Solve (1/2*19/7)div(2/4-1/6)+3

$$( \frac { 1 } { 2 } \times \frac { 19 } { 7 } ) \div ( \frac { 2 } { 4 } - \frac { 1 } { 6 } ) + 3$$

Evaluate

$$\frac{99}{14}\approx 7.071428571$$

Solution Steps

Multiply \frac{1}{2} times \frac{19}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{1\times 19}{2\times 7}}{\frac{2}{4}-\frac{1}{6}}+3$$

Do the multiplications in the fraction \frac{1\times 19}{2\times 7}.

$$\frac{\frac{19}{14}}{\frac{2}{4}-\frac{1}{6}}+3$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{19}{14}}{\frac{1}{2}-\frac{1}{6}}+3$$

Least common multiple of 2 and 6 is 6. Convert \frac{1}{2} and \frac{1}{6} to fractions with denominator 6.

$$\frac{\frac{19}{14}}{\frac{3}{6}-\frac{1}{6}}+3$$

Since \frac{3}{6} and \frac{1}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{19}{14}}{\frac{3-1}{6}}+3$$

Subtract 1 from 3 to get 2.

$$\frac{\frac{19}{14}}{\frac{2}{6}}+3$$

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{19}{14}}{\frac{1}{3}}+3$$

Divide \frac{19}{14} by \frac{1}{3} by multiplying \frac{19}{14} by the reciprocal of \frac{1}{3}.

$$\frac{19}{14}\times 3+3$$

Express \frac{19}{14}\times 3 as a single fraction.

$$\frac{19\times 3}{14}+3$$

Multiply 19 and 3 to get 57.

$$\frac{57}{14}+3$$

Convert 3 to fraction \frac{42}{14}.

$$\frac{57}{14}+\frac{42}{14}$$

Since \frac{57}{14} and \frac{42}{14} have the same denominator, add them by adding their numerators.

$$\frac{57+42}{14}$$

Add 57 and 42 to get 99.

$$\frac{99}{14}$$

Factor

$$\frac{3 ^ {2} \cdot 11}{2 \cdot 7} = 7\frac{1}{14} = 7.071428571428571$$