Solve the Mixed Number Equation: Finding the Value When x - 4⅐ = 1⅗

$?-4\frac{1}{7}=1\frac{3}{7}$

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

• Step 1: Convert the mixed fractions to improper fractions.
• Step 2: Rearrange the equation to solve for the unknown variable.
• Step 3: Perform addition and convert back to a mixed fraction if necessary.

Now, let's work through each step:
Step 1: Convert $4\frac{1}{7}$ and $1\frac{3}{7}$ to improper fractions.
- $4\frac{1}{7}$ becomes $\frac{29}{7}$ because $4 \times 7 + 1 = 29$.
- $1\frac{3}{7}$ becomes $\frac{10}{7}$ because $1 \times 7 + 3 = 10$.

Step 2: The equation is $x - \frac{29}{7} = \frac{10}{7}$. Rearranging gives us $x = \frac{29}{7} + \frac{10}{7}$.

Step 3: Perform the addition:
- Adding the improper fractions gives $\frac{29}{7} + \frac{10}{7} = \frac{39}{7}$.

Step 4: Convert $\frac{39}{7}$ back to a mixed fraction:
- Divide $39$ by $7$, which gives $5$ with a remainder of $4$.
- So, $\frac{39}{7}$ is equivalent to $5\frac{4}{7}$.

Therefore, the number we are looking for is $5\frac{4}{7}$.