Solve 1/2+11/14-(2/3+12/25)

$$\frac { 1 } { 2 } + \frac { 11 } { 14 } - ( \frac { 2 } { 3 } + \frac { 12 } { 25 } )$$

Evaluate

$$\frac{73}{525}\approx 0.139047619$$

Solution Steps

Least common multiple of 2 and 14 is 14. Convert \frac{1}{2} and \frac{11}{14} to fractions with denominator 14.

$$\frac{7}{14}+\frac{11}{14}-\left(\frac{2}{3}+\frac{12}{25}\right)$$

Since \frac{7}{14} and \frac{11}{14} have the same denominator, add them by adding their numerators.

$$\frac{7+11}{14}-\left(\frac{2}{3}+\frac{12}{25}\right)$$

Add 7 and 11 to get 18.

$$\frac{18}{14}-\left(\frac{2}{3}+\frac{12}{25}\right)$$

Reduce the fraction \frac{18}{14} to lowest terms by extracting and canceling out 2.

$$\frac{9}{7}-\left(\frac{2}{3}+\frac{12}{25}\right)$$

Least common multiple of 3 and 25 is 75. Convert \frac{2}{3} and \frac{12}{25} to fractions with denominator 75.

$$\frac{9}{7}-\left(\frac{50}{75}+\frac{36}{75}\right)$$

Since \frac{50}{75} and \frac{36}{75} have the same denominator, add them by adding their numerators.

$$\frac{9}{7}-\frac{50+36}{75}$$

Add 50 and 36 to get 86.

$$\frac{9}{7}-\frac{86}{75}$$

Least common multiple of 7 and 75 is 525. Convert \frac{9}{7} and \frac{86}{75} to fractions with denominator 525.

$$\frac{675}{525}-\frac{602}{525}$$

Since \frac{675}{525} and \frac{602}{525} have the same denominator, subtract them by subtracting their numerators.

$$\frac{675-602}{525}$$

Subtract 602 from 675 to get 73.

$$\frac{73}{525}$$

Factor

$$\frac{73}{3 \cdot 5 ^ {2} \cdot 7} = 0.13904761904761906$$