Understanding Algebraic Expressions: Terms, Factors, and Coefficients
When dealing with algebraic expressions, it's essential to grasp terms, factors, and coefficients. Expressions consist of numbers, operations, and variables, with terms being the building blocks separated by addition or subtraction signs. Factors are the components of each term that produce the given product when multiplied. Coefficients represent the numbers multiplied by variables, while exponents indicate how many times a factor is multiplied by itself. This understanding helps interpret expressions representing quantities effectively.
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WARM UP Ella purchased 2 DVDs and 3 CDs from Tyler s Electronics at the prices listed below. After taxes, her total cost increased by $5.60. 1. How can you write the cost of 2 DVDs as an algebraic expression? 2. How can you write the cost of 2 DVDs and 3 CDs as an algebraic expression? 3. How can you write the cost of 2 DVDs and 3 CDs, increased by $5.60 for taxes, as an algebraic expression?
1. How can you write the cost of 2 DVDs as an algebraic expression? The cost of 2 DVDs can be written as an expression of multiplication, 2d. 2. How can you write the cost of 2 DVDs and 3 CDs as an algebraic expression? The cost of 2 DVDs and 3 CDs can be written as the expression 2d + 3c. 3. How can you write the cost of 2 DVDs and 3 CDs, increased by $5.60 for taxes, as an algebraic expression? Increased by $5.60 for taxes means to add 5.60. 2d + 3c + 5.60 would represent the cost of 2 DVDs and 3 CDs increased by $5.60.
REVIEW WARM UP NUMBER TALKS OPENING
IDENTIFYING TERMS, FACTORS, AND COEFFICIENTS MGSE9-12.A.SSE.1 Interpret expressions that represent a quantity in terms of its context. Essential Question: How can I identify terms, factors, and coefficients?
Thoughts or feelings in language are often conveyed through expressions; however, mathematical ideas are conveyed through algebraic expressions. Algebraic expressions are mathematical statements that include numbers, operations, and variables to represent a number or quantity. Variables are letters used to represent values or unknown quantities that can change or vary. One example of an algebraic expression is 3? 4. Notice the variable, ?. INTRODUCTION
Expressions are made up of terms. A term is a number, a variable, or the product of a number and variable(s). An addition or subtraction sign separates each term of an expression. In the expression 4?2 + 3? + 7, there are 3 terms: 4?2, 3?, and 7. The factors of each term are the numbers or expressions that when multiplied produce a given product. In the example above, the factors of 4?2 are 4 and ?2. The factors of 3?are 3 and ?. KEY CONCEPTS
4 is also known as the coefficient of the term 4?2. A coefficient is the number multiplied by a variable in an algebraic expression. The coefficient of 3?is 3. The term 4?2 also has an exponent. Exponents indicate the number of times a factor is being multiplied by itself. In this term, 2 is the exponent and indicates that x is multiplied by itself 2 times. Terms that do not contain a variable are called constants because the quantity does not change. In this example, 7 is a constant. KEY CONCEPTS
Terms with the same variable raised to the same exponent are called like terms. In the example 5? + 3? 9, 5? and 3? are like terms. Like terms can be combined following the order of operations by evaluating grouping symbols, evaluating exponents, completing multiplication and division, and completing addition and subtraction from left to right. In this example, the sum of 5? and 3? is 8?. KEY CONCEPTS
Guided Practice Example 1 Identify each term, coefficient, constant, and factor of 2(3 + ?) + ?(1 4?) + 5.
Guided Practice Example 2 A smartphone is on sale for 25% off its list price. The sale price of the smartphone is $149.25. What expression can be used to represent the list price of the smartphone? Identify each term, coefficient, constant, and factor of the expression described.
Guided Practice Example 3 Helen purchased 3 books from an online bookstore and received a 20% discount. The shipping cost was $10 and was not discounted. Write an expression that can be used to represent the total amount Helen paid for 3 books plus the shipping cost. Identify each term, coefficient, constant, and factor of the expression described.
Problem-Based Task: Identifying Parts of an Expression in Context Tara and two friends had dinner at a Spanish tapas restaurant that charged $6 per tapa, or appetizer. The three of them shared several tapas. The total bill included taxes of $4.32. What are the terms, factors, and coefficients of the algebraic expression that represents the number of tapas ordered, including taxes?
