- Identify the operation on the variable \(g\) (division by 8).
- Apply the inverse operation (multiplication by 8) to both sides of the equation.
- Simplify to isolate \(g\): \(g = 4 \times 8\).
- State the final result: \(g = \boxed{32}\).
Explanation
- Analyzing the Equation
To solve for the variable \(g\) in the equation \(\frac{g}{8} = 4\), we first identify the operation performed on \(g\). The variable \(g\) is being divided by 8. To isolate \(g\), we need to perform the inverse operation, which is multiplication. By multiplying both sides of the equation by 8, we can undo the division and determine the value of \(g\).
- Solving for g
We start with the given equation:
\[\frac{g}{8} = 4\]
To isolate \(g\), multiply both sides of the equation by 8:
\[8 \cdot \left(\frac{g}{8}\right) = 8 \cdot 4\]
The 8 on the left side cancels out, leaving:
\[g = 32\]
Therefore, the value of \(g\) that satisfies the equation is 32.
Examples
Imagine you are distributing 32 apples equally among 8 baskets. To find out how many apples are in each basket, you divide the total number of apples by the number of baskets: \(\frac{32}{8} = 4\). By understanding how to solve equations like \(\frac{g}{8} = 4\), you can easily determine the total quantity when you know the number of groups and the amount in each, which is a fundamental skill in everyday resource management and planning.