Multiply 5 × 1¼: Mixed Number Multiplication Step-by-Step

To solve this problem, let us proceed with the outlined steps:

• Step 1: Convert the mixed number $1\frac{1}{4}$ into an improper fraction. Use the formula: $\frac{ac + b}{c}$, where $a = 1$, $b = 1$, and $c = 4$. Therefore, $1\frac{1}{4} = \frac{1 \times 4 + 1}{4} = \frac{5}{4}$.
• Step 2: Multiply the whole number $5$ by the improper fraction $\frac{5}{4}$:
  $5 \times \frac{5}{4} = \frac{5 \times 5}{4} = \frac{25}{4}$.
• Step 3: Convert the improper fraction $\frac{25}{4}$ back into a mixed number. Divide $25$ by $4$ to get $6$ as the whole number and the remainder is $1$, thus the mixed number is $6\frac{1}{4}$.

Therefore, the result of $5 \times 1\frac{1}{4}$ is $6\frac{1}{4}$.

The correct multiple-choice answer, corresponding to this result, is choice 4: $6\frac{1}{4}$.