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To solve an equation like \( \frac{z}{6} = 12 \), our main goal is to find the value of the variable \( z \). We do this by isolating the variable on one side of the equation.
In this case, isolating \( z \) means getting it alone on one side of the equation. Think about it like peeling layers off an onion until we get to the core.
Since \( z \) is currently divided by 6, we need to do the opposite operation (multiplying by 6) to both sides of the equation to cancel out the division.
This is because multiplying by 6 will reverse the division of 6, leaving \( z \) by itself.
Here’s how it looks in action:
\( \frac{z}{6} \times 6 = 12 \times 6 \)
This simplifies to \( z = 72 \), isolating the variable \( z \). Now \( z \) stands alone, and we've successfully solved for it.

Multiplication is a key mathematical operation we'll use to isolate the variable. Here, we multiplied both sides of the equation by 6, because the original equation was \( \frac{z}{6} = 12 \).
Remember:

• Whatever you do to one side of the equation, you must do to the other side as well. This keeps the equation balanced, like a perfectly balanced scale.
• Multiplication is used here to get rid of the fraction.

Let’s break it down:
\( 12 \times 6 \).
If we multiply 12 by 6, we get 72.
So after performing the multiplication, you get \( z = 72 \). That’s the magic of multiplication helping us to find our variable.

To ensure our solution is correct, we always check by substituting the value back into the original equation. This tells us if we've solved it accurately.
Let’s substitute \( z = 72 \) back into \( \frac{z}{6} = 12 \):
\( \frac{72}{6} = 12 \).
Now, we perform the division:
\( \frac{72}{6} = 12 \).
Since both sides of the equation equal 12, our solution is confirmed to be correct. This step is essential because it verifies that the solution fits within the context of the original problem.
It’s like double-checking your homework to make sure you didn’t make any mistakes.