Solve 25/6div20/3+(3/2)^2*1/30

$$\frac { 25 } { 6 } \div \frac { 20 } { 3 } + ( \frac { 3 } { 2 } ) ^ { 2 } \cdot \frac { 1 } { 30 }$$

Evaluate

$$\frac{7}{10}=0.7$$

Solution Steps

Divide \frac{25}{6} by \frac{20}{3} by multiplying \frac{25}{6} by the reciprocal of \frac{20}{3}.

$$\frac{25}{6}\times \frac{3}{20}+\left(\frac{3}{2}\right)^{2}\times \frac{1}{30}$$

Multiply \frac{25}{6} times \frac{3}{20} by multiplying numerator times numerator and denominator times denominator.

$$\frac{25\times 3}{6\times 20}+\left(\frac{3}{2}\right)^{2}\times \frac{1}{30}$$

Do the multiplications in the fraction \frac{25\times 3}{6\times 20}.

$$\frac{75}{120}+\left(\frac{3}{2}\right)^{2}\times \frac{1}{30}$$

Reduce the fraction \frac{75}{120} to lowest terms by extracting and canceling out 15.

$$\frac{5}{8}+\left(\frac{3}{2}\right)^{2}\times \frac{1}{30}$$

Calculate \frac{3}{2} to the power of 2 and get \frac{9}{4}.

$$\frac{5}{8}+\frac{9}{4}\times \frac{1}{30}$$

Multiply \frac{9}{4} times \frac{1}{30} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5}{8}+\frac{9\times 1}{4\times 30}$$

Do the multiplications in the fraction \frac{9\times 1}{4\times 30}.

$$\frac{5}{8}+\frac{9}{120}$$

Reduce the fraction \frac{9}{120} to lowest terms by extracting and canceling out 3.

$$\frac{5}{8}+\frac{3}{40}$$

Least common multiple of 8 and 40 is 40. Convert \frac{5}{8} and \frac{3}{40} to fractions with denominator 40.

$$\frac{25}{40}+\frac{3}{40}$$

Since \frac{25}{40} and \frac{3}{40} have the same denominator, add them by adding their numerators.

$$\frac{25+3}{40}$$

Add 25 and 3 to get 28.

$$\frac{28}{40}$$

Reduce the fraction \frac{28}{40} to lowest terms by extracting and canceling out 4.

$$\frac{7}{10}$$

Factor

$$\frac{7}{2 \cdot 5} = 0.7$$