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Write the sum of the numbers as a product of their GCF and another sum.

2. [tex]36 + 45[/tex]

What is the GCF of 36 and 45? [tex]$\qquad$[/tex]

Write each number as a product of the GCF and another number. Then use the Distributive Property to rewrite the sum.

[tex]$\square \times (\square + \square)$[/tex]



Answer :

GinnyAnswer
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.

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