Solve 1/2+1/4div1/3+(5/2)^2-sqrt{frac{81}{25}}

$$\frac { 1 } { 2 } + \frac { 1 } { 4 } \div \frac { 1 } { 3 } + ( \frac { 5 } { 2 } ) ^ { 2 } - \sqrt { \frac { 81 } { 25 } }$$

Evaluate

$$\frac{57}{10}=5.7$$

Solution Steps

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

$$\frac{1}{2}+\frac{1}{4}\times 3+\left(\frac{5}{2}\right)^{2}-\sqrt{\frac{81}{25}}$$

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

$$\frac{1}{2}+\frac{3}{4}+\left(\frac{5}{2}\right)^{2}-\sqrt{\frac{81}{25}}$$

Least common multiple of 2 and 4 is 4. Convert \frac{1}{2} and \frac{3}{4} to fractions with denominator 4.

$$\frac{2}{4}+\frac{3}{4}+\left(\frac{5}{2}\right)^{2}-\sqrt{\frac{81}{25}}$$

Since \frac{2}{4} and \frac{3}{4} have the same denominator, add them by adding their numerators.

$$\frac{2+3}{4}+\left(\frac{5}{2}\right)^{2}-\sqrt{\frac{81}{25}}$$

Add 2 and 3 to get 5.

$$\frac{5}{4}+\left(\frac{5}{2}\right)^{2}-\sqrt{\frac{81}{25}}$$

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

$$\frac{5}{4}+\frac{25}{4}-\sqrt{\frac{81}{25}}$$

Since \frac{5}{4} and \frac{25}{4} have the same denominator, add them by adding their numerators.

$$\frac{5+25}{4}-\sqrt{\frac{81}{25}}$$

Add 5 and 25 to get 30.

$$\frac{30}{4}-\sqrt{\frac{81}{25}}$$

Reduce the fraction \frac{30}{4} to lowest terms by extracting and canceling out 2.

$$\frac{15}{2}-\sqrt{\frac{81}{25}}$$

Rewrite the square root of the division \frac{81}{25} as the division of square roots \frac{\sqrt{81}}{\sqrt{25}}. Take the square root of both numerator and denominator.

$$\frac{15}{2}-\frac{9}{5}$$

Least common multiple of 2 and 5 is 10. Convert \frac{15}{2} and \frac{9}{5} to fractions with denominator 10.

$$\frac{75}{10}-\frac{18}{10}$$

Since \frac{75}{10} and \frac{18}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{75-18}{10}$$

Subtract 18 from 75 to get 57.

$$\frac{57}{10}$$

Factor

$$\frac{3 \cdot 19}{2 \cdot 5} = 5\frac{7}{10} = 5.7$$