Solve 3/4-21/3+7/2-1/5

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

Evaluate

$$\frac{103}{60}\approx 1.716666667$$

Solution Steps

Multiply 2 and 3 to get 6.

$$\frac{3}{4}-\frac{6+1}{3}+\frac{7}{2}-\frac{1}{5}$$

Add 6 and 1 to get 7.

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

Least common multiple of 4 and 3 is 12. Convert \frac{3}{4} and \frac{7}{3} to fractions with denominator 12.

$$\frac{9}{12}-\frac{28}{12}+\frac{7}{2}-\frac{1}{5}$$

Since \frac{9}{12} and \frac{28}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9-28}{12}+\frac{7}{2}-\frac{1}{5}$$

Subtract 28 from 9 to get -19.

$$-\frac{19}{12}+\frac{7}{2}-\frac{1}{5}$$

Least common multiple of 12 and 2 is 12. Convert -\frac{19}{12} and \frac{7}{2} to fractions with denominator 12.

$$-\frac{19}{12}+\frac{42}{12}-\frac{1}{5}$$

Since -\frac{19}{12} and \frac{42}{12} have the same denominator, add them by adding their numerators.

$$\frac{-19+42}{12}-\frac{1}{5}$$

Add -19 and 42 to get 23.

$$\frac{23}{12}-\frac{1}{5}$$

Least common multiple of 12 and 5 is 60. Convert \frac{23}{12} and \frac{1}{5} to fractions with denominator 60.

$$\frac{115}{60}-\frac{12}{60}$$

Since \frac{115}{60} and \frac{12}{60} have the same denominator, subtract them by subtracting their numerators.

$$\frac{115-12}{60}$$

Subtract 12 from 115 to get 103.

$$\frac{103}{60}$$

Factor

$$\frac{103}{2 ^ {2} \cdot 3 \cdot 5} = 1\frac{43}{60} = 1.7166666666666666$$