The Denominator is Key
When adding fractions together, the first step is to see if the denominators are the same.
If you said problems a and c, then you are correct. In problem a, 5 is the denominator for both fractions. In problem c, both fractions have 9 as the denominator.
Add Fractions with Like Denominators
If the denominators are the same, then all you need to add together are the numerators. Just don’t forget to move your denominator over to the answer too! Let’s work a few problems including a and c from earlier. Notice that adding fractions together can result in another fraction, a mixed number, or even a whole number!
Add Fractions with Unlike Denominators
No need to fret when you encounter a problem where the denominators are not the same. It is up to you to make them the same. You do this by finding the lowest common denominator (LCD), also known as the least common multiple. For simplicity, we will refer to it by the abbreviation, LCD. The LCD is the lowest number that both denominators can divide into equally. For example, if 3 and 5 are the denominators, then 15 is the lowest number that both of those will divide into equally. Therefore, 15 will be the new denominator.
Can you think of some examples? Think of two numbers and then think about what their LCD would be.
Liesel has some examples:
- 5, 10 LCD is 10
- 12, 32 LCD is 96
- 3, 7 LCD is 21
After the LCD
Set up your problem vertically if it isn’t already. Vertically, you can set the LCD, ahem, new denominator next to the original. Next, divide the old denominator into the new one. Remember you should get an equal number. If you don’t, revisit finding your LCD. After you divide, take that number and multiply by the numerator in the original to get your new numerator. Now, you have the problem ready to be answered with both fractions sharing the same denominator. Add the numerators together for the final answer.
