Sure, let's break down the solution step-by-step:
### Step 1 - Finding the GCF:
Firstly, we need to find the greatest common factor (GCF) of the numbers 36 and 45.
The GCF of 36 and 45 is 9.
### Step 2 - Express Each Number as a Product of the GCF and Another Number:
Now, we'll express each number as a product of the GCF and another number.
- For 36:
We divide 36 by the GCF (9), resulting in:
[tex]\[
36 = 9 \times 4
\][/tex]
- For 45:
We divide 45 by the GCF (9), resulting in:
[tex]\[
45 = 9 \times 5
\][/tex]
### Step 3 - Represent the Sum Using the Distributive Property:
We now need to rewrite the sum [tex]\( 36 + 45 \)[/tex] using the distributive property. Let's substitute the factored forms of 36 and 45:
[tex]\[
36 + 45 = (9 \times 4) + (9 \times 5)
\][/tex]
### Step 4 - Apply the Distributive Property:
Using the distributive property, we can factor out the GCF (9) from the expression:
[tex]\[
(9 \times 4) + (9 \times 5) = 9 \times (4 + 5)
\][/tex]
So, [tex]\( 36 + 45 \)[/tex] can be rewritten as:
[tex]\[
9 \times (4 + 5)
\][/tex]
### Step 5 - Simplify the Expression:
Finally, we simplify the expression inside the parentheses:
[tex]\[
4 + 5 = 9
\][/tex]
So, the sum expressed as a product is:
[tex]\[
9 \times 9 = \boxed{81}
\][/tex]
### Summary:
We have used the GCF of 36 and 45, which is 9, to rewrite the sum [tex]\( 36 + 45 \)[/tex] using the distributive property as [tex]\( 9 \times (4 + 5) \)[/tex], which simplifies to [tex]\( 9 \times 9 \)[/tex] equaling [tex]\( 81 \)[/tex].
