Solve a/16+19/24-1/2

$$\frac { a } { 16 } + \frac { 19 } { 24 } - \frac { 1 } { 2 }$$

Evaluate

$$\frac{a}{16}+\frac{7}{24}$$

Short Solution Steps

Least common multiple of 24 and 2 is 24. Convert \frac{19}{24} and \frac{1}{2} to fractions with denominator 24.

$$\frac{a}{16}+\frac{19}{24}-\frac{12}{24}$$

Since \frac{19}{24} and \frac{12}{24} have the same denominator, subtract them by subtracting their numerators.

$$\frac{a}{16}+\frac{19-12}{24}$$

Subtract 12 from 19 to get 7.

$$\frac{a}{16}+\frac{7}{24}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 16 and 24 is 48. Multiply \frac{a}{16} times \frac{3}{3}. Multiply \frac{7}{24} times \frac{2}{2}.

$$\frac{3a}{48}+\frac{7\times 2}{48}$$

Since \frac{3a}{48} and \frac{7\times 2}{48} have the same denominator, add them by adding their numerators.

$$\frac{3a+7\times 2}{48}$$

Do the multiplications in 3a+7\times 2.

$$\frac{3a+14}{48}$$

Factor

$$\frac{3a+14}{48}$$

Solution Steps

Factor out \frac{1}{48}.

$$\frac{3a+14}{48}$$

Consider 3a+38-24. Multiply and combine like terms.

$$3a+14$$

Rewrite the complete factored expression.

$$\frac{3a+14}{48}$$