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

[tex]\[
36 + 45
\][/tex]

1. What is the GCF of 36 and 45?

[tex]\[
\text{GCF} = \quad
\][/tex]

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

[tex]\[
36 + 45 = (9 \times 4) + (9 \times 5) = 9 \times (4 + 5)
\][/tex]

Therefore,

[tex]\[
36 + 45 = 9 \times (4 + 5)
\][/tex]

Sagot :

GinnyAnsweridn
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].
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