Solve 2/7*21/8-1/7*(5/2-4)=

$$\frac { 2 } { 7 } \cdot \frac { 21 } { 8 } - \frac { 1 } { 7 } \cdot ( \frac { 5 } { 2 } - 4 ) =$$

Evaluate

$$\frac{27}{28}\approx 0.964285714$$

Solution Steps

Multiply \frac{2}{7} times \frac{21}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 21}{7\times 8}-\frac{1}{7}\left(\frac{5}{2}-4\right)$$

Do the multiplications in the fraction \frac{2\times 21}{7\times 8}.

$$\frac{42}{56}-\frac{1}{7}\left(\frac{5}{2}-4\right)$$

Reduce the fraction \frac{42}{56} to lowest terms by extracting and canceling out 14.

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

Convert 4 to fraction \frac{8}{2}.

$$\frac{3}{4}-\frac{1}{7}\left(\frac{5}{2}-\frac{8}{2}\right)$$

Since \frac{5}{2} and \frac{8}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3}{4}-\frac{1}{7}\times \frac{5-8}{2}$$

Subtract 8 from 5 to get -3.

$$\frac{3}{4}-\frac{1}{7}\left(-\frac{3}{2}\right)$$

Multiply \frac{1}{7} times -\frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3}{4}-\frac{1\left(-3\right)}{7\times 2}$$

Do the multiplications in the fraction \frac{1\left(-3\right)}{7\times 2}.

$$\frac{3}{4}-\frac{-3}{14}$$

Fraction \frac{-3}{14} can be rewritten as -\frac{3}{14} by extracting the negative sign.

$$\frac{3}{4}-\left(-\frac{3}{14}\right)$$

The opposite of -\frac{3}{14} is \frac{3}{14}.

$$\frac{3}{4}+\frac{3}{14}$$

Least common multiple of 4 and 14 is 28. Convert \frac{3}{4} and \frac{3}{14} to fractions with denominator 28.

$$\frac{21}{28}+\frac{6}{28}$$

Since \frac{21}{28} and \frac{6}{28} have the same denominator, add them by adding their numerators.

$$\frac{21+6}{28}$$

Add 21 and 6 to get 27.

$$\frac{27}{28}$$

Factor

$$\frac{3 ^ {3}}{2 ^ {2} \cdot 7} = 0.9642857142857143$$