Solve 22/7*({left(7/2right)}^2-{left(1/4right)}^2)*140

$$\frac{ 22 }{ 7 } \times ( { \left( \frac{ 7 }{ 2 } \right) }^{ 2 } - { \left( \frac{ 1 }{ 4 } \right) }^{ 2 } ) \times 140$$

Evaluate

$$\frac{10725}{2}=5362.5$$

Solution Steps

Calculate \frac{7}{2} to the power of 2 and get \frac{49}{4}.

$$\frac{22}{7}\left(\frac{49}{4}-\left(\frac{1}{4}\right)^{2}\right)\times 140$$

Calculate \frac{1}{4} to the power of 2 and get \frac{1}{16}.

$$\frac{22}{7}\left(\frac{49}{4}-\frac{1}{16}\right)\times 140$$

Least common multiple of 4 and 16 is 16. Convert \frac{49}{4} and \frac{1}{16} to fractions with denominator 16.

$$\frac{22}{7}\left(\frac{196}{16}-\frac{1}{16}\right)\times 140$$

Since \frac{196}{16} and \frac{1}{16} have the same denominator, subtract them by subtracting their numerators.

$$\frac{22}{7}\times \frac{196-1}{16}\times 140$$

Subtract 1 from 196 to get 195.

$$\frac{22}{7}\times \frac{195}{16}\times 140$$

Multiply \frac{22}{7} times \frac{195}{16} by multiplying numerator times numerator and denominator times denominator.

$$\frac{22\times 195}{7\times 16}\times 140$$

Do the multiplications in the fraction \frac{22\times 195}{7\times 16}.

$$\frac{4290}{112}\times 140$$

Reduce the fraction \frac{4290}{112} to lowest terms by extracting and canceling out 2.

$$\frac{2145}{56}\times 140$$

Express \frac{2145}{56}\times 140 as a single fraction.

$$\frac{2145\times 140}{56}$$

Multiply 2145 and 140 to get 300300.

$$\frac{300300}{56}$$

Reduce the fraction \frac{300300}{56} to lowest terms by extracting and canceling out 28.

$$\frac{10725}{2}$$

Factor

$$\frac{3 \cdot 5 ^ {2} \cdot 11 \cdot 13}{2} = 5362\frac{1}{2} = 5362.5$$