Solve (1/11-3/7+14/23)div2/3

$$( \frac{ 1 }{ 11 } - \frac{ 3 }{ 7 } + \frac{ 14 }{ 23 } ) \div \frac{ 2 }{ 3 }$$

Evaluate

$$\frac{720}{1771}\approx 0.406549972$$

Solution Steps

Least common multiple of 11 and 7 is 77. Convert \frac{1}{11} and \frac{3}{7} to fractions with denominator 77.

$$\frac{\frac{7}{77}-\frac{33}{77}+\frac{14}{23}}{\frac{2}{3}}$$

Since \frac{7}{77} and \frac{33}{77} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{7-33}{77}+\frac{14}{23}}{\frac{2}{3}}$$

Subtract 33 from 7 to get -26.

$$\frac{-\frac{26}{77}+\frac{14}{23}}{\frac{2}{3}}$$

Least common multiple of 77 and 23 is 1771. Convert -\frac{26}{77} and \frac{14}{23} to fractions with denominator 1771.

$$\frac{-\frac{598}{1771}+\frac{1078}{1771}}{\frac{2}{3}}$$

Since -\frac{598}{1771} and \frac{1078}{1771} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-598+1078}{1771}}{\frac{2}{3}}$$

Add -598 and 1078 to get 480.

$$\frac{\frac{480}{1771}}{\frac{2}{3}}$$

Divide \frac{480}{1771} by \frac{2}{3} by multiplying \frac{480}{1771} by the reciprocal of \frac{2}{3}.

$$\frac{480}{1771}\times \frac{3}{2}$$

Multiply \frac{480}{1771} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{480\times 3}{1771\times 2}$$

Do the multiplications in the fraction \frac{480\times 3}{1771\times 2}.

$$\frac{1440}{3542}$$

Reduce the fraction \frac{1440}{3542} to lowest terms by extracting and canceling out 2.

$$\frac{720}{1771}$$

Factor

$$\frac{2 ^ {4} \cdot 3 ^ {2} \cdot 5}{7 \cdot 11 \cdot 23} = 0.40654997176736307$$