Solve Mixed Number Division: 1⅝ ÷ 1⅓ Step by Step

To solve this division of mixed numbers, follow these detailed steps:

• Step 1: Convert each mixed number to an improper fraction.
• Step 2: Divide by multiplying by the reciprocal of the second fraction.
• Step 3: Simplify the resulting fraction and convert it back to a mixed number, if necessary.

Let's perform each step with the given numbers:

Step 1: Convert the mixed numbers to improper fractions.
$1\frac{5}{7} = \frac{1 \times 7 + 5}{7} = \frac{12}{7}$
$1\frac{1}{3} = \frac{1 \times 3 + 1}{3} = \frac{4}{3}$

Step 2: Instead of dividing by $\frac{4}{3}$, multiply by its reciprocal, which is $\frac{3}{4}$.
$\frac{12}{7} \times \frac{3}{4} = \frac{12 \times 3}{7 \times 4} = \frac{36}{28}$

Step 3: Simplify the fraction $\frac{36}{28}$.
Both the numerator and the denominator are divisible by 4:
$\frac{36 \div 4}{28 \div 4} = \frac{9}{7}$

Convert $\frac{9}{7}$ back to a mixed number:
Since $9$ divided by $7$ is $1$ with a remainder of $2$, it becomes:
$1\frac{2}{7}$

Therefore, the solution to the problem is $1\frac{2}{7}$.