48+60 using the gcf to the factor the expression and using the distributive property

To factor the expression \( 48 + 60 \) using the greatest common factor (GCF) and apply the distributive property, follow these steps:

### Step 1: Find the GCF of 48 and 60
First, find the greatest common factor (GCF) of 48 and 60 by determining the factors of each number.

- Factors of 48: \( 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 \)
- Factors of 60: \( 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 \)

The largest common factor is \( 12 \).

### Step 2: Factor out the GCF
Now, factor out the GCF (12) from both terms in the expression \( 48 + 60 \):

\[
48 + 60 = 12 \times (4 + 5)
\]

### Step 3: Apply the distributive property
Using the distributive property, you can expand back:

\[
12 \times (4 + 5) = 12 \times 4 + 12 \times 5 = 48 + 60
\]

So, the factored form of \( 48 + 60 \) is \( 12 \times (4 + 5) \), and using the distributive property confirms that it's equal to \( 48 + 60 \).

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you find the GCF of two numbers?
2. What is the distributive property in mathematics?
3. Can you factor other numbers like 72 + 96 using the same method?
4. How would you factor a three-term expression like \( 24 + 36 + 48 \)?
5. How do prime factorization methods help in finding the GCF?

**Tip:** When factoring expressions, always check for the largest GCF to simplify as much as possible.

48 + 60 using the GCF to factor the expression and using the distributive property

Learn how to factor the expression 48 + 60 by finding the greatest common factor (GCF) and applying the distributive property. This step-by-step guide helps students in Grades 6-8 understand key concepts in factoring and the use of the GCF in simplifying expressions.

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