Final answer:
To add fractions 1/4, 2/9, and 2/3, we first find the least common denominator which is 36, convert each fraction to an equivalent fraction with this denominator, then add the numerators to get the final result of 41/36.
Step-by-step explanation:
Understanding Addition of Fractions
When adding fractions such as 1/4, 2/9, and 2/3, we need to find a common denominator to combine them. Our intuition can guide us to understand that the common denominator must be a multiple of the original denominators, 4, 9, and 3. To add the fractions, we convert each to an equivalent fraction with the common denominator, then add their numerators.
The least common denominator (LCD) for 4, 9, and 3 is 36. We convert each fraction:
- 1/4 becomes 9/36 because 4×9=36, so we multiply the numerator by 9 as well.
- 2/9 becomes 8/36 because 9×4=36, so we multiply the numerator by 4.
- 2/3 becomes 24/36 because 3×12=36, so we multiply the numerator by 12.
Now, we can add the numerators: 9+8+24=41.
Our resulting fraction is 41/36, which is already in its simplest form because there are no common factors between 41 and 36 other than 1.
By using our intuition and understanding of common denominators, we can simplify the process of adding fractions and assure the correctness of our results.