Master Algebraic Expressions with M6 5.3 Notes
Table of Contents
- Introduction to Algebraic Expressions
- Adding Variables to Expressions
- Coefficients and Constants
- Terms and Like Terms
- Key Words for Operations
- Writing Algebraic Expressions
- Example 1: Ten Dollars More Than Anthony Earned
- Example 2: Twelve Dollars Less Than the Original Price
- Example 3: Four and One-Half Times the Number of Gallons
- Example 4: Six Times More Money than Courtney Saved
- Example 5: Cost for Each Pound of Grapes
- Example 6: Alex Increasing the Number of Shoes
- Expressions with Multiple Steps
- Example 1: Five Less Than Three Times the Number of Points
- Example 2: Two Less Than One-Third of the Points
- Example 3: Twice a Number Decreased by Seven
- Example 4: Four Times a Number Increased by Nine
- Example 5: Mason's Score Compared to Gavin's Score
Introduction to Algebraic Expressions
Algebraic expressions are mathematical phrases that involve numbers, variables, and operations. Unlike numerical expressions, algebraic expressions do not have an equal sign. In this article, we will explore the concept of algebraic expressions and learn how to write them.
Adding Variables to Expressions
To add variables to expressions, we need to understand the concept of coefficients and constants. A coefficient is the number multiplied by the variable, while a constant is a fixed value that does not change. We can have more than one variable in an expression, each with its own coefficient.
Coefficients and Constants
Coefficients play a vital role in algebraic expressions as they determine the scaling factor of the variable. Constants, on the other HAND, do not have variables associated with them and remain the same throughout the expression. Understanding coefficients and constants enables us to manipulate algebraic expressions effectively.
Terms and Like Terms
Terms in algebraic expressions are separated by addition or subtraction operations. Each term consists of coefficients and variables. Like terms are terms that have the same variable(s). It's important to note that constants are also considered like terms as they don't have variables. Identifying like terms helps us simplify and combine expressions.
Key Words for Operations
To write algebraic expressions accurately, we need to understand the key words that represent different operations. For addition, words like "plus," "sum," "more than," and "total" indicate the need to use addition. Similarly, words like "minus," "difference," and "decreased by" suggest subtraction. "Times," "multiplied by," and "product" signify multiplication, while "shared," "quotient," and "divided by" indicate division.
Writing Algebraic Expressions
Now that we have a good understanding of the concepts involved, let's practice writing algebraic expressions with several examples.
Example 1: Ten Dollars More Than Anthony Earned
Let's define a variable to represent Anthony's earnings. We'll use the letter "a" for this unknown value. Since the expression asks for ten dollars more than Anthony earned, we can write it as "a + 10."
Example 2: Twelve Dollars Less Than the Original Price
In this case, we want to find the original price, so let's use the variable "p" to represent it. The expression would be "p - 12" since it asks for twelve dollars less than the original price.
Example 3: Four and One-Half Times the Number of Gallons
To represent the number of gallons, we can use the variable "g." The expression would then be "4.5g" or "4 1/2g" since we want to multiply four and a half by the number of gallons.
Example 4: Six Times More Money than Courtney Saved
Let's use the variable "c" to represent the money Courtney saved. As the expression asks for six times the amount, it can be written as "6c."
Example 5: Cost for Each Pound of Grapes
In this example, the unknown value is the number of pounds of grapes, so let's use the variable "p" to represent it. The cost for each pound is given as one dollar and nineteen cents, which would be written as "1.19p" or "1.19 * p."
Example 6: Alex Increasing the Number of Shoes
In this situation, we want to express the increase in the number of shoes Alex owns. Let's use the variable "s" to represent the shoes. The expression would be "s + 6" since it asks for six pairs more.
Expressions with Multiple Steps
Now let's look at expressions that involve multiple steps or operations.
Example 1: Five Less Than Three Times the Number of Points
To solve this expression, we first define a variable "n" to represent the number of points. The expression would be "3n - 5" since it asks for five less than three times the number of points.
Example 2: Two Less Than One-Third of the Points
Let's use the variable "p" to represent the points. The expression would be "(1/3)p - 2" since it asks for two less than one-third of the points.
Example 3: Twice a Number Decreased by Seven
In this example, we want to express the result of doubling a number and then subtracting seven. Let's use the variable "n" to represent the number. The expression would be "2n - 7."
Example 4: Four Times a Number Increased by Nine
Using the variable "n" for the number, the expression would be "4n + 9" since it asks for four times the number increased by nine.
Example 5: Mason's Score Compared to Gavin's Score
Let's use "g" to represent Gavin's score and "m" to represent Mason's score. Given that Gavin scored twelve points, we can substitute "g" with twelve. The expression becomes "2g - 4." By evaluating the expression, we find that Mason scored twenty points.
Conclusion
In this article, we've learned how to write algebraic expressions by adding variables, coefficients, and constants. We've also explored key words associated with different operations. By practicing various examples, we can enhance our ability to write and simplify algebraic expressions effectively.
Highlights:
- Algebraic expressions involve numbers, variables, and operations.
- Coefficients determine the scaling factor of variables, while constants remain fixed.
- Terms in expressions are separated by addition or subtraction operations.
- Like terms have the same variable(s) or are constants.
- Key words such as "plus," "minus," "times," and "divided by" represent different operations.
- Practice writing expressions with examples involving single and multiple steps.
FAQ:
Q: What are algebraic expressions?
A: Algebraic expressions are mathematical phrases that include numbers, variables, and operations.
Q: How can I add variables to algebraic expressions?
A: Variables can be added to expressions by assigning a letter to represent the unknown value and combining it with coefficients and constants.
Q: What are coefficients and constants?
A: Coefficients are numbers multiplied by variables in expressions, while constants are fixed values that do not change.
Q: How do I identify like terms in expressions?
A: Like terms share the same variable(s) or are constants.
Q: How do key words help in writing algebraic expressions?
A: Key words indicate the type of operation (addition, subtraction, multiplication, or division) used in the expression.
Q: Can You provide some examples of writing algebraic expressions?
A: Sure! Some examples include expressions for earning money, calculating costs, and scoring points in sports.
Q: What is the difference between single-step and multiple-step expressions?
A: Single-step expressions involve one operation, while multiple-step expressions involve multiple operations to achieve the final result.
Q: How can I simplify algebraic expressions?
A: Simplification involves combining like terms and applying appropriate operations following the order of operations.
Q: What is the importance of writing algebraic expressions?
A: Writing algebraic expressions allows us to represent real-life situations mathematically and solve problems effectively.