How to Sum Fractions with Different Denominators?

To sum fractions with different denominators, you first need to find a common denominator. Here's a step-by-step guide:

1. Find a Common Denominator: The most common approach is to find the Least Common Multiple (LCM) of the denominators. This will be your new common denominator. Alternatively, you can simply multiply all the denominators together, but this may result in a larger number that you'll need to simplify later.

2. Convert the Fractions: For each fraction, determine what number you need to multiply its denominator by to reach the common denominator. Then, multiply both the numerator and the denominator of that fraction by that number. This creates an equivalent fraction.

3. Add the Numerators: Once all fractions have the same denominator, you can add their numerators. Keep the common denominator the same.

4. Simplify the Result: If possible, simplify the resulting fraction. This means reducing it to its lowest terms by dividing both the numerator and the denominator by their greatest common factor (GCF). If the result is an improper fraction (numerator is greater than or equal to the denominator), you might need to convert it to a mixed number.

Example:

Let's add 1/3 + 1/4:

1. Find a Common Denominator: The LCM of 3 and 4 is 12. So, our common denominator is 12.

2. Convert the Fractions:

   • To convert 1/3 to have a denominator of 12, we multiply both the numerator and the denominator by 4: (1 4) / (3 4) = 4/12
   • To convert 1/4 to have a denominator of 12, we multiply both the numerator and the denominator by 3: (1 3) / (4 3) = 3/12

3. Add the Numerators: Now we have 4/12 + 3/12. Adding the numerators gives us 7/12.

4. Simplify the Result: The fraction 7/12 is already in its simplest form, as 7 and 12 have no common factors other than 1.

Therefore, 1/3 + 1/4 = 7/12.