Mike J answered
What you want to do here is find the least common denominator (LCD) for the two fractions. This is similar to least common multiple. To do this, list multiples of both denominators. The lowest number that both numbers have as a common multiple will be your least common denominator.
- 3: 3, 6, 9, 12.
- 4: 4, 8, 12.
The common denominator is 12, so you will change the denominator for both fractions to 12.
How do you do this? - We'll start with 2/3. You want to change the denominator from 3 to 12. In order to do so, you need to multiply the denominator by 4. What you do to the denominator, you must also do to the numerator. So, multiply 2 and 3 by 4.
Your 2/3 will now change to 8/12. Keep this in your back pocket for later, as you'll need it to solve the problem.
Now you want to change 2/4 to a fraction with a denominator of 12. To change the denominator to 12, multiply 4 by 3. Do the same to the numerator by solving 2 times 3. Your new fraction is 6/12.
Now, to find the sum of both fractions with common denominators, just add the numerators together.
8/12 + 6/12 = 14/12, which simplifies to 7/6.
If you need to list it as a mixed number, your answer would be 1 and 1/6.
So you have two different answers you can use, 7/6 or 1 and 1/6.
