2 1/4 + 5 7/8 = a. 7 1/8 b. 7 8/12 c. 8 1/8 d. 8 8/12

1 answer

To add the mixed numbers \(2 \frac{1}{4}\) and \(5 \frac{7}{8}\), we can follow these steps:

  1. Convert both mixed numbers to improper fractions:

    • For \(2 \frac{1}{4}\): \[ 2 \times 4 + 1 = 8 + 1 = 9 \quad \Rightarrow \quad \frac{9}{4} \]
    • For \(5 \frac{7}{8}\): \[ 5 \times 8 + 7 = 40 + 7 = 47 \quad \Rightarrow \quad \frac{47}{8} \]
  2. Find a common denominator to add these fractions. The least common multiple (LCM) of 4 and 8 is 8.

  3. Convert \(\frac{9}{4}\) to have a denominator of 8: \[ \frac{9}{4} = \frac{9 \times 2}{4 \times 2} = \frac{18}{8} \]

  4. Now we can add the two fractions: \[ \frac{18}{8} + \frac{47}{8} = \frac{18 + 47}{8} = \frac{65}{8} \]

  5. Convert \(\frac{65}{8}\) back to a mixed number:

    • Divide 65 by 8, which goes 8 times (since \(8 \times 8 = 64\)) with a remainder of 1. \[ \frac{65}{8} = 8 \frac{1}{8} \]

Thus, \(2 \frac{1}{4} + 5 \frac{7}{8} = 8 \frac{1}{8}\).

The answer is \(c. 8 \frac{1}{8}\).