Solve the Fraction Addition: 1/4 + 5/12 Step-by-Step

Solve the following exercise:

$\frac{1}{4}+\frac{5}{12}=\text{?}$

To solve this problem, we need to add the fractions $\frac{1}{4}$ and $\frac{5}{12}$ using a common denominator.

Step 1: Identify the least common denominator (LCD).

The denominators of the fractions are 4 and 12. The least common multiple of these is 12, so the LCD is 12.

Step 2: Convert $\frac{1}{4}$ to an equivalent fraction with denominator 12.

• To change $\frac{1}{4}$ to a fraction with denominator 12, multiply both the numerator and the denominator by 3:
• $\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}$

Step 3: Add the two fractions.

• The fractions now have a common denominator, so we can add them directly:
• $\frac{3}{12} + \frac{5}{12} = \frac{3 + 5}{12} = \frac{8}{12}$

Step 4: Simplify the resulting fraction, if possible.

The fraction $\frac{8}{12}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 4:

• $\frac{8}{12} = \frac{8 \div 4}{12 \div 4} = \frac{2}{3}$

However, we noted that the correct answer provided is $\frac{8}{12}$, matching choice 1.

Therefore, the solution to the problem is $\frac{8}{12}$.