Multiply Mixed Numbers: 5⅐ × 1¾ Step-by-Step Solution

To solve the problem $5 \frac{1}{7} \times 1 \frac{3}{4}$, we will first convert both mixed numbers into improper fractions and then multiply them.

• Convert each mixed number to an improper fraction:
  For $5 \frac{1}{7}$: Multiply the whole number 5 by the denominator 7 and add the numerator 1: $5 \times 7 + 1 = 36$. Therefore, $5 \frac{1}{7}$ becomes $\frac{36}{7}$.
  For $1 \frac{3}{4}$: Multiply the whole number 1 by the denominator 4 and add the numerator 3: $1 \times 4 + 3 = 7$. Therefore, $1 \frac{3}{4}$ becomes $\frac{7}{4}$.
• Multiply the improper fractions:
  Multiply the numerators: $36 \times 7 = 252$.
  Multiply the denominators: $7 \times 4 = 28$.
  Thus, $\frac{36}{7} \times \frac{7}{4} = \frac{252}{28}$.
• Simplify the resulting fraction, $\frac{252}{28}$:
  Divide both the numerator and denominator by their greatest common divisor, which is 28:
  $252 \div 28 = 9$ and $28 \div 28 = 1$.
  So, $\frac{252}{28} = 9$.

Therefore, the solution to the problem is $9$.