Solve Mixed Number Multiplication: 4⅔ × 1⅕ Step-by-Step

$4\frac{2}{3}\times1\frac{1}{5}$

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

• Step 1: Convert $4\frac{2}{3}$ and $1\frac{1}{5}$ to improper fractions.
• Step 2: Multiply these improper fractions.
• Step 3: Simplify the result, if necessary, and convert it back to a mixed number.

Now, let's work through each step:
Step 1: Convert mixed numbers to improper fractions:
For $4\frac{2}{3}$:
Multiply the whole number 4 by the denominator 3 and add the numerator 2:
$4 \times 3 + 2 = 12 + 2 = 14$.
Thus, $4\frac{2}{3} = \frac{14}{3}$.
For $1\frac{1}{5}$:
Multiply the whole number 1 by the denominator 5 and add the numerator 1:
$1 \times 5 + 1 = 5 + 1 = 6$.
Thus, $1\frac{1}{5} = \frac{6}{5}$.

Step 2: Multiply the improper fractions $\frac{14}{3}$ and $\frac{6}{5}$:
$\frac{14}{3} \times \frac{6}{5} = \frac{14 \times 6}{3 \times 5} = \frac{84}{15}$.

Step 3: Simplify the resulting fraction $\frac{84}{15}$ and convert it to a mixed number if necessary:
Find the greatest common divisor (GCD) of 84 and 15, which is 3.
Divide both numerator and denominator by their GCD:
$\frac{84 \div 3}{15 \div 3} = \frac{28}{5}$.

Convert the improper fraction $\frac{28}{5}$ to a mixed number:
Divide 28 by 5: Quotient is 5, remainder is 3.
Thus, $\frac{28}{5} = 5\frac{3}{5}$.

Therefore, the solution to the problem is $5\frac{3}{5}$.