Solve 5/6+(13/4div22/5)

$$\frac { 5 } { 6 } + ( 1 \frac { 3 } { 4 } \div 2 \frac { 2 } { 5 } )$$

Evaluate

$$\frac{25}{16}=1.5625$$

Solution Steps

Divide \frac{1\times 4+3}{4} by \frac{2\times 5+2}{5} by multiplying \frac{1\times 4+3}{4} by the reciprocal of \frac{2\times 5+2}{5}.

$$\frac{5}{6}+\frac{\left(1\times 4+3\right)\times 5}{4\left(2\times 5+2\right)}$$

Multiply 1 and 4 to get 4.

$$\frac{5}{6}+\frac{\left(4+3\right)\times 5}{4\left(2\times 5+2\right)}$$

Add 4 and 3 to get 7.

$$\frac{5}{6}+\frac{7\times 5}{4\left(2\times 5+2\right)}$$

Multiply 7 and 5 to get 35.

$$\frac{5}{6}+\frac{35}{4\left(2\times 5+2\right)}$$

Multiply 2 and 5 to get 10.

$$\frac{5}{6}+\frac{35}{4\left(10+2\right)}$$

Add 10 and 2 to get 12.

$$\frac{5}{6}+\frac{35}{4\times 12}$$

Multiply 4 and 12 to get 48.

$$\frac{5}{6}+\frac{35}{48}$$

Least common multiple of 6 and 48 is 48. Convert \frac{5}{6} and \frac{35}{48} to fractions with denominator 48.

$$\frac{40}{48}+\frac{35}{48}$$

Since \frac{40}{48} and \frac{35}{48} have the same denominator, add them by adding their numerators.

$$\frac{40+35}{48}$$

Add 40 and 35 to get 75.

$$\frac{75}{48}$$

Reduce the fraction \frac{75}{48} to lowest terms by extracting and canceling out 3.

$$\frac{25}{16}$$

Factor

$$\frac{5 ^ {2}}{2 ^ {4}} = 1\frac{9}{16} = 1.5625$$