Solve 4*(1-1/2+1/6-1/2+1/2-frac{1}{4}+frac{1}{5})

$$4 \times ( 1 - \frac { 1 } { 2 } + \frac { 1 } { 6 } - \frac { 1 } { 2 } + \frac { 1 } { 2 } - \frac { 1 } { 4 } + \frac { 1 } { 5 } )$$

Evaluate

$$\frac{37}{15}\approx 2.466666667$$

Solution Steps

Convert 1 to fraction \frac{2}{2}.

$$4\left(\frac{2}{2}-\frac{1}{2}+\frac{1}{6}-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{5}\right)$$

Since \frac{2}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

$$4\left(\frac{2-1}{2}+\frac{1}{6}-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{5}\right)$$

Subtract 1 from 2 to get 1.

$$4\left(\frac{1}{2}+\frac{1}{6}-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{5}\right)$$

Least common multiple of 2 and 6 is 6. Convert \frac{1}{2} and \frac{1}{6} to fractions with denominator 6.

$$4\left(\frac{3}{6}+\frac{1}{6}-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{5}\right)$$

Since \frac{3}{6} and \frac{1}{6} have the same denominator, add them by adding their numerators.

$$4\left(\frac{3+1}{6}-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{5}\right)$$

Add 3 and 1 to get 4.

$$4\left(\frac{4}{6}-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{5}\right)$$

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

$$4\left(\frac{2}{3}-\frac{1}{2}+\frac{1}{2}-\frac{1}{4}+\frac{1}{5}\right)$$

Least common multiple of 3 and 2 is 6. Convert \frac{2}{3} and \frac{1}{2} to fractions with denominator 6.

$$4\left(\frac{4}{6}-\frac{3}{6}+\frac{1}{2}-\frac{1}{4}+\frac{1}{5}\right)$$

Since \frac{4}{6} and \frac{3}{6} have the same denominator, subtract them by subtracting their numerators.

$$4\left(\frac{4-3}{6}+\frac{1}{2}-\frac{1}{4}+\frac{1}{5}\right)$$

Subtract 3 from 4 to get 1.

$$4\left(\frac{1}{6}+\frac{1}{2}-\frac{1}{4}+\frac{1}{5}\right)$$

Least common multiple of 6 and 2 is 6. Convert \frac{1}{6} and \frac{1}{2} to fractions with denominator 6.

$$4\left(\frac{1}{6}+\frac{3}{6}-\frac{1}{4}+\frac{1}{5}\right)$$

Since \frac{1}{6} and \frac{3}{6} have the same denominator, add them by adding their numerators.

$$4\left(\frac{1+3}{6}-\frac{1}{4}+\frac{1}{5}\right)$$

Add 1 and 3 to get 4.

$$4\left(\frac{4}{6}-\frac{1}{4}+\frac{1}{5}\right)$$

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

$$4\left(\frac{2}{3}-\frac{1}{4}+\frac{1}{5}\right)$$

Least common multiple of 3 and 4 is 12. Convert \frac{2}{3} and \frac{1}{4} to fractions with denominator 12.

$$4\left(\frac{8}{12}-\frac{3}{12}+\frac{1}{5}\right)$$

Since \frac{8}{12} and \frac{3}{12} have the same denominator, subtract them by subtracting their numerators.

$$4\left(\frac{8-3}{12}+\frac{1}{5}\right)$$

Subtract 3 from 8 to get 5.

$$4\left(\frac{5}{12}+\frac{1}{5}\right)$$

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

$$4\left(\frac{25}{60}+\frac{12}{60}\right)$$

Since \frac{25}{60} and \frac{12}{60} have the same denominator, add them by adding their numerators.

$$4\times \frac{25+12}{60}$$

Add 25 and 12 to get 37.

$$4\times \frac{37}{60}$$

Express 4\times \frac{37}{60} as a single fraction.

$$\frac{4\times 37}{60}$$

Multiply 4 and 37 to get 148.

$$\frac{148}{60}$$

Reduce the fraction \frac{148}{60} to lowest terms by extracting and canceling out 4.

$$\frac{37}{15}$$

Factor

$$\frac{37}{3 \cdot 5} = 2\frac{7}{15} = 2.466666666666667$$