Solve 23/14-35/6-2/5+21/2

$$2 \frac { 3 } { 14 } - 3 \frac { 5 } { 6 } - \frac { 2 } { 5 } + 2 \frac { 1 } { 2 }$$

Evaluate

$$\frac{101}{210}\approx 0.480952381$$

Solution Steps

Multiply 2 and 14 to get 28.

$$\frac{28+3}{14}-\frac{3\times 6+5}{6}-\frac{2}{5}+\frac{2\times 2+1}{2}$$

Add 28 and 3 to get 31.

$$\frac{31}{14}-\frac{3\times 6+5}{6}-\frac{2}{5}+\frac{2\times 2+1}{2}$$

Multiply 3 and 6 to get 18.

$$\frac{31}{14}-\frac{18+5}{6}-\frac{2}{5}+\frac{2\times 2+1}{2}$$

Add 18 and 5 to get 23.

$$\frac{31}{14}-\frac{23}{6}-\frac{2}{5}+\frac{2\times 2+1}{2}$$

Least common multiple of 14 and 6 is 42. Convert \frac{31}{14} and \frac{23}{6} to fractions with denominator 42.

$$\frac{93}{42}-\frac{161}{42}-\frac{2}{5}+\frac{2\times 2+1}{2}$$

Since \frac{93}{42} and \frac{161}{42} have the same denominator, subtract them by subtracting their numerators.

$$\frac{93-161}{42}-\frac{2}{5}+\frac{2\times 2+1}{2}$$

Subtract 161 from 93 to get -68.

$$\frac{-68}{42}-\frac{2}{5}+\frac{2\times 2+1}{2}$$

Reduce the fraction \frac{-68}{42} to lowest terms by extracting and canceling out 2.

$$-\frac{34}{21}-\frac{2}{5}+\frac{2\times 2+1}{2}$$

Least common multiple of 21 and 5 is 105. Convert -\frac{34}{21} and \frac{2}{5} to fractions with denominator 105.

$$-\frac{170}{105}-\frac{42}{105}+\frac{2\times 2+1}{2}$$

Since -\frac{170}{105} and \frac{42}{105} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-170-42}{105}+\frac{2\times 2+1}{2}$$

Subtract 42 from -170 to get -212.

$$-\frac{212}{105}+\frac{2\times 2+1}{2}$$

Multiply 2 and 2 to get 4.

$$-\frac{212}{105}+\frac{4+1}{2}$$

Add 4 and 1 to get 5.

$$-\frac{212}{105}+\frac{5}{2}$$

Least common multiple of 105 and 2 is 210. Convert -\frac{212}{105} and \frac{5}{2} to fractions with denominator 210.

$$-\frac{424}{210}+\frac{525}{210}$$

Since -\frac{424}{210} and \frac{525}{210} have the same denominator, add them by adding their numerators.

$$\frac{-424+525}{210}$$

Add -424 and 525 to get 101.

$$\frac{101}{210}$$

Factor

$$\frac{101}{2 \cdot 3 \cdot 5 \cdot 7} = 0.48095238095238096$$