Solve Mixed Number Addition: 3 2/9 + 5 3/4 Step-by-Step

To solve this problem, we'll follow these steps:

• Step 1: Convert each mixed number to an improper fraction.
• Step 2: Find a common denominator for the fractions.
• Step 3: Add the fractions.
• Step 4: Convert the result back into a mixed number.

Now, let's proceed with each step:

Step 1: Convert to improper fractions.
For $3\frac{2}{9}$, you have:

$3\frac{2}{9} = \frac{3 \times 9 + 2}{9} = \frac{27 + 2}{9} = \frac{29}{9}$

For $5\frac{3}{4}$, you have:

$5\frac{3}{4} = \frac{5 \times 4 + 3}{4} = \frac{20 + 3}{4} = \frac{23}{4}$

Step 2: Find a common denominator.
The denominators are 9 and 4. The least common multiple (LCM) of 9 and 4 is 36.

Convert the fractions to have this common denominator:

$\frac{29}{9} \rightarrow \frac{29 \times 4}{36} = \frac{116}{36}$

$\frac{23}{4} \rightarrow \frac{23 \times 9}{36} = \frac{207}{36}$

Step 3: Add the fractions.

$\frac{116}{36} + \frac{207}{36} = \frac{323}{36}$

Step 4: Convert into a mixed number.

Divide 323 by 36:

323 divided by 36 is 8 with a remainder of 35, so:

$\frac{323}{36} = 8\frac{35}{36}$

Therefore, the solution to the problem is $8\frac{35}{36}$.