Solve 4a+b/10-a-b/2-a+b/3+2a-b/4

$$\frac { 4 a + b } { 10 } - \frac { a - b } { 2 } - \frac { a + b } { 3 } + \frac { 2 a - b } { 4 }$$

Evaluate

$$\frac{4a+b}{60}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 10 and 2 is 10. Multiply \frac{a-b}{2} times \frac{5}{5}.

$$\frac{4a+b}{10}-\frac{5\left(a-b\right)}{10}-\frac{a+b}{3}+\frac{2a-b}{4}$$

Since \frac{4a+b}{10} and \frac{5\left(a-b\right)}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4a+b-5\left(a-b\right)}{10}-\frac{a+b}{3}+\frac{2a-b}{4}$$

Do the multiplications in 4a+b-5\left(a-b\right).

$$\frac{4a+b-5a+5b}{10}-\frac{a+b}{3}+\frac{2a-b}{4}$$

Combine like terms in 4a+b-5a+5b.

$$\frac{-a+6b}{10}-\frac{a+b}{3}+\frac{2a-b}{4}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 10 and 3 is 30. Multiply \frac{-a+6b}{10} times \frac{3}{3}. Multiply \frac{a+b}{3} times \frac{10}{10}.

$$\frac{3\left(-a+6b\right)}{30}-\frac{10\left(a+b\right)}{30}+\frac{2a-b}{4}$$

Since \frac{3\left(-a+6b\right)}{30} and \frac{10\left(a+b\right)}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\left(-a+6b\right)-10\left(a+b\right)}{30}+\frac{2a-b}{4}$$

Do the multiplications in 3\left(-a+6b\right)-10\left(a+b\right).

$$\frac{-3a+18b-10a-10b}{30}+\frac{2a-b}{4}$$

Combine like terms in -3a+18b-10a-10b.

$$\frac{-13a+8b}{30}+\frac{2a-b}{4}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 30 and 4 is 60. Multiply \frac{-13a+8b}{30} times \frac{2}{2}. Multiply \frac{2a-b}{4} times \frac{15}{15}.

$$\frac{2\left(-13a+8b\right)}{60}+\frac{15\left(2a-b\right)}{60}$$

Since \frac{2\left(-13a+8b\right)}{60} and \frac{15\left(2a-b\right)}{60} have the same denominator, add them by adding their numerators.

$$\frac{2\left(-13a+8b\right)+15\left(2a-b\right)}{60}$$

Do the multiplications in 2\left(-13a+8b\right)+15\left(2a-b\right).

$$\frac{-26a+16b+30a-15b}{60}$$

Combine like terms in -26a+16b+30a-15b.

$$\frac{4a+b}{60}$$

Expand

$$\frac{a}{15}+\frac{b}{60}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 10 and 2 is 10. Multiply \frac{a-b}{2} times \frac{5}{5}.

$$\frac{4a+b}{10}-\frac{5\left(a-b\right)}{10}-\frac{a+b}{3}+\frac{2a-b}{4}$$

Since \frac{4a+b}{10} and \frac{5\left(a-b\right)}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4a+b-5\left(a-b\right)}{10}-\frac{a+b}{3}+\frac{2a-b}{4}$$

Do the multiplications in 4a+b-5\left(a-b\right).

$$\frac{4a+b-5a+5b}{10}-\frac{a+b}{3}+\frac{2a-b}{4}$$

Combine like terms in 4a+b-5a+5b.

$$\frac{-a+6b}{10}-\frac{a+b}{3}+\frac{2a-b}{4}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 10 and 3 is 30. Multiply \frac{-a+6b}{10} times \frac{3}{3}. Multiply \frac{a+b}{3} times \frac{10}{10}.

$$\frac{3\left(-a+6b\right)}{30}-\frac{10\left(a+b\right)}{30}+\frac{2a-b}{4}$$

Since \frac{3\left(-a+6b\right)}{30} and \frac{10\left(a+b\right)}{30} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3\left(-a+6b\right)-10\left(a+b\right)}{30}+\frac{2a-b}{4}$$

Do the multiplications in 3\left(-a+6b\right)-10\left(a+b\right).

$$\frac{-3a+18b-10a-10b}{30}+\frac{2a-b}{4}$$

Combine like terms in -3a+18b-10a-10b.

$$\frac{-13a+8b}{30}+\frac{2a-b}{4}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 30 and 4 is 60. Multiply \frac{-13a+8b}{30} times \frac{2}{2}. Multiply \frac{2a-b}{4} times \frac{15}{15}.

$$\frac{2\left(-13a+8b\right)}{60}+\frac{15\left(2a-b\right)}{60}$$

Since \frac{2\left(-13a+8b\right)}{60} and \frac{15\left(2a-b\right)}{60} have the same denominator, add them by adding their numerators.

$$\frac{2\left(-13a+8b\right)+15\left(2a-b\right)}{60}$$

Do the multiplications in 2\left(-13a+8b\right)+15\left(2a-b\right).

$$\frac{-26a+16b+30a-15b}{60}$$

Combine like terms in -26a+16b+30a-15b.

$$\frac{4a+b}{60}$$