Sure, let's solve this problem step-by-step.
### Step 1: Identify the GCF of 36 and 45
First, 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
Next, we need to express each given number as a product of its GCF (which we found to be 9) and another factor.
So,
For 36:
[tex]\[ 36 = 9 \times 4 \][/tex]
For 45:
[tex]\[ 45 = 9 \times 5 \][/tex]
### Step 3: Rewrite the original sum using the Distributive Property
Now, we are going to rewrite the sum [tex]\( 36 + 45 \)[/tex] using the Distributive Property.
[tex]\[ 36 + 45 \][/tex]
We substitute the products we found:
[tex]\[ (9 \times 4) + (9 \times 5) \][/tex]
Next, factor out the common factor (which is 9):
[tex]\[ 9 \times (4 + 5) \][/tex]
### Step 4: Simplify the expression inside the parentheses
Finally, simplify the expression inside the parentheses:
[tex]\[ 4 + 5 = 9 \][/tex]
So, the rewritten sum is:
[tex]\[ 36 + 45 = 9 \times 9 \][/tex]
### Final Answer
Rewriting the sum of 36 and 45 as a product using the distributive property gives:
[tex]\[ 36 + 45 = 9 \times (4 + 5) = 9 \times 9 = 81 \][/tex]
So, filling in the boxes:
[tex]\[ 9 \times (4 + 5) \][/tex]
In conclusion:
[tex]\[ \boxed{36 + 45 = 9 \times (4 + 5)} \][/tex]
This uses the distributive property to rewrite the sum as asked.
