Solve 2/5*1/2+9/10div9/20quadfrac{3}{16}+(frac{7}{10})

$$\frac { 2 } { 5 } \times \frac { 1 } { 2 } + \frac { 9 } { 10 } \div \frac { 9 } { 20 } \quad \frac { 3 } { 16 } + ( \frac { 7 } { 10 } )$$

Evaluate

$$\frac{51}{40}=1.275$$

Solution Steps

Multiply \frac{2}{5} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 1}{5\times 2}+\frac{\frac{9}{10}}{\frac{9}{20}}\times \frac{3}{16}+\frac{7}{10}$$

Cancel out 2 in both numerator and denominator.

$$\frac{1}{5}+\frac{\frac{9}{10}}{\frac{9}{20}}\times \frac{3}{16}+\frac{7}{10}$$

Divide \frac{9}{10} by \frac{9}{20} by multiplying \frac{9}{10} by the reciprocal of \frac{9}{20}.

$$\frac{1}{5}+\frac{9}{10}\times \frac{20}{9}\times \frac{3}{16}+\frac{7}{10}$$

Multiply \frac{9}{10} times \frac{20}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{5}+\frac{9\times 20}{10\times 9}\times \frac{3}{16}+\frac{7}{10}$$

Cancel out 9 in both numerator and denominator.

$$\frac{1}{5}+\frac{20}{10}\times \frac{3}{16}+\frac{7}{10}$$

Divide 20 by 10 to get 2.

$$\frac{1}{5}+2\times \frac{3}{16}+\frac{7}{10}$$

Express 2\times \frac{3}{16} as a single fraction.

$$\frac{1}{5}+\frac{2\times 3}{16}+\frac{7}{10}$$

Multiply 2 and 3 to get 6.

$$\frac{1}{5}+\frac{6}{16}+\frac{7}{10}$$

Reduce the fraction \frac{6}{16} to lowest terms by extracting and canceling out 2.

$$\frac{1}{5}+\frac{3}{8}+\frac{7}{10}$$

Least common multiple of 5 and 8 is 40. Convert \frac{1}{5} and \frac{3}{8} to fractions with denominator 40.

$$\frac{8}{40}+\frac{15}{40}+\frac{7}{10}$$

Since \frac{8}{40} and \frac{15}{40} have the same denominator, add them by adding their numerators.

$$\frac{8+15}{40}+\frac{7}{10}$$

Add 8 and 15 to get 23.

$$\frac{23}{40}+\frac{7}{10}$$

Least common multiple of 40 and 10 is 40. Convert \frac{23}{40} and \frac{7}{10} to fractions with denominator 40.

$$\frac{23}{40}+\frac{28}{40}$$

Since \frac{23}{40} and \frac{28}{40} have the same denominator, add them by adding their numerators.

$$\frac{23+28}{40}$$

Add 23 and 28 to get 51.

$$\frac{51}{40}$$

Factor

$$\frac{3 \cdot 17}{2 ^ {3} \cdot 5} = 1\frac{11}{40} = 1.275$$