Sum of Fractions:

To find the sum of fractions, we need to have the same denominator for both fractions. Once we have the same denominator, we can simply add the numerators together to get the sum. Let's solve the given problem step by step.

Step 1: Denominators
The given fractions have different denominators, which are 3 and 4. To find the common denominator, we need to find the least common multiple (LCM) of these two numbers, which is the smallest number that is divisible by both denominators.

Step 2: Finding the LCM
To find the LCM of 3 and 4, we can list the multiples of each number and find the smallest number that appears in both lists.

Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ...
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, ...

From the lists, we can see that the smallest number that appears in both lists is 12. Therefore, the LCM of 3 and 4 is 12.

Step 3: Equivalent Fractions
To make the fractions have the same denominator, we need to convert them into equivalent fractions with a denominator of 12.

For the fraction 1/3, we can multiply both the numerator and denominator by 4 to get an equivalent fraction with a denominator of 12:
1/3 * 4/4 = 4/12

For the fraction 3/4, we can multiply both the numerator and denominator by 3 to get an equivalent fraction with a denominator of 12:
3/4 * 3/3 = 9/12

Now, the fractions are 4/12 and 9/12.

Step 4: Adding the Fractions
Now that the fractions have the same denominator, we can add the numerators together to find the sum:
4/12 + 9/12 = 13/12

Therefore, the sum of 1/3 and 3/4 is 13/12.

Conclusion:
To find the sum of fractions, we need to have the same denominator. In this case, we found the least common multiple of 3 and 4, which is 12. We then converted the fractions into equivalent fractions with a denominator of 12. Finally, we added the numerators together to find the sum, which is 13/12.