Solve 9/5:18/5-1/4*3/2+frac{2}{5}

$$\frac { 9 } { 5 } : \frac { 18 } { 5 } - \frac { 1 } { 4 } \times \frac { 3 } { 2 } + \frac { 2 } { 5 }$$

Evaluate

$$\frac{21}{40}=0.525$$

Solution Steps

Divide \frac{9}{5} by \frac{18}{5} by multiplying \frac{9}{5} by the reciprocal of \frac{18}{5}.

$$\frac{9}{5}\times \frac{5}{18}-\frac{1}{4}\times \frac{3}{2}+\frac{2}{5}$$

Multiply \frac{9}{5} times \frac{5}{18} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9\times 5}{5\times 18}-\frac{1}{4}\times \frac{3}{2}+\frac{2}{5}$$

Cancel out 5 in both numerator and denominator.

$$\frac{9}{18}-\frac{1}{4}\times \frac{3}{2}+\frac{2}{5}$$

Reduce the fraction \frac{9}{18} to lowest terms by extracting and canceling out 9.

$$\frac{1}{2}-\frac{1}{4}\times \frac{3}{2}+\frac{2}{5}$$

Multiply \frac{1}{4} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{2}-\frac{1\times 3}{4\times 2}+\frac{2}{5}$$

Do the multiplications in the fraction \frac{1\times 3}{4\times 2}.

$$\frac{1}{2}-\frac{3}{8}+\frac{2}{5}$$

Least common multiple of 2 and 8 is 8. Convert \frac{1}{2} and \frac{3}{8} to fractions with denominator 8.

$$\frac{4}{8}-\frac{3}{8}+\frac{2}{5}$$

Since \frac{4}{8} and \frac{3}{8} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4-3}{8}+\frac{2}{5}$$

Subtract 3 from 4 to get 1.

$$\frac{1}{8}+\frac{2}{5}$$

Least common multiple of 8 and 5 is 40. Convert \frac{1}{8} and \frac{2}{5} to fractions with denominator 40.

$$\frac{5}{40}+\frac{16}{40}$$

Since \frac{5}{40} and \frac{16}{40} have the same denominator, add them by adding their numerators.

$$\frac{5+16}{40}$$

Add 5 and 16 to get 21.

$$\frac{21}{40}$$

Factor

$$\frac{3 \cdot 7}{2 ^ {3} \cdot 5} = 0.525$$