Solve 4/7+3/11(5/6-2/4)

$$\frac { 4 } { 7 } + \frac { 3 } { 11 } ( \frac { 5 } { 6 } - \frac { 2 } { 4 } )$$

Evaluate

$$\frac{51}{77}\approx 0.662337662$$

Solution Steps

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

$$\frac{4}{7}+\frac{3}{11}\left(\frac{5}{6}-\frac{1}{2}\right)$$

Least common multiple of 6 and 2 is 6. Convert \frac{5}{6} and \frac{1}{2} to fractions with denominator 6.

$$\frac{4}{7}+\frac{3}{11}\left(\frac{5}{6}-\frac{3}{6}\right)$$

Since \frac{5}{6} and \frac{3}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4}{7}+\frac{3}{11}\times \frac{5-3}{6}$$

Subtract 3 from 5 to get 2.

$$\frac{4}{7}+\frac{3}{11}\times \frac{2}{6}$$

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

$$\frac{4}{7}+\frac{3}{11}\times \frac{1}{3}$$

Multiply \frac{3}{11} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4}{7}+\frac{3\times 1}{11\times 3}$$

Cancel out 3 in both numerator and denominator.

$$\frac{4}{7}+\frac{1}{11}$$

Least common multiple of 7 and 11 is 77. Convert \frac{4}{7} and \frac{1}{11} to fractions with denominator 77.

$$\frac{44}{77}+\frac{7}{77}$$

Since \frac{44}{77} and \frac{7}{77} have the same denominator, add them by adding their numerators.

$$\frac{44+7}{77}$$

Add 44 and 7 to get 51.

$$\frac{51}{77}$$

Factor

$$\frac{3 \cdot 17}{7 \cdot 11} = 0.6623376623376623$$