frac{77}{384}\left(\frac{5}{7}-\frac{5}{11}\right)$$

Express 2016\times \frac{77}{384} as a single fraction.

$$\frac{2016\times 77}{384}\left(\frac{5}{7}-\frac{5}{11}\right)$$

Multiply 2016 and 77 to get 155232.

$$\frac{155232}{384}\left(\frac{5}{7}-\frac{5}{11}\right)$$

Reduce the fraction \frac{155232}{384} to lowest terms by extracting and canceling out 96.

$$\frac{1617}{4}\left(\frac{5}{7}-\frac{5}{11}\right)$$

Least common multiple of 7 and 11 is 77. Convert \frac{5}{7} and \frac{5}{11} to fractions with denominator 77.

$$\frac{1617}{4}\left(\frac{55}{77}-\frac{35}{77}\right)$$

Since \frac{55}{77} and \frac{35}{77} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1617}{4}\times \frac{55-35}{77}$$

Subtract 35 from 55 to get 20.

$$\frac{1617}{4}\times \frac{20}{77}$$

Multiply \frac{1617}{4} times \frac{20}{77} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1617\times 20}{4\times 77}$$

Do the multiplications in the fraction \frac{1617\times 20}{4\times 77}.

$$\frac{32340}{308}$$

Divide 32340 by 308 to get 105.

$$105$$

Factor

$$3\times 5\times 7$$