Solve 7div2-[21+4div(2+5)*(25div8)div(5div2)^2]

$$7 \div 2 - [ 21 + 4 \div ( 2 + 5 ) \times ( 25 \div 8 ) \div ( 5 \div 2 ) ^ { 2 } ]$$

Evaluate

$$-\frac{249}{14}\approx -17.785714286$$

Solution Steps

Add 2 and 5 to get 7.

$$\frac{7}{2}-\left(21+\frac{\frac{4}{7}\times \frac{25}{8}}{\left(\frac{5}{2}\right)^{2}}\right)$$

Multiply \frac{4}{7} times \frac{25}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7}{2}-\left(21+\frac{\frac{4\times 25}{7\times 8}}{\left(\frac{5}{2}\right)^{2}}\right)$$

Do the multiplications in the fraction \frac{4\times 25}{7\times 8}.

$$\frac{7}{2}-\left(21+\frac{\frac{100}{56}}{\left(\frac{5}{2}\right)^{2}}\right)$$

Reduce the fraction \frac{100}{56} to lowest terms by extracting and canceling out 4.

$$\frac{7}{2}-\left(21+\frac{\frac{25}{14}}{\left(\frac{5}{2}\right)^{2}}\right)$$

Calculate \frac{5}{2} to the power of 2 and get \frac{25}{4}.

$$\frac{7}{2}-\left(21+\frac{\frac{25}{14}}{\frac{25}{4}}\right)$$

Divide \frac{25}{14} by \frac{25}{4} by multiplying \frac{25}{14} by the reciprocal of \frac{25}{4}.

$$\frac{7}{2}-\left(21+\frac{25}{14}\times \frac{4}{25}\right)$$

Multiply \frac{25}{14} times \frac{4}{25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{7}{2}-\left(21+\frac{25\times 4}{14\times 25}\right)$$

Cancel out 25 in both numerator and denominator.

$$\frac{7}{2}-\left(21+\frac{4}{14}\right)$$

Reduce the fraction \frac{4}{14} to lowest terms by extracting and canceling out 2.

$$\frac{7}{2}-\left(21+\frac{2}{7}\right)$$

Convert 21 to fraction \frac{147}{7}.

$$\frac{7}{2}-\left(\frac{147}{7}+\frac{2}{7}\right)$$

Since \frac{147}{7} and \frac{2}{7} have the same denominator, add them by adding their numerators.

$$\frac{7}{2}-\frac{147+2}{7}$$

Add 147 and 2 to get 149.

$$\frac{7}{2}-\frac{149}{7}$$

Least common multiple of 2 and 7 is 14. Convert \frac{7}{2} and \frac{149}{7} to fractions with denominator 14.

$$\frac{49}{14}-\frac{298}{14}$$

Since \frac{49}{14} and \frac{298}{14} have the same denominator, subtract them by subtracting their numerators.

$$\frac{49-298}{14}$$

Subtract 298 from 49 to get -249.

$$-\frac{249}{14}$$

Factor

$$-\frac{249}{14} = -17\frac{11}{14} = -17.785714285714285$$