Solve [1/4(N+1)-1/2]+[1/4(n+1)+1/2]

$$[ \frac { 1 } { 4 } ( N + 1 ) - \frac { 1 } { 2 } ] + [ \frac { 1 } { 4 } ( n + 1 ) + \frac { 1 } { 2 } ]$$

Evaluate

$$\frac{n+N+2}{4}$$

Solution Steps

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

$$\frac{1}{4}N+\frac{1}{4}-\frac{1}{2}+\frac{1}{4}\left(n+1\right)+\frac{1}{2}$$

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

$$\frac{1}{4}N+\frac{1}{4}-\frac{2}{4}+\frac{1}{4}\left(n+1\right)+\frac{1}{2}$$

Since \frac{1}{4} and \frac{2}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{4}N+\frac{1-2}{4}+\frac{1}{4}\left(n+1\right)+\frac{1}{2}$$

Subtract 2 from 1 to get -1.

$$\frac{1}{4}N-\frac{1}{4}+\frac{1}{4}\left(n+1\right)+\frac{1}{2}$$

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

$$\frac{1}{4}N-\frac{1}{4}+\frac{1}{4}n+\frac{1}{4}+\frac{1}{2}$$

Add -\frac{1}{4} and \frac{1}{4} to get 0.

$$\frac{1}{4}N+\frac{1}{4}n+\frac{1}{2}$$

Expand

$$\frac{N}{4}+\frac{n}{4}+\frac{1}{2}$$

Solution Steps

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

$$\frac{1}{4}N+\frac{1}{4}-\frac{1}{2}+\frac{1}{4}\left(n+1\right)+\frac{1}{2}$$

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

$$\frac{1}{4}N+\frac{1}{4}-\frac{2}{4}+\frac{1}{4}\left(n+1\right)+\frac{1}{2}$$

Since \frac{1}{4} and \frac{2}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{4}N+\frac{1-2}{4}+\frac{1}{4}\left(n+1\right)+\frac{1}{2}$$

Subtract 2 from 1 to get -1.

$$\frac{1}{4}N-\frac{1}{4}+\frac{1}{4}\left(n+1\right)+\frac{1}{2}$$

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

$$\frac{1}{4}N-\frac{1}{4}+\frac{1}{4}n+\frac{1}{4}+\frac{1}{2}$$

Add -\frac{1}{4} and \frac{1}{4} to get 0.

$$\frac{1}{4}N+\frac{1}{4}n+\frac{1}{2}$$