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1-4 Variables and Algebraic Expressions
Warm UpWarm Up
Lesson PresentationLesson PresentationProblem of the DayProblem of the Day
Lesson QuizzesLesson Quizzes
1-4 Variables and Algebraic Expressions
Warm UpEvaluate.
1. 5(7) – 12. 7(18 – 11)3. 22 + 17 8 + 34. 36 + 15(40 – 35)5. 33 + 7(12 – 4)
3449
16111183
1-4 Variables and Algebraic Expressions
Problem of the DayIf charged per cut, how much will it cost to cut a log into eight pieces if cutting it into four pieces costs $12?$28
1-4 Variables and Algebraic Expressions
Prep for MA.7.A.3.3 Formulate and use different strategies to solve one-step…linear equations…Review MA.6.A.3.1Also Prep for MA.7.A.3.2
Sunshine State Standards
1-4 Variables and Algebraic Expressions
Vocabularyvariableconstantalgebraic expressionevaluate
1-4 Variables and Algebraic Expressions
Harrison Ford was born in 1942. You can find out what year Harrison turned 18 by adding the year he was born to his age.
1942 + 18
In algebra, letters are often used to represent numbers. You can use a letter such as a to represent Harrison Ford’s age. When he turns a years old, the year will be
1942 + a.
1-4 Variables and Algebraic Expressions
The letter a has a value that can change, or vary. When a letter represents a number that can vary, it is called a variable. The year 1954 is a constant because the number cannot change.
An algebraic expression consists of one or more variables. It usually contains constants and operations. For example, 1942 + a is an algebraic expression for the year Ron Howard turns a certain age.
1-4 Variables and Algebraic Expressions
To evaluate an algebraic expression, substitute a number for the variable.
Age Year born + age = year at age
18 1942 + 18 196025 1942 + 25 196736 1942 + 36 197863 1942 + 63 2005a 1942 + a
1-4 Variables and Algebraic Expressions
Evaluate k + 9 for each value of k.
Additional Example 1: Evaluating Algebraic Expressions
A. k = 5 k + 9
5 + 914
Substitute 5 for k.Add.
B. k = 2 k + 9
2 + 9 Substitute 2 for k.
11 Add.
1-4 Variables and Algebraic ExpressionsCheck It Out: Example 1
Evaluate a + 6 for each value of a.
A. a = 3 a + 6
3 + 69
Substitute 3 for a.
Add.
B. a = 5 a + 6
5 + 6 Substitute 5 for a.
11 Add.
1-4 Variables and Algebraic Expressions
Multiplication and division of variables can be written in several ways, as shown in the table.
When evaluating expressions, use the order of operations.
1-4 Variables and Algebraic Expressions
Evaluate the expression for the given value of the variable.
Additional Example 2: Evaluating Algebraic Expressions Involving Order of Operations
A. 4x – 3 for x = 24(2) – 3
8 – 35
Substitute 2 for x.Multiply.Subtract.
1-4 Variables and Algebraic ExpressionsAdditional Example 2: Evaluating Algebraic Expressions
Involving Order of Operations
B. s ÷ 5 + s, for s = 15 15 ÷ 5 + 15
3 + 1518
C. 5x2 + 3x, for x = 2 5(2)2 + 3(2)5(4) + 3(2)
20 + 626
Substitute 15 for s.Divide.Add.
Substitute 2 for x.Evaluate the power.Multiply.Add.
1-4 Variables and Algebraic ExpressionsCheck It Out: Example 2A
Evaluate the expression for the given value of the variable.A. 3x – 2 for x = 3
3(3) – 29 – 2
7
Substitute 3 for x.Multiply.Subtract.
1-4 Variables and Algebraic ExpressionsCheck It Out: Example 2
B. r ÷ 3 + r, for r = 12 12 ÷ 3 + 12
4 + 1216
C. 4y2 + 2y, for y = 3 4(3)2 + 2(3)4(9) + 2(3)
36 + 642
Substitute 12 for r.Divide.Add.
Substitute 3 for y.Evaluate the power.Multiply.Add.
1-4 Variables and Algebraic Expressions
Evaluate
Additional Example 3: Evaluating Algebraic Expressions with Two Variables
6a + 4b, for a = 3 and b = 2.6a + 4b
63 + 4(2)
2 + 8
10
Substitute 3 for a and 2 for b.
Divide and multiply from left to right.Add.
1-4 Variables and Algebraic ExpressionsCheck It Out: Example 3
Evaluate 8w + 2x, for w = 4 and x = 2.8w + 2x
84 + 2(2)
2 + 4
6
Substitute 4 for w and 2 for x.Divide and multiply from left to right.Add.
1-4 Variables and Algebraic Expressions
Standard Lesson Quiz
Lesson Quizzes
Lesson Quiz for Student Response Systems
1-4 Variables and Algebraic ExpressionsLesson Quiz
Evaluate n + 7 for each value of n.
1. n = 25 2. n =31 Evaluate each algebraic expression for the given value of the variables
3. 6y – 5 for y = 7
4. 4x2 + 3x for x = 6
5. + 3y for x = 4 and y = 36. The expression 7d gives the number of days in
d weeks. Evaluate 7d for d = 12. How many days are in 12 weeks?
3832
37
16256x 23
84
1-4 Variables and Algebraic Expressions
1. Evaluate m + 4 for m = 19. A. 21B. 27C. 23D. 28
Lesson Quiz for Student Response Systems
1-4 Variables and Algebraic Expressions
2. Evaluate 7x – 8 for x = 5. A. 20B. 27C. 22D. 32
Lesson Quiz for Student Response Systems
1-4 Variables and Algebraic Expressions
3. Evaluate 6x2 + 5x for x = 5.A. 185B. 85C. 175 D. 50
Lesson Quiz for Student Response Systems
1-4 Variables and Algebraic Expressions
4. Evaluate + 5y for x = 3 and y = 5.A. 38B. 44C. 54D. 64
Lesson Quiz for Student Response Systems
39y
1-4 Variables and Algebraic Expressions
5. The expression 12n gives the number of months in n years. Evaluate 12n for n = 3. How many months are in 3 years?
A. 12 monthsB. 24 monthsC. 36 monthsD. 48 months
Lesson Quiz for Student Response Systems