Final answer:
To rewrite 2/9 + 5/12 with a common denominator, find the least common denominator, which is 36. Convert each fraction to have the LCD as its denominator, and then add them resulting in the sum of 23/36.
Step-by-step explanation:
To rewrite 2/9 + 5/12 with a common denominator, you need to find a number that both 9 and 12 can divide into without leaving a remainder. This number is called the least common denominator (LCD). The LCD for 9 and 12 is 36, since it's the smallest number that both denominators can divide into evenly.
Now, to convert each fraction to have a denominator of 36, you multiply both the numerator and denominator by whatever number is needed to make the denominator 36.
- For 2/9, multiply the numerator and denominator by 4, this gives us 8/36.
- For 5/12, multiply the numerator and denominator by 3, which gives us 15/36.
Once both fractions have the common denominator, you can add them together:
2/9 + 5/12 = 8/36 + 15/36 = (8 + 15)/36 = 23/36