$$ 3 \frac{2}{5} $$ of $$ 3 \frac{1}{3} $$

Question

UpStudy AI · Accepted Answer

Let's solve the problem step by step.

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

The first mixed number is $$ 3\frac{2}{5} $$.

$$
3\frac{2}{5} = \frac{3 \times 5 + 2}{5} = \frac{15 + 2}{5} = \frac{17}{5}
$$

The second mixed number is $$ 3\frac{1}{3} $$.

$$
3\frac{1}{3} = \frac{3 \times 3 + 1}{3} = \frac{9 + 1}{3} = \frac{10}{3}
$$

### Step 2: Multiply the Improper Fractions

Now, multiply the two fractions:

$$
\frac{17}{5} \times \frac{10}{3} = \frac{17 \times 10}{5 \times 3} = \frac{170}{15}
$$

### Step 3: Simplify the Fraction

To simplify $$\frac{170}{15}$$, notice that both the numerator and the denominator are divisible by $$5$$.

$$
\frac{170 \div 5}{15 \div 5} = \frac{34}{3}
$$

### Step 4: Convert the Improper Fraction to a Mixed Number

Divide $$34$$ by $$3$$:

$$
34 \div 3 = 11 \text{ remainder } 1
$$

Thus, $$\frac{34}{3}$$ can be written as:

$$
11\frac{1}{3}
$$

### Final Answer

The product of $$ 3\frac{2}{5} $$ and $$ 3\frac{1}{3} $$ is:

$$
11\frac{1}{3}
$$
The product is $$11\frac{1}{3}$$.

\( 3 \frac{2}{5} \) of \( 3 \frac{1}{3} \)