Solve (1/6*3/5)+7/2-(1/4divfrac{2}{7})=

$$( \frac { 1 } { 6 } \times \frac { 3 } { 5 } ) + \frac { 7 } { 2 } - ( \frac { 1 } { 4 } \div \frac { 2 } { 7 } ) =$$

Evaluate

$$\frac{109}{40}=2.725$$

Solution Steps

Multiply \frac{1}{6} times \frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 3}{6\times 5}+\frac{7}{2}-\frac{\frac{1}{4}}{\frac{2}{7}}$$

Do the multiplications in the fraction \frac{1\times 3}{6\times 5}.

$$\frac{3}{30}+\frac{7}{2}-\frac{\frac{1}{4}}{\frac{2}{7}}$$

Reduce the fraction \frac{3}{30} to lowest terms by extracting and canceling out 3.

$$\frac{1}{10}+\frac{7}{2}-\frac{\frac{1}{4}}{\frac{2}{7}}$$

Least common multiple of 10 and 2 is 10. Convert \frac{1}{10} and \frac{7}{2} to fractions with denominator 10.

$$\frac{1}{10}+\frac{35}{10}-\frac{\frac{1}{4}}{\frac{2}{7}}$$

Since \frac{1}{10} and \frac{35}{10} have the same denominator, add them by adding their numerators.

$$\frac{1+35}{10}-\frac{\frac{1}{4}}{\frac{2}{7}}$$

Add 1 and 35 to get 36.

$$\frac{36}{10}-\frac{\frac{1}{4}}{\frac{2}{7}}$$

Reduce the fraction \frac{36}{10} to lowest terms by extracting and canceling out 2.

$$\frac{18}{5}-\frac{\frac{1}{4}}{\frac{2}{7}}$$

Divide \frac{1}{4} by \frac{2}{7} by multiplying \frac{1}{4} by the reciprocal of \frac{2}{7}.

$$\frac{18}{5}-\frac{1}{4}\times \frac{7}{2}$$

Multiply \frac{1}{4} times \frac{7}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{18}{5}-\frac{1\times 7}{4\times 2}$$

Do the multiplications in the fraction \frac{1\times 7}{4\times 2}.

$$\frac{18}{5}-\frac{7}{8}$$

Least common multiple of 5 and 8 is 40. Convert \frac{18}{5} and \frac{7}{8} to fractions with denominator 40.

$$\frac{144}{40}-\frac{35}{40}$$

Since \frac{144}{40} and \frac{35}{40} have the same denominator, subtract them by subtracting their numerators.

$$\frac{144-35}{40}$$

Subtract 35 from 144 to get 109.

$$\frac{109}{40}$$

Factor

$$\frac{109}{2 ^ {3} \cdot 5} = 2\frac{29}{40} = 2.725$$