Solve (5/8+2/5)div35/12*11/2*2

$$( \frac { 5 } { 8 } + \frac { 2 } { 5 } ) \div 3 \frac { 5 } { 12 } \times 1 \frac { 1 } { 2 } \times 2$$

Evaluate

$$\frac{9}{10}=0.9$$

Solution Steps

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

$$\frac{\frac{25}{40}+\frac{16}{40}}{\frac{3\times 12+5}{12}}\times \frac{1\times 2+1}{2}\times 2$$

Since \frac{25}{40} and \frac{16}{40} have the same denominator, add them by adding their numerators.

$$\frac{\frac{25+16}{40}}{\frac{3\times 12+5}{12}}\times \frac{1\times 2+1}{2}\times 2$$

Add 25 and 16 to get 41.

$$\frac{\frac{41}{40}}{\frac{3\times 12+5}{12}}\times \frac{1\times 2+1}{2}\times 2$$

Multiply 3 and 12 to get 36.

$$\frac{\frac{41}{40}}{\frac{36+5}{12}}\times \frac{1\times 2+1}{2}\times 2$$

Add 36 and 5 to get 41.

$$\frac{\frac{41}{40}}{\frac{41}{12}}\times \frac{1\times 2+1}{2}\times 2$$

Divide \frac{41}{40} by \frac{41}{12} by multiplying \frac{41}{40} by the reciprocal of \frac{41}{12}.

$$\frac{41}{40}\times \frac{12}{41}\times \frac{1\times 2+1}{2}\times 2$$

Multiply \frac{41}{40} times \frac{12}{41} by multiplying numerator times numerator and denominator times denominator.

$$\frac{41\times 12}{40\times 41}\times \frac{1\times 2+1}{2}\times 2$$

Cancel out 41 in both numerator and denominator.

$$\frac{12}{40}\times \frac{1\times 2+1}{2}\times 2$$

Reduce the fraction \frac{12}{40} to lowest terms by extracting and canceling out 4.

$$\frac{3}{10}\times \frac{1\times 2+1}{2}\times 2$$

Multiply 1 and 2 to get 2.

$$\frac{3}{10}\times \frac{2+1}{2}\times 2$$

Add 2 and 1 to get 3.

$$\frac{3}{10}\times \frac{3}{2}\times 2$$

Multiply \frac{3}{10} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 3}{10\times 2}\times 2$$

Do the multiplications in the fraction \frac{3\times 3}{10\times 2}.

$$\frac{9}{20}\times 2$$

Express \frac{9}{20}\times 2 as a single fraction.

$$\frac{9\times 2}{20}$$

Multiply 9 and 2 to get 18.

$$\frac{18}{20}$$

Reduce the fraction \frac{18}{20} to lowest terms by extracting and canceling out 2.

$$\frac{9}{10}$$

Factor

$$\frac{3 ^ {2}}{2 \cdot 5} = 0.9$$