Use Properties To Find The Product.${ \begin{aligned} 2 \cdot 88 & = 2 \cdot (90 - \square) \ & = (2 \cdot 90) - (2 \cdot \square) \ & = 180 - \square \ & = \square \end{aligned} }$
Introduction
In mathematics, properties play a crucial role in solving equations and finding the product of numbers. One of the most common properties used in mathematics is the distributive property, which states that for any numbers a, b, and c, a(b + c) = ab + ac. In this article, we will use the distributive property to find the product of two numbers.
The Distributive Property
The distributive property is a fundamental concept in mathematics that allows us to expand expressions by multiplying each term inside the parentheses with the term outside the parentheses. The distributive property can be written as:
a(b + c) = ab + ac
where a, b, and c are numbers.
Example Problem
Let's consider the following problem:
2 × 88 = 2 × (90 - x)
where x is a number. Our goal is to find the value of x.
Step 1: Apply the Distributive Property
To solve this problem, we will apply the distributive property to the expression 2 × (90 - x). This will allow us to expand the expression and simplify it.
2 × (90 - x) = 2 × 90 - 2 × x
Step 2: Simplify the Expression
Now that we have expanded the expression, we can simplify it by combining like terms.
2 × 90 - 2 × x = 180 - 2x
Step 3: Equate the Expressions
Since the two expressions are equal, we can set them equal to each other and solve for x.
180 - 2x = 88
Step 4: Solve for x
To solve for x, we will add 2x to both sides of the equation and then divide both sides by 2.
180 = 88 + 2x
180 - 88 = 2x
92 = 2x
x = 92/2
x = 46
Conclusion
In this article, we used the distributive property to find the product of two numbers. We started with the equation 2 × 88 = 2 × (90 - x) and applied the distributive property to expand the expression. We then simplified the expression and equated it to the original expression. Finally, we solved for x and found that x = 46.
Real-World Applications
The distributive property is used in many real-world applications, including:
- Algebra: The distributive property is used to expand and simplify algebraic expressions.
- Geometry: The distributive property is used to find the area and perimeter of shapes.
- Physics: The distributive property is used to solve problems involving motion and forces.
Tips and Tricks
Here are some tips and tricks to help you use the distributive property:
- Use the distributive property to expand expressions: The distributive property can be used to expand expressions by multiplying each term inside the parentheses with the term outside the parentheses.
- Simplify expressions: The distributive property can be used to simplify expressions by combining like terms.
- Equate expressions: The distributive property can be used to equate expressions by setting them equal to each other and solving for a variable.
Common Mistakes
Here are some common mistakes to avoid when using the distributive property:
- Not applying the distributive property: Failing to apply the distributive property can lead to incorrect solutions.
- Not simplifying expressions: Failing to simplify expressions can lead to incorrect solutions.
- Not equating expressions: Failing to equate expressions can lead to incorrect solutions.
Conclusion
Introduction
In our previous article, we used the distributive property to find the product of two numbers. In this article, we will answer some frequently asked questions about using properties to find the product.
Q: What is the distributive property?
A: The distributive property is a fundamental concept in mathematics that allows us to expand expressions by multiplying each term inside the parentheses with the term outside the parentheses. It can be written as:
a(b + c) = ab + ac
Q: How do I apply the distributive property?
A: To apply the distributive property, you need to multiply each term inside the parentheses with the term outside the parentheses. For example, if you have the expression 2 × (90 - x), you would multiply 2 by 90 and 2 by -x.
2 × (90 - x) = 2 × 90 - 2 × x
Q: What is the difference between the distributive property and the commutative property?
A: The distributive property and the commutative property are two different properties in mathematics. The distributive property allows us to expand expressions by multiplying each term inside the parentheses with the term outside the parentheses. The commutative property, on the other hand, allows us to change the order of the terms in an expression without changing the value of the expression.
For example, if you have the expression 2 × 3, you can change the order of the terms to 3 × 2, and the value of the expression will remain the same.
Q: Can I use the distributive property to find the product of three numbers?
A: Yes, you can use the distributive property to find the product of three numbers. For example, if you have the expression 2 × (3 + 4), you can apply the distributive property to expand the expression.
2 × (3 + 4) = 2 × 3 + 2 × 4
Q: What are some common mistakes to avoid when using the distributive property?
A: Some common mistakes to avoid when using the distributive property include:
- Not applying the distributive property
- Not simplifying expressions
- Not equating expressions
- Not following the order of operations
Q: How do I know when to use the distributive property?
A: You should use the distributive property when you have an expression with parentheses and you need to expand it. For example, if you have the expression 2 × (90 - x), you would use the distributive property to expand the expression.
Q: Can I use the distributive property to solve equations?
A: Yes, you can use the distributive property to solve equations. For example, if you have the equation 2 × (90 - x) = 88, you can apply the distributive property to expand the expression and then solve for x.
Conclusion
In conclusion, the distributive property is a powerful tool in mathematics that allows us to expand and simplify expressions. By applying the distributive property, we can solve problems involving the product of numbers. Remember to use the distributive property to expand expressions, simplify expressions, and equate expressions. With practice and patience, you will become proficient in using the distributive property to solve problems.
Additional Resources
If you want to learn more about the distributive property and how to use it to solve problems, here are some additional resources:
- Math textbooks: You can find math textbooks that cover the distributive property and how to use it to solve problems.
- Online tutorials: You can find online tutorials that provide step-by-step instructions on how to use the distributive property to solve problems.
- Practice problems: You can find practice problems that allow you to apply the distributive property to solve problems.
Conclusion
In conclusion, the distributive property is a fundamental concept in mathematics that allows us to expand and simplify expressions. By applying the distributive property, we can solve problems involving the product of numbers. Remember to use the distributive property to expand expressions, simplify expressions, and equate expressions. With practice and patience, you will become proficient in using the distributive property to solve problems.