What divided by what equals 8?
Understand the Problem
The question is asking us to find two numbers that, when one is divided by the other, the result equals 8. This involves identifying potential numerator and denominator pairs.
Answer
The solution pairs are in the form $(8y, y)$, such as $(8, 1)$ and $(16, 2)$.
Answer for screen readers
The pairs of numbers that satisfy the condition are in the form $(8y, y)$, such as $(8, 1)$ and $(16, 2)$.
Steps to Solve
- Set up the equation
Let the two numbers be $x$ (numerator) and $y$ (denominator). The equation derived from the problem is
$$ \frac{x}{y} = 8 $$
This means that $x$ is 8 times $y$.
- Express one variable in terms of the other
From the equation above, we can express $x$ in terms of $y$:
$$ x = 8y $$
- Choose a value for $y$
To find specific pairs, we can choose a value for $y$. Let's choose $y = 1$ as a simple case.
- Calculate $x$ using the chosen $y$
Now substitute $y$ into the equation for $x$:
$$ x = 8(1) = 8 $$
Thus, one pair of numbers is $(8, 1)$.
- Find additional pairs
We can repeat this process by choosing different values for $y$. For example, if we choose $y = 2$:
$$ x = 8(2) = 16 $$
So another pair of numbers is $(16, 2)$.
- General solution
The general pairs will be of the form $(8y, y)$ for any non-zero value of $y$.
The pairs of numbers that satisfy the condition are in the form $(8y, y)$, such as $(8, 1)$ and $(16, 2)$.
More Information
This means that for any positive non-zero value of $y$, the corresponding $x$ can always be found by multiplying $y$ by 8. There are an infinite number of solutions, as you can select any non-zero value for $y$.
Tips
- Choosing $y$ as 0. Remember that division by zero is undefined, so always select non-zero values for $y$.
