Use The Distributive Property Of Multiplication To Make The Statement Below True. 9 ( 6 + 5 ) = _ _ _ _ _ _ _ 9(6+5) = \, \_\_\_\_\_\_\_ 9 ( 6 + 5 ) = _______ Calculate The Following: 10 + 12 − ( 8 − 3 10 + 12 - (8 - 3 10 + 12 − ( 8 − 3 ]$\begin{array}{l} 10 + 12 - (8 - 3) \ = (8 - 3) - 10 + 12 \ = 5 - 2^2

Introduction

The distributive property of multiplication is a fundamental concept in mathematics that allows us to simplify complex expressions by breaking them down into more manageable parts. In this article, we will explore how to use the distributive property to make a statement true, and then apply this concept to calculate a more complex expression.

Understanding the Distributive Property

The distributive property of multiplication states that for any numbers a, b, and c:

a(b + c) = ab + ac

This means that we can distribute the multiplication operation to each term inside the parentheses.

Applying the Distributive Property to the Given Statement

Let's apply the distributive property to the statement:

$9(6+5) = \, \_\_\_\_\_\_\_$

Using the distributive property, we can rewrite the expression as:

$9(6+5) = 9(6) + 9(5)$

Now, we can simplify each term:

$9(6) = 54$

$9(5) = 45$

Therefore, the statement becomes:

$9(6+5) = 54 + 45$

Calculating the Result

Now, let's calculate the result:

$54 + 45 = 99$

So, the final answer is:

$9(6+5) = 99$

Calculating the Complex Expression

Now, let's move on to the complex expression:

$10 + 12 - (8 - 3)$

Step 1: Apply the Distributive Property

Using the distributive property, we can rewrite the expression as:

$(8 - 3) - 10 + 12$

Step 2: Simplify the Expression

Now, let's simplify the expression:

$(8 - 3) = 5$

$5 - 10 = -5$

$-5 + 12 = 7$

Therefore, the final answer is:

$10 + 12 - (8 - 3) = 7$

Discussion

In this article, we have seen how to use the distributive property of multiplication to make a statement true, and then apply this concept to calculate a more complex expression. The distributive property is a powerful tool that allows us to simplify complex expressions by breaking them down into more manageable parts.

Conclusion

In conclusion, the distributive property of multiplication is a fundamental concept in mathematics that allows us to simplify complex expressions by breaking them down into more manageable parts. By applying the distributive property, we can make statements true and calculate complex expressions with ease.

Additional Examples

Here are some additional examples of how to use the distributive property:

• $4(2+3) = 4(2) + 4(3) = 8 + 12 = 20$
• $3(5-2) = 3(5) - 3(2) = 15 - 6 = 9$
• $2(8+1) = 2(8) + 2(1) = 16 + 2 = 18$

Practice Problems

Here are some practice problems to help you master the distributive property:

• $6(3+2) = \, \_\_\_\_\_\_\_$ (Answer: 30)
• $9(4-1) = \, \_\_\_\_\_\_\_$ (Answer: 27)
• $5(7+3) = \, \_\_\_\_\_\_\_$ (Answer: 50)

Final Thoughts

Q: What is the distributive property of multiplication?

A: The distributive property of multiplication is a fundamental concept in mathematics that allows us to simplify complex expressions by breaking them down into more manageable parts. It states that for any numbers a, b, and c:

a(b + c) = ab + ac

Q: How do I apply the distributive property to a given expression?

A: To apply the distributive property, simply multiply the number outside the parentheses to each term inside the parentheses. For example:

$9(6+5) = 9(6) + 9(5)$

Q: What if I have a negative number inside the parentheses?

A: If you have a negative number inside the parentheses, you can still apply the distributive property. For example:

$-3(4+2) = -3(4) + (-3)(2)$

Q: Can I apply the distributive property to expressions with variables?

A: Yes, you can apply the distributive property to expressions with variables. For example:

$2(x+3) = 2x + 6$

Q: How do I simplify expressions with multiple sets of parentheses?

A: To simplify expressions with multiple sets of parentheses, apply the distributive property to each set of parentheses separately. For example:

$3(2(4+1)) = 3(2(4)) + 3(2(1))$

Q: What if I have a fraction inside the parentheses?

A: If you have a fraction inside the parentheses, you can still apply the distributive property. For example:

$\frac{1}{2}(3+4) = \frac{1}{2}(3) + \frac{1}{2}(4)$

Q: Can I apply the distributive property to expressions with exponents?

A: Yes, you can apply the distributive property to expressions with exponents. For example:

$2^3(4+2) = 2^3(4) + 2^3(2)$

Q: How do I know when to apply the distributive property?

A: You should apply the distributive property whenever you see a number outside a set of parentheses and a sum or difference inside the parentheses.

Q: Can I use the distributive property to simplify expressions with decimals?

A: Yes, you can use the distributive property to simplify expressions with decimals. For example:

$3.5(2+1.2) = 3.5(2) + 3.5(1.2)$

Q: What if I have a mixed expression with addition and multiplication?

A: If you have a mixed expression with addition and multiplication, you can still apply the distributive property. For example:

$2(3+4) + 5 = 2(3) + 2(4) + 5$

Q: Can I use the distributive property to solve equations?

A: Yes, you can use the distributive property to solve equations. For example:

$2x + 3 = 5$

$2x + 3 - 3 = 5 - 3$

$2x = 2$

$x = 1$

Conclusion

In conclusion, the distributive property of multiplication is a powerful tool that allows us to simplify complex expressions by breaking them down into more manageable parts. By applying the distributive property, we can make statements true and calculate complex expressions with ease. With practice and patience, you will become proficient in using the distributive property to solve a wide range of mathematical problems.