Solve 15/7*(5div5/6-5/6div5)

$$1 \frac { 5 } { 7 } \times ( 5 \div \frac { 5 } { 6 } - \frac { 5 } { 6 } \div 5 )$$

Evaluate

$$10$$

Solution Steps

Multiply 1 and 7 to get 7.

$$\frac{7+5}{7}\left(\frac{5}{\frac{5}{6}}-\frac{\frac{5}{6}}{5}\right)$$

Add 7 and 5 to get 12.

$$\frac{12}{7}\left(\frac{5}{\frac{5}{6}}-\frac{\frac{5}{6}}{5}\right)$$

Divide 5 by \frac{5}{6} by multiplying 5 by the reciprocal of \frac{5}{6}.

$$\frac{12}{7}\left(5\times \frac{6}{5}-\frac{\frac{5}{6}}{5}\right)$$

Cancel out 5 and 5.

$$\frac{12}{7}\left(6-\frac{\frac{5}{6}}{5}\right)$$

Express \frac{\frac{5}{6}}{5} as a single fraction.

$$\frac{12}{7}\left(6-\frac{5}{6\times 5}\right)$$

Cancel out 5 in both numerator and denominator.

$$\frac{12}{7}\left(6-\frac{1}{6}\right)$$

Convert 6 to fraction \frac{36}{6}.

$$\frac{12}{7}\left(\frac{36}{6}-\frac{1}{6}\right)$$

Since \frac{36}{6} and \frac{1}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{12}{7}\times \frac{36-1}{6}$$

Subtract 1 from 36 to get 35.

$$\frac{12}{7}\times \frac{35}{6}$$

Multiply \frac{12}{7} times \frac{35}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{12\times 35}{7\times 6}$$

Do the multiplications in the fraction \frac{12\times 35}{7\times 6}.

$$\frac{420}{42}$$

Divide 420 by 42 to get 10.

$$10$$

Factor

$$2\times 5$$