Multiplying Fractions with Cross Canceling - Free Printable

It looks like you're referring to a math problem being written on a whiteboard in an image. Based on the visible content, here's what we can see:

The equation on the board is:

$$
\frac{18}{2 \cdot 18} \cdot \frac{18^3}{81} = \left(\frac{3}{2}\right)
$$

Let’s solve and verify this step by step.

---

Step 1: Simplify the first fraction

$$
\frac{18}{2 \cdot 18} = \frac{18}{36} = \frac{1}{2}
$$

---

Step 2: Simplify the second fraction

$$
\frac{18^3}{81}
$$

Note that:
- $18^3 = 18 \times 18 \times 18 = 5832$
- $81 = 9^2 = 3^4$, but also note that $81 = 18 \times 4.5$? Not helpful directly.

But let’s factor:
- $18 = 2 \cdot 3^2$
- So $18^3 = (2 \cdot 3^2)^3 = 2^3 \cdot 3^6 = 8 \cdot 729 = 5832$
- $81 = 3^4$

So:
$$
\frac{18^3}{81} = \frac{2^3 \cdot 3^6}{3^4} = 2^3 \cdot 3^{6-4} = 8 \cdot 3^2 = 8 \cdot 9 = 72
$$

So:
$$
\frac{18^3}{81} = 72
$$

---

Step 3: Multiply both simplified parts

$$
\frac{1}{2} \cdot 72 = 36
$$

But the right-hand side of the equation says:
$$
\left(\frac{3}{2}\right)
$$

Wait — that doesn't match! We got 36, not $ \frac{3}{2} $. So either there's a mistake in the problem or in our interpretation.

But wait — look at the original expression again:

$$
\frac{18}{2 \cdot 18} \cdot \frac{18^3}{81}
$$

We already computed this as:
$$
\frac{1}{2} \cdot 72 = 36
$$

But the person writing it has written:
$$
= \left( \frac{3}{2} \right)
$$

That cannot be correct unless there's a typo or misunderstanding.

Wait — perhaps the expression was meant to be different?

Let’s double-check if there’s a misinterpretation.

Alternative idea: Maybe the expression is:
$$
\frac{18}{2 \cdot 18} \cdot \frac{18^3}{81} = ?
$$

We did:
- $ \frac{18}{36} = \frac{1}{2} $
- $ \frac{18^3}{81} = \frac{5832}{81} $

Let’s divide:
$$
5832 ÷ 81
$$

Try dividing:
- $81 × 72 = ?$
- $80 × 72 = 5760$
- $1 × 72 = 72$
- Total: $5760 + 72 = 5832$

Yes! So $ \frac{5832}{81} = 72 $

Then:
$$
\frac{1}{2} × 72 = 36
$$

So the left-hand side equals 36, not $ \frac{3}{2} $

So either:
- The equation is wrong,
- Or there’s a typo in the problem.

Alternatively, maybe the original expression was supposed to be something else?

Let’s check the other expressions on the board:
- $1 \cdot 2 = 2$
- $ \frac{2}{2} = 1 $

These are just examples of simplification.

Perhaps the main expression is meant to simplify to $ \frac{3}{2} $, but as written, it doesn’t.

Wait — could the numerator be different?

Maybe it's:
$$
\frac{18}{2 \cdot 18} \cdot \frac{18^3}{81} = ?
$$

But we already did that.

Wait — could it be:
$$
\frac{18}{2 \cdot 18} \cdot \frac{18^3}{81} = \frac{1}{2} \cdot \frac{18^3}{81}
$$

And $ \frac{18^3}{81} = \frac{5832}{81} = 72 $, so $ \frac{1}{2} \cdot 72 = 36 $

Still 36.

But $ \frac{3}{2} = 1.5 $, which is nowhere near.

So unless there's a typo in the problem, the equation as written is incorrect.

---

Possible correction?

Suppose instead the expression was:
$$
\frac{18}{2 \cdot 18} \cdot \frac{18^3}{81} = ?
$$

We have:
$$
= \frac{1}{2} \cdot \frac{18^3}{81}
$$

Now $18^3 = 5832$, $81 = 81$, $5832 / 81 = 72$, so $ \frac{1}{2} \cdot 72 = 36 $

Still 36.

What if it was:
$$
\frac{18}{2 \cdot 18} \cdot \frac{18^3}{81} = \text{something}
$$

No.

Wait — maybe the expression is:
$$
\frac{18}{2 \cdot 18} \cdot \frac{18^3}{81} = \frac{1}{2} \cdot \frac{18^3}{81}
$$

But still 36.

Unless the exponent is different.

Wait — maybe it's:
$$
\frac{18}{2 \cdot 18} \cdot \frac{18^3}{81} = \frac{1}{2} \cdot \frac{18^3}{81}
$$

But $18^3 = (2 \cdot 3^2)^3 = 2^3 \cdot 3^6$, $81 = 3^4$, so:

$$
\frac{2^3 \cdot 3^6}{3^4} = 2^3 \cdot 3^2 = 8 \cdot 9 = 72
$$

Then $ \frac{1}{2} \cdot 72 = 36 $

So final answer is 36

But the person wrote $ = \left( \frac{3}{2} \right) $, which is incorrect.

---

Conclusion:

There is likely a mistake in the equation written on the board.

The correct value of:
$$
\frac{18}{2 \cdot 18} \cdot \frac{18^3}{81} = \frac{1}{2} \cdot 72 = 36
$$

So the correct answer is 36, not $ \frac{3}{2} $

If you were asked to solve this expression, the solution is:

$$
\boxed{36}
$$

Let me know if the original problem was different or if there's more context!