Solve (7/15-1/10)-31/2+4*(11/20-frac{4}{15})

$$( \frac { 7 } { 15 } - \frac { 1 } { 10 } ) - 3 \frac { 1 } { 2 } + 4 \cdot ( \frac { 11 } { 20 } - \frac { 4 } { 15 } )$$

Evaluate

$$-2$$

Solution Steps

Least common multiple of 15 and 10 is 30. Convert \frac{7}{15} and \frac{1}{10} to fractions with denominator 30.

$$\frac{14}{30}-\frac{3}{30}-\frac{3\times 2+1}{2}+4\left(\frac{11}{20}-\frac{4}{15}\right)$$

Since \frac{14}{30} and \frac{3}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{14-3}{30}-\frac{3\times 2+1}{2}+4\left(\frac{11}{20}-\frac{4}{15}\right)$$

Subtract 3 from 14 to get 11.

$$\frac{11}{30}-\frac{3\times 2+1}{2}+4\left(\frac{11}{20}-\frac{4}{15}\right)$$

Multiply 3 and 2 to get 6.

$$\frac{11}{30}-\frac{6+1}{2}+4\left(\frac{11}{20}-\frac{4}{15}\right)$$

Add 6 and 1 to get 7.

$$\frac{11}{30}-\frac{7}{2}+4\left(\frac{11}{20}-\frac{4}{15}\right)$$

Least common multiple of 30 and 2 is 30. Convert \frac{11}{30} and \frac{7}{2} to fractions with denominator 30.

$$\frac{11}{30}-\frac{105}{30}+4\left(\frac{11}{20}-\frac{4}{15}\right)$$

Since \frac{11}{30} and \frac{105}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{11-105}{30}+4\left(\frac{11}{20}-\frac{4}{15}\right)$$

Subtract 105 from 11 to get -94.

$$\frac{-94}{30}+4\left(\frac{11}{20}-\frac{4}{15}\right)$$

Reduce the fraction \frac{-94}{30} to lowest terms by extracting and canceling out 2.

$$-\frac{47}{15}+4\left(\frac{11}{20}-\frac{4}{15}\right)$$

Least common multiple of 20 and 15 is 60. Convert \frac{11}{20} and \frac{4}{15} to fractions with denominator 60.

$$-\frac{47}{15}+4\left(\frac{33}{60}-\frac{16}{60}\right)$$

Since \frac{33}{60} and \frac{16}{60} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{47}{15}+4\times \frac{33-16}{60}$$

Subtract 16 from 33 to get 17.

$$-\frac{47}{15}+4\times \frac{17}{60}$$

Express 4\times \frac{17}{60} as a single fraction.

$$-\frac{47}{15}+\frac{4\times 17}{60}$$

Multiply 4 and 17 to get 68.

$$-\frac{47}{15}+\frac{68}{60}$$

Reduce the fraction \frac{68}{60} to lowest terms by extracting and canceling out 4.

$$-\frac{47}{15}+\frac{17}{15}$$

Since -\frac{47}{15} and \frac{17}{15} have the same denominator, add them by adding their numerators.

$$\frac{-47+17}{15}$$

Add -47 and 17 to get -30.

$$\frac{-30}{15}$$

Divide -30 by 15 to get -2.

$$-2$$

Factor

$$-2$$