Simplifying Expressions: 12x6 12x18 72x6 72x18 Made Easy

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Simplifying expressions is a fundamental skill in mathematics, and it can be made easier with the right approach. In this article, we will focus on simplifying expressions with multiplication, specifically expressions like 12x6, 12x18, 72x6, and 72x18. We will break down the process into manageable steps and provide examples to illustrate each point.

Understanding the Basics

Before we dive into simplifying expressions, it's essential to understand the basics of multiplication and the properties of numbers. Multiplication is a way of quickly adding a number a certain number of times. For example, 12x6 means adding 12 together 6 times. In this case, the result is 72.

Simplifying Expressions with Multiplication

Now that we understand the basics, let's move on to simplifying expressions with multiplication. The key to simplifying these expressions is to identify the greatest common factor (GCF) of the numbers involved.

Identifying the Greatest Common Factor (GCF)

The GCF is the largest number that divides both numbers without leaving a remainder. For example, the GCF of 12 and 6 is 6, because 6 is the largest number that divides both 12 and 6 without leaving a remainder.

Simplifying 12x6 and 12x18

Let's use the GCF to simplify the expressions 12x6 and 12x18.

• 12x6 = 6x(2x6) = 6x12 = 72
• 12x18 = 6x(2x18) = 6x36 = 216

As you can see, identifying the GCF makes it easier to simplify the expressions.

Simplifying 72x6 and 72x18

Now let's simplify the expressions 72x6 and 72x18.

• 72x6 = 6x(12x6) = 6x72 = 432
• 72x18 = 6x(12x18) = 6x216 = 1296

Again, identifying the GCF makes it easier to simplify the expressions.

Using the Distributive Property

Another way to simplify expressions with multiplication is to use the distributive property. The distributive property states that a(b+c) = ab + ac. This property can be used to simplify expressions like 12x(6+18).

• 12x(6+18) = 12x6 + 12x18 = 72 + 216 = 288

As you can see, using the distributive property makes it easier to simplify the expression.

Example Problems

Here are some example problems to illustrate the concepts:

• 24x8 =?
• 48x12 =?
• 96x4 =?

Answers:

• 24x8 = 8x(3x8) = 8x24 = 192
• 48x12 = 12x(4x12) = 12x48 = 576
• 96x4 = 4x(24x4) = 4x96 = 384

Conclusion

Simplifying expressions with multiplication can be made easier by identifying the greatest common factor (GCF) and using the distributive property. By breaking down the process into manageable steps and using these strategies, you can simplify expressions like 12x6, 12x18, 72x6, and 72x18 with ease. Remember to practice regularly to become proficient in simplifying expressions.

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