Question
Add. \[ \frac{3}{4}+\frac{7}{9} \] Write your answer as a fraction in simplest form.
Ask by Elliott Craig. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The sum of \( \frac{3}{4} \) and \( \frac{7}{9} \) is \( \frac{55}{36} \).
Solution
To add the fractions, we first find a common denominator. The denominators are 4 and 9, and the least common denominator (LCD) is 36.
Convert each fraction:
• 3/4 = (3 × 9) / (4 × 9) = 27/36
• 7/9 = (7 × 4) / (9 × 4) = 28/36
Now add the fractions:
27/36 + 28/36 = (27 + 28) / 36 = 55/36
Since 55 and 36 have no common factors other than 1, 55/36 is already in its simplest form.
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Simplify this solution Mind Expander
To add the fractions \(\frac{3}{4}\) and \(\frac{7}{9}\), we first need to find a common denominator. The least common multiple (LCM) of 4 and 9 is 36. Next, we convert each fraction: \[ \frac{3}{4} = \frac{3 \times 9}{4 \times 9} = \frac{27}{36} \] \[ \frac{7}{9} = \frac{7 \times 4}{9 \times 4} = \frac{28}{36} \] Now, add the two fractions: \[ \frac{27}{36} + \frac{28}{36} = \frac{27 + 28}{36} = \frac{55}{36} \] The fraction \(\frac{55}{36}\) is already in its simplest form (55 and 36 have no common factors other than 1). Therefore, the answer is \[ \frac{55}{36} \]
