Solve: 3/4 Divided by 1 1/3 - Mixed Number Division

$\frac{3}{4}:1\frac{1}{3}=$

To solve this division problem, we will follow these steps:

• Step 1: Convert the mixed number to an improper fraction.
• Step 2: Replace division with multiplication by the reciprocal.
• Step 3: Perform the multiplication and simplify the result.

Let's begin with the solution:

Step 1: Convert the mixed number $1\frac{1}{3}$ into an improper fraction.

To convert, multiply 1 (the whole number) by 3 (the denominator) and add 1 (the numerator):

$1 \times 3 + 1 = 3 + 1 = 4$

Therefore, $1\frac{1}{3} = \frac{4}{3}$.

Step 2: Write the division problem as multiplication by the reciprocal of $\frac{4}{3}$.

The reciprocal of $\frac{4}{3}$ is $\frac{3}{4}$. So,

$\frac{3}{4} \div 1\frac{1}{3} = \frac{3}{4} \times \frac{3}{4}$.

Step 3: Multiply the fractions and simplify if possible.

Multiply the numerators and the denominators:

$\text{Numerators: } 3 \times 3 = 9$

$\text{Denominators: } 4 \times 4 = 16$

Thus, $\frac{3}{4} \times \frac{3}{4} = \frac{9}{16}$.

No further simplification is required as 9 and 16 are relatively prime.

Therefore, the solution to the problem is $\frac{9}{16}$.