The problem asks to estimate the difference between the given fractions $4\frac{3}{23}$ and $\frac{13}{15}$ using the benchmarks $0$, $\frac{1}{2}$, and $1$.

1. Problem Description

The problem asks to estimate the difference between the given fractions $4\frac{3}{23}$ and $\frac{13}{15}$ using the benchmarks $0$, $\frac{1}{2}$, and $1$.

2. Solution Steps

First, we need to estimate $4\frac{3}{23}$. The fraction $\frac{3}{23}$ is close to 0, so we can approximate $4\frac{3}{23}$ as $4+0 = 4$.

Next, we need to estimate $\frac{13}{15}$. We compare $\frac{13}{15}$ with the benchmark values $0$, $\frac{1}{2}$ and $1$.

Half of $15$ is $7.5$. Since $13$ is greater than $7.5$ and also close to $15$, $\frac{13}{15}$ is close to $1$.

So we approximate $\frac{13}{15}$ as $1$.

Finally, we subtract the approximations: $4 - 1 = 3$.

3. Final Answer

$3$