Solve 10div(2/23-1/15)

$$10 \div ( \frac{ 2 }{ 23 } - \frac{ 1 }{ 15 } )$$

Evaluate

$$\frac{3450}{7}\approx 492.857142857$$

Solution Steps

Least common multiple of 23 and 15 is 345. Convert \frac{2}{23} and \frac{1}{15} to fractions with denominator 345.

$$\frac{10}{\frac{30}{345}-\frac{23}{345}}$$

Since \frac{30}{345} and \frac{23}{345} have the same denominator, subtract them by subtracting their numerators.

$$\frac{10}{\frac{30-23}{345}}$$

Subtract 23 from 30 to get 7.

$$\frac{10}{\frac{7}{345}}$$

Divide 10 by \frac{7}{345} by multiplying 10 by the reciprocal of \frac{7}{345}.

$$10\times \frac{345}{7}$$

Express 10\times \frac{345}{7} as a single fraction.

$$\frac{10\times 345}{7}$$

Multiply 10 and 345 to get 3450.

$$\frac{3450}{7}$$

Factor

$$\frac{2 \cdot 3 \cdot 5 ^ {2} \cdot 23}{7} = 492\frac{6}{7} = 492.85714285714283$$