Solve 1/2(a-1)+1/3(a+4)

$$\frac { 1 } { 2 } ( a - 1 ) + \frac { 1 } { 3 } ( a + 4 )$$

Evaluate

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

Solution Steps

Use the distributive property to multiply \frac{1}{2} by a-1.

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

Multiply \frac{1}{2} and -1 to get -\frac{1}{2}.

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

Use the distributive property to multiply \frac{1}{3} by a+4.

$$\frac{1}{2}a-\frac{1}{2}+\frac{1}{3}a+\frac{1}{3}\times 4$$

Multiply \frac{1}{3} and 4 to get \frac{4}{3}.

$$\frac{1}{2}a-\frac{1}{2}+\frac{1}{3}a+\frac{4}{3}$$

Combine \frac{1}{2}a and \frac{1}{3}a to get \frac{5}{6}a.

$$\frac{5}{6}a-\frac{1}{2}+\frac{4}{3}$$

Least common multiple of 2 and 3 is 6. Convert -\frac{1}{2} and \frac{4}{3} to fractions with denominator 6.

$$\frac{5}{6}a-\frac{3}{6}+\frac{8}{6}$$

Since -\frac{3}{6} and \frac{8}{6} have the same denominator, add them by adding their numerators.

$$\frac{5}{6}a+\frac{-3+8}{6}$$

Add -3 and 8 to get 5.

$$\frac{5}{6}a+\frac{5}{6}$$

Expand

$$\frac{5a+5}{6}$$

Solution Steps

Use the distributive property to multiply \frac{1}{2} by a-1.

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

Multiply \frac{1}{2} and -1 to get -\frac{1}{2}.

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

Use the distributive property to multiply \frac{1}{3} by a+4.

$$\frac{1}{2}a-\frac{1}{2}+\frac{1}{3}a+\frac{1}{3}\times 4$$

Multiply \frac{1}{3} and 4 to get \frac{4}{3}.

$$\frac{1}{2}a-\frac{1}{2}+\frac{1}{3}a+\frac{4}{3}$$

Combine \frac{1}{2}a and \frac{1}{3}a to get \frac{5}{6}a.

$$\frac{5}{6}a-\frac{1}{2}+\frac{4}{3}$$

Least common multiple of 2 and 3 is 6. Convert -\frac{1}{2} and \frac{4}{3} to fractions with denominator 6.

$$\frac{5}{6}a-\frac{3}{6}+\frac{8}{6}$$

Since -\frac{3}{6} and \frac{8}{6} have the same denominator, add them by adding their numerators.

$$\frac{5}{6}a+\frac{-3+8}{6}$$

Add -3 and 8 to get 5.

$$\frac{5}{6}a+\frac{5}{6}$$