Solve 4/5*(21/6-6/7)=

$$\frac { 4 } { 5 } \cdot ( \frac { 21 } { 6 } - \frac { 6 } { 7 } ) =$$

Evaluate

$$\frac{74}{35}\approx 2.114285714$$

Solution Steps

Reduce the fraction \frac{21}{6} to lowest terms by extracting and canceling out 3.

$$\frac{4}{5}\left(\frac{7}{2}-\frac{6}{7}\right)$$

Least common multiple of 2 and 7 is 14. Convert \frac{7}{2} and \frac{6}{7} to fractions with denominator 14.

$$\frac{4}{5}\left(\frac{49}{14}-\frac{12}{14}\right)$$

Since \frac{49}{14} and \frac{12}{14} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4}{5}\times \frac{49-12}{14}$$

Subtract 12 from 49 to get 37.

$$\frac{4}{5}\times \frac{37}{14}$$

Multiply \frac{4}{5} times \frac{37}{14} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4\times 37}{5\times 14}$$

Do the multiplications in the fraction \frac{4\times 37}{5\times 14}.

$$\frac{148}{70}$$

Reduce the fraction \frac{148}{70} to lowest terms by extracting and canceling out 2.

$$\frac{74}{35}$$

Factor

$$\frac{2 \cdot 37}{5 \cdot 7} = 2\frac{4}{35} = 2.1142857142857143$$