Solve 1+3/4-2/5+7/3-12/8=

$$1 + \frac { 3 } { 4 } - \frac { 2 } { 5 } + \frac { 7 } { 3 } - \frac { 12 } { 8 } =$$

Evaluate

$$\frac{131}{60}\approx 2.183333333$$

Solution Steps

Convert 1 to fraction \frac{4}{4}.

$$\frac{4}{4}+\frac{3}{4}-\frac{2}{5}+\frac{7}{3}-\frac{12}{8}$$

Since \frac{4}{4} and \frac{3}{4} have the same denominator, add them by adding their numerators.

$$\frac{4+3}{4}-\frac{2}{5}+\frac{7}{3}-\frac{12}{8}$$

Add 4 and 3 to get 7.

$$\frac{7}{4}-\frac{2}{5}+\frac{7}{3}-\frac{12}{8}$$

Least common multiple of 4 and 5 is 20. Convert \frac{7}{4} and \frac{2}{5} to fractions with denominator 20.

$$\frac{35}{20}-\frac{8}{20}+\frac{7}{3}-\frac{12}{8}$$

Since \frac{35}{20} and \frac{8}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{35-8}{20}+\frac{7}{3}-\frac{12}{8}$$

Subtract 8 from 35 to get 27.

$$\frac{27}{20}+\frac{7}{3}-\frac{12}{8}$$

Least common multiple of 20 and 3 is 60. Convert \frac{27}{20} and \frac{7}{3} to fractions with denominator 60.

$$\frac{81}{60}+\frac{140}{60}-\frac{12}{8}$$

Since \frac{81}{60} and \frac{140}{60} have the same denominator, add them by adding their numerators.

$$\frac{81+140}{60}-\frac{12}{8}$$

Add 81 and 140 to get 221.

$$\frac{221}{60}-\frac{12}{8}$$

Reduce the fraction \frac{12}{8} to lowest terms by extracting and canceling out 4.

$$\frac{221}{60}-\frac{3}{2}$$

Least common multiple of 60 and 2 is 60. Convert \frac{221}{60} and \frac{3}{2} to fractions with denominator 60.

$$\frac{221}{60}-\frac{90}{60}$$

Since \frac{221}{60} and \frac{90}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{221-90}{60}$$

Subtract 90 from 221 to get 131.

$$\frac{131}{60}$$

Factor

$$\frac{131}{2 ^ {2} \cdot 3 \cdot 5} = 2\frac{11}{60} = 2.183333333333333$$