Solve 112/17-9/45+3/6+21

$$\frac { 112 } { 17 } - \frac { 9 } { 45 } + \frac { 3 } { 6 } + 21$$

Evaluate

$$\frac{4741}{170}\approx 27.888235294$$

Solution Steps

Reduce the fraction \frac{9}{45} to lowest terms by extracting and canceling out 9.

$$\frac{112}{17}-\frac{1}{5}+\frac{3}{6}+21$$

Least common multiple of 17 and 5 is 85. Convert \frac{112}{17} and \frac{1}{5} to fractions with denominator 85.

$$\frac{560}{85}-\frac{17}{85}+\frac{3}{6}+21$$

Since \frac{560}{85} and \frac{17}{85} have the same denominator, subtract them by subtracting their numerators.

$$\frac{560-17}{85}+\frac{3}{6}+21$$

Subtract 17 from 560 to get 543.

$$\frac{543}{85}+\frac{3}{6}+21$$

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

$$\frac{543}{85}+\frac{1}{2}+21$$

Least common multiple of 85 and 2 is 170. Convert \frac{543}{85} and \frac{1}{2} to fractions with denominator 170.

$$\frac{1086}{170}+\frac{85}{170}+21$$

Since \frac{1086}{170} and \frac{85}{170} have the same denominator, add them by adding their numerators.

$$\frac{1086+85}{170}+21$$

Add 1086 and 85 to get 1171.

$$\frac{1171}{170}+21$$

Convert 21 to fraction \frac{3570}{170}.

$$\frac{1171}{170}+\frac{3570}{170}$$

Since \frac{1171}{170} and \frac{3570}{170} have the same denominator, add them by adding their numerators.

$$\frac{1171+3570}{170}$$

Add 1171 and 3570 to get 4741.

$$\frac{4741}{170}$$

Factor

$$\frac{11 \cdot 431}{2 \cdot 5 \cdot 17} = 27\frac{151}{170} = 27.888235294117646$$