Solve Fraction Addition: 5/12 + 11/36 Step by Step

To solve this problem, we'll follow these steps:

• Step 1: Identify the least common denominator (LCD) of the fractions.
• Step 2: Rewrite the fractions with the common denominator.
• Step 3: Add the fractions.
• Step 4: Simplify the resulting fraction.

Let's work through these steps:

Step 1: The denominators of our fractions are 12 and 36. The least common denominator is 36. This is because 36 is the smallest number that both 12 and 36 divide into evenly.

Step 2: Rewrite $\frac{5}{12}$ with the denominator 36. To do this, find what number 12 must be multiplied by to become 36, which is 3. Thus, multiply both the numerator and the denominator of $\frac{5}{12}$ by 3:

$\frac{5}{12} = \frac{5 \times 3}{12 \times 3} = \frac{15}{36}$.

Step 3: Now add the fractions $\frac{15}{36}$ and $\frac{11}{36}$, since they have a common denominator:

$\frac{15}{36} + \frac{11}{36} = \frac{15 + 11}{36} = \frac{26}{36}$.

Step 4: Simplify $\frac{26}{36}$. The greatest common divisor (GCD) of 26 and 36 is 2. Divide both the numerator and the denominator by 2:

$\frac{26}{36} = \frac{26 \div 2}{36 \div 2} = \frac{13}{18}$.

Therefore, the sum of $\frac{5}{12} + \frac{11}{36}$ is $\frac{13}{18}$.

The correct choice that matches this solution is choice 4.