Questions: Find the sum. Write your answer in mixed number form, and reduce if possible. 21 13/24 + 22 9/16

Solution Steps

To find the sum of two mixed numbers, we need to follow these steps:

1. Convert each mixed number to an improper fraction.
2. Find a common denominator for the fractions.
3. Add the fractions.
4. Convert the resulting improper fraction back to a mixed number.
5. Simplify the mixed number if possible.

First, we convert the mixed numbers \(21 \frac{13}{24}\) and \(22 \frac{9}{16}\) to improper fractions.

\[ 21 \frac{13}{24} = \frac{21 \times 24 + 13}{24} = \frac{504 + 13}{24} = \frac{517}{24} \]

\[ 22 \frac{9}{16} = \frac{22 \times 16 + 9}{16} = \frac{352 + 9}{16} = \frac{361}{16} \]

Next, we find a common denominator for the fractions \(\frac{517}{24}\) and \(\frac{361}{16}\). The least common multiple (LCM) of 24 and 16 is 48.

\[ \frac{517}{24} = \frac{517 \times 2}{24 \times 2} = \frac{1034}{48} \]

\[ \frac{361}{16} = \frac{361 \times 3}{16 \times 3} = \frac{1083}{48} \]

Now, we add the fractions:

\[ \frac{1034}{48} + \frac{1083}{48} = \frac{1034 + 1083}{48} = \frac{2117}{48} \]

We convert the improper fraction \(\frac{2117}{48}\) back to a mixed number.

\[ 2117 \div 48 = 44 \text{ remainder } 5 \]

So,

\[ \frac{2117}{48} = 44 \frac{5}{48} \]

The fraction \(\frac{5}{48}\) is already in its simplest form since the greatest common divisor (GCD) of 5 and 48 is 1.

Final Answer