Solve 3/10-51/20+2-41/4+7/15

$$\frac { 3 } { 10 } - 5 \frac { 1 } { 20 } + 2 - 4 \frac { 1 } { 4 } + \frac { 7 } { 15 }$$

Evaluate

$$-\frac{98}{15}\approx -6.533333333$$

Solution Steps

Multiply 5 and 20 to get 100.

$$\frac{3}{10}-\frac{100+1}{20}+2-\frac{4\times 4+1}{4}+\frac{7}{15}$$

Add 100 and 1 to get 101.

$$\frac{3}{10}-\frac{101}{20}+2-\frac{4\times 4+1}{4}+\frac{7}{15}$$

Least common multiple of 10 and 20 is 20. Convert \frac{3}{10} and \frac{101}{20} to fractions with denominator 20.

$$\frac{6}{20}-\frac{101}{20}+2-\frac{4\times 4+1}{4}+\frac{7}{15}$$

Since \frac{6}{20} and \frac{101}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6-101}{20}+2-\frac{4\times 4+1}{4}+\frac{7}{15}$$

Subtract 101 from 6 to get -95.

$$\frac{-95}{20}+2-\frac{4\times 4+1}{4}+\frac{7}{15}$$

Reduce the fraction \frac{-95}{20} to lowest terms by extracting and canceling out 5.

$$-\frac{19}{4}+2-\frac{4\times 4+1}{4}+\frac{7}{15}$$

Convert 2 to fraction \frac{8}{4}.

$$-\frac{19}{4}+\frac{8}{4}-\frac{4\times 4+1}{4}+\frac{7}{15}$$

Since -\frac{19}{4} and \frac{8}{4} have the same denominator, add them by adding their numerators.

$$\frac{-19+8}{4}-\frac{4\times 4+1}{4}+\frac{7}{15}$$

Add -19 and 8 to get -11.

$$-\frac{11}{4}-\frac{4\times 4+1}{4}+\frac{7}{15}$$

Multiply 4 and 4 to get 16.

$$-\frac{11}{4}-\frac{16+1}{4}+\frac{7}{15}$$

Add 16 and 1 to get 17.

$$-\frac{11}{4}-\frac{17}{4}+\frac{7}{15}$$

Since -\frac{11}{4} and \frac{17}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-11-17}{4}+\frac{7}{15}$$

Subtract 17 from -11 to get -28.

$$\frac{-28}{4}+\frac{7}{15}$$

Divide -28 by 4 to get -7.

$$-7+\frac{7}{15}$$

Convert -7 to fraction -\frac{105}{15}.

$$-\frac{105}{15}+\frac{7}{15}$$

Since -\frac{105}{15} and \frac{7}{15} have the same denominator, add them by adding their numerators.

$$\frac{-105+7}{15}$$

Add -105 and 7 to get -98.

$$-\frac{98}{15}$$

Factor

$$-\frac{98}{15} = -6\frac{8}{15} = -6.533333333333333$$