Solve 1/2+1/4div1/3(5/2)^2-frac{sqrt{81}}{2}

$$\frac { 1 } { 2 } + \frac { 1 } { 4 } \div \frac { 1 } { 3 } ( \frac { 5 } { 2 } ) ^ { 2 } - \frac { \sqrt { 81 } } { 2 }$$

Evaluate

$$\frac{11}{16}=0.6875$$

Solution Steps

Divide \frac{1}{4} by \frac{1}{3} by multiplying \frac{1}{4} by the reciprocal of \frac{1}{3}.

$$\frac{1}{2}+\frac{1}{4}\times 3\times \left(\frac{5}{2}\right)^{2}-\frac{\sqrt{81}}{2}$$

Multiply \frac{1}{4} and 3 to get \frac{3}{4}.

$$\frac{1}{2}+\frac{3}{4}\times \left(\frac{5}{2}\right)^{2}-\frac{\sqrt{81}}{2}$$

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

$$\frac{1}{2}+\frac{3}{4}\times \frac{25}{4}-\frac{\sqrt{81}}{2}$$

Multiply \frac{3}{4} times \frac{25}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{2}+\frac{3\times 25}{4\times 4}-\frac{\sqrt{81}}{2}$$

Do the multiplications in the fraction \frac{3\times 25}{4\times 4}.

$$\frac{1}{2}+\frac{75}{16}-\frac{\sqrt{81}}{2}$$

Least common multiple of 2 and 16 is 16. Convert \frac{1}{2} and \frac{75}{16} to fractions with denominator 16.

$$\frac{8}{16}+\frac{75}{16}-\frac{\sqrt{81}}{2}$$

Since \frac{8}{16} and \frac{75}{16} have the same denominator, add them by adding their numerators.

$$\frac{8+75}{16}-\frac{\sqrt{81}}{2}$$

Add 8 and 75 to get 83.

$$\frac{83}{16}-\frac{\sqrt{81}}{2}$$

Calculate the square root of 81 and get 9.

$$\frac{83}{16}-\frac{9}{2}$$

Least common multiple of 16 and 2 is 16. Convert \frac{83}{16} and \frac{9}{2} to fractions with denominator 16.

$$\frac{83}{16}-\frac{72}{16}$$

Since \frac{83}{16} and \frac{72}{16} have the same denominator, subtract them by subtracting their numerators.

$$\frac{83-72}{16}$$

Subtract 72 from 83 to get 11.

$$\frac{11}{16}$$

Factor

$$\frac{11}{2 ^ {4}} = 0.6875$$