Solve 20*1/12+2*4/n+(-1)*2/n+(-5)*5/12

$$20 \cdot \frac { 1 } { 12 } + 2 \cdot \frac { 4 } { n } + ( - 1 ) \cdot \frac { 2 } { n } + ( - 5 ) \cdot \frac { 5 } { 12 }$$

Evaluate

$$-\frac{5}{12}+\frac{6}{n}$$

Short Solution Steps

Multiply 20 and \frac{1}{12} to get \frac{20}{12}.

$$\frac{20}{12}+2\times \frac{4}{n}-\frac{2}{n}-5\times \frac{5}{12}$$

Reduce the fraction \frac{20}{12} to lowest terms by extracting and canceling out 4.

$$\frac{5}{3}+2\times \frac{4}{n}-\frac{2}{n}-5\times \frac{5}{12}$$

Express 2\times \frac{4}{n} as a single fraction.

$$\frac{5}{3}+\frac{2\times 4}{n}-\frac{2}{n}-5\times \frac{5}{12}$$

Express -5\times \frac{5}{12} as a single fraction.

$$\frac{5}{3}+\frac{2\times 4}{n}-\frac{2}{n}+\frac{-5\times 5}{12}$$

Multiply -5 and 5 to get -25.

$$\frac{5}{3}+\frac{2\times 4}{n}-\frac{2}{n}+\frac{-25}{12}$$

Fraction \frac{-25}{12} can be rewritten as -\frac{25}{12} by extracting the negative sign.

$$\frac{5}{3}+\frac{2\times 4}{n}-\frac{2}{n}-\frac{25}{12}$$

Least common multiple of 3 and 12 is 12. Convert \frac{5}{3} and \frac{25}{12} to fractions with denominator 12.

$$\frac{20}{12}+\frac{2\times 4}{n}-\frac{2}{n}-\frac{25}{12}$$

Since \frac{20}{12} and \frac{25}{12} have the same denominator, subtract them by subtracting their numerators.

$$\frac{20-25}{12}+\frac{2\times 4}{n}-\frac{2}{n}$$

Subtract 25 from 20 to get -5.

$$-\frac{5}{12}+\frac{2\times 4}{n}-\frac{2}{n}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 12 and n is 12n. Multiply -\frac{5}{12} times \frac{n}{n}. Multiply \frac{2\times 4}{n} times \frac{12}{12}.

$$-\frac{5n}{12n}+\frac{12\times 2\times 4}{12n}-\frac{2}{n}$$

Since -\frac{5n}{12n} and \frac{12\times 2\times 4}{12n} have the same denominator, add them by adding their numerators.

$$\frac{-5n+12\times 2\times 4}{12n}-\frac{2}{n}$$

Do the multiplications in -5n+12\times 2\times 4.

$$\frac{-5n+96}{12n}-\frac{2}{n}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 12n and n is 12n. Multiply \frac{2}{n} times \frac{12}{12}.

$$\frac{-5n+96}{12n}-\frac{2\times 12}{12n}$$

Since \frac{-5n+96}{12n} and \frac{2\times 12}{12n} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-5n+96-2\times 12}{12n}$$

Do the multiplications in -5n+96-2\times 12.

$$\frac{-5n+96-24}{12n}$$

Combine like terms in -5n+96-24.

$$\frac{-5n+72}{12n}$$

Factor

$$-\frac{\frac{1}{12}\left(5n-72\right)}{n}$$