To sum fractions, you need to follow specific steps that depend on whether the fractions have the same or different denominators.
Summing Fractions with the Same Denominator
When fractions have the same denominator, the process is straightforward.
- Keep the denominator: The denominator remains the same in the sum.
- Add the numerators: Add the numerators together.
For example, as shown in the reference:
- 1/5 + 2/5 = (1 + 2)/5 = 3/5
- Here, the denominator, 5, remains the same, and the numerators, 1 and 2, are added.
Summing Fractions with Different Denominators
Adding fractions with different denominators requires an extra step:
- Find the Least Common Denominator (LCD):
- The LCD is the smallest multiple that all denominators share.
- This is the number you will use as the denominator for all your fractions.
- Convert the fractions:
- Adjust each fraction so it has the LCD as its new denominator.
- Multiply both the numerator and the denominator by the same number, so that the denominator becomes the LCD.
- Add the numerators:
- Once the fractions all have the same denominator (LCD), you can add the numerators.
- Keep the common denominator.
For example, from the reference:
- 1/4 + 2/? (There is no denominator, which may have been left out for clarification, but let's assume we want to add 1/4 + 2/5)
- The denominators are 4 and 5.
- The LCD is 20. (4 x 5)
- Convert 1/4: 1/4 * (5/5) = 5/20
- Convert 2/5: 2/5 * (4/4) = 8/20
- Add the numerators: 5/20 + 8/20 = (5+8)/20 = 13/20
Table Summary of Fraction Addition
| Step | Same Denominator | Different Denominator |
|---|---|---|
| 1. Denominator Handling | Keep the same denominator | Find the Least Common Denominator (LCD) |
| 2. Convert Fractions | N/A | Convert each fraction to have the LCD |
| 3. Numerator Addition | Add numerators | Add numerators |
| 4. Sum Fraction | Combine to form a sum | Combine to form a sum |
By following these steps you can easily sum fractions.
