mple \#1: $$ 5 \frac{1}{3}+3 \frac{1}{4}= $$

Question

UpStudy AI · Accepted Answer

Certainly! Let's solve the expression step by step:

$$
5 \frac{1}{3} + 3 \frac{1}{4}
$$

### Step 1: Convert Mixed Numbers to Improper Fractions

First, convert each mixed number to an improper fraction.

$$
5 \frac{1}{3} = \frac{5 \times 3 + 1}{3} = \frac{15 + 1}{3} = \frac{16}{3}
$$

$$
3 \frac{1}{4} = \frac{3 \times 4 + 1}{4} = \frac{12 + 1}{4} = \frac{13}{4}
$$

### Step 2: Find a Common Denominator

The denominators are 3 and 4. The least common denominator (LCD) is 12.

$$
\frac{16}{3} = \frac{16 \times 4}{3 \times 4} = \frac{64}{12}
$$

$$
\frac{13}{4} = \frac{13 \times 3}{4 \times 3} = \frac{39}{12}
$$

### Step 3: Add the Fractions

Now, add the two fractions with the common denominator.

$$
\frac{64}{12} + \frac{39}{12} = \frac{64 + 39}{12} = \frac{103}{12}
$$

### Step 4: Convert Back to a Mixed Number

Finally, convert the improper fraction back to a mixed number.

$$
\frac{103}{12} = 8 \frac{7}{12}
$$

### Final Answer

$$
5 \frac{1}{3} + 3 \frac{1}{4} = 8 \frac{7}{12}
$$
$$ 5 \frac{1}{3} + 3 \frac{1}{4} = 8 \frac{7}{12} $$

mple #1: