Add.

Question

Add.
7/9 + 5/12
Write your answer as a fraction in simplest form.

GPT-4o mini · Answer

To add the fractions $ \frac{7}{9} $ and $ \frac{5}{12} $, we first need to find a common denominator. The denominators are 9 and 12. The least common multiple (LCM) of 9 and 12 can be found by determining the multiples: - The multiples of 9 are: 9, 18, 27, 36, ... - The multiples of 12 are: 12, 24, 36, ... The smallest common multiple is 36. Therefore, the common denominator is 36. Now we convert both fractions to have the common denominator of 36: 1. For $ \frac{7}{9} $: $$ \frac{7}{9} = \frac{7 \times 4}{9 \times 4} = \frac{28}{36} $$ 2. For $ \frac{5}{12} $: $$ \frac{5}{12} = \frac{5 \times 3}{12 \times 3} = \frac{15}{36} $$ Now we can add the two fractions: $$ \frac{28}{36} + \frac{15}{36} = \frac{28 + 15}{36} = \frac{43}{36} $$ Finally, we check if $ \frac{43}{36} $ can be simplified. Since 43 is a prime number and does not divide 36, $ \frac{43}{36} $ is already in its simplest form. Thus, the final answer is: $$ \frac{43}{36} $$

Sunshine · Answer

wrong

GPT-4o mini · Answer

I apologize for any confusion. Let's go through the calculation step by step again to ensure accuracy.

To add $ \frac{7}{9} $ and $ \frac{5}{12} $, we need to find a common denominator.

Identify the denominators: The denominators are 9 and 12.
Find the least common multiple (LCM):
- The LCM of 9 and 12 is 36.
Convert each fraction to have the common denominator of 36:
- For $ \frac{7}{9} $: \[ \frac{7}{9} = \frac{7 \times 4}{9 \times 4} = \frac{28}{36} \]
- For $ \frac{5}{12} $: \[ \frac{5}{12} = \frac{5 \times 3}{12 \times 3} = \frac{15}{36} \]
Add the two fractions: \[ \frac{28}{36} + \frac{15}{36} = \frac{28 + 15}{36} = \frac{43}{36} \]
Check for simplification:
- The numerator is 43, which is a prime number, and the denominator is 36, so there are no common factors other than 1.

Therefore, the sum $ \frac{7}{9} + \frac{5}{12} $ is indeed

\[ \frac{43}{36} \]

This is in its simplest form as $ 43 $ and $ 36 $ have no common factors. If there's another aspect you'd like me to address or if you're looking for a different method, please let me know!