The problem asks to estimate the mixed number $4\frac{6}{11}$ using the benchmarks $0$, $\frac{1}{2}$, and $1$ to estimate the fractional part.

1. Problem Description

The problem asks to estimate the mixed number $4\frac{6}{11}$ using the benchmarks $0$, $\frac{1}{2}$, and $1$ to estimate the fractional part.

2. Solution Steps

We want to estimate the fraction $\frac{6}{11}$ using the benchmarks $0$, $\frac{1}{2}$, and $1$.

First, we find half of the denominator:

$\frac{1}{2} \times 11 = 5.5$

Now, we compare the numerator (6) with 5.

5. Since $6 > 5.5$, the fraction $\frac{6}{11}$ is greater than $\frac{1}{2}$.

Next, we compare the fraction $\frac{6}{11}$ with

1. Since $6 < 11$, the fraction $\frac{6}{11}$ is less than

1. Since 6 is close to 5.5 (half of 11) and closer to 11 than to 0, we can estimate $\frac{6}{11}$ to be closer to $\frac{1}{2}$ than to $0$, but still closer to $\frac{1}{2}$ than to

1.

Therefore, we estimate $\frac{6}{11}$ to be approximately $\frac{1}{2}$.

So, the mixed number $4\frac{6}{11}$ is approximately $4 + \frac{1}{2} = 4\frac{1}{2}$.

3. Final Answer

$4\frac{1}{2}$