Download presentation

Presentation is loading. Please wait.

Published byBryce Randall Modified over 8 years ago

1
Algebraic Expressions

2
Education's purpose is to replace an empty mind with an open one. Malcolm Forbes

3
Expressions Math expressions represent a convenient way to translate verbal expressions

4
What is the area of a rectangle? Length times Width If the length is 3 meters and the width is 2 meters, what is the area? A = L x W A = 3 x 2 = 6 m 2 A, L and W are the variables. It is any letter that represents an unknown number.

5
An algebraic expression is a quantity that contains numbers and variables. x + y, 3a 2 a, 3x + 2y z A term is a number, a variable, or a product of numbers and variables. Terms Algebraic Expression

6
Components of an Algebraic Expression Constant term: fancy name for a number Variable term: terms with letters Example: 3xy – 4z + 17 Variable expression with 3 terms: 3xy, -4z, 17 2 variable terms and 1 constant term

7
Variable Terms Consist of two parts The variable(letter) part The number part Example: 2xy has a coefficient of 2 -6j has a coefficient of –6 W has a coefficient of 1

8
In expressions, there are many different ways to write multiplication. 1)ab 2)a b 3)a(b) or (a)b 4)(a)(b) 5)a x b We are not going to use the multiplication symbol any more. Why?

9
Division, on the other hand, is written as: 1) 2) x ÷ 3

10
Example of evaluating an expression. Evaluate 3xy – 2x + 7y when x = 2 and y = 3 3(2)(3) – 2(2) + 7(3) 18 – 4 + 21 14 + 21 35 The value of the expression is 35.

11
Word Phrases as Algebraic Expressions Addition (+) Subtraction (–) Multiplication (·) Division ( ) sum plus added to more than increased by total difference minus subtract less than decreased by less product times multiply of double/triple quotient divide shared equally among ratio of

12
Word Phrases as Algebraic Expressions Write as an algebraic expression. Use x to represent “a number.” In words: 5 decreased by a number 5 Translate: 5 decreased bya number –x

13
Word Phrases as Algebraic Expressions Write as an algebraic expression. Use x to represent “a number.” The quotient of a number and 12 In words:a number Translate: x and12 The quotient of

14
Write an algebraic expression for the following m increased by 5 7 times the product of x and t. m + 5 7(xt) or 7xt

15
Write an algebraic expression for the following 11 less than 4 times a number. two more than 6 times a number. 4n - 11 6n + 2

16
Which of the following expressions represents: 7 times a number decreased by 13 1. 7x + 13 2. 7x - 13 3. 13 - 7x 4. 13 + 7x

17
Which one of the following expressions represents: 28 less than three times a number 1. 28 - 3x 2. 3x - 28 3. 28 + 3x 4. 3x + 28

18
Which of the following verbal expressions represents: 2x + 9 1. 9 increased by twice a number 2. a number increased by nine 3. twice a number decreased by 9 4. 9 less than twice a number

19
Which of the following verbal expressions represents: x 2 + 2x 1. the sum of a number squared and twice a number 2. the sum of a number and twice the number 3. twice a number less than the number squared 4. the sum of a number and twice the number squared

20
Which of the following expressions represents: four less than the cube of a number 1. 4 – x 3 2. 4 – 3x 3. 3x – 4 4. x 3 – 4

21
Terms Like terms Terms with the same variable part Same means same letter(s) and power(s) 2x, -5x ¾x 2, 7x 2 31xy, 4xy

22
Terms We simplify variable expressions by combining like terms. To combine like terms, work with the coefficients of the like terms

23
Terms We simplify variable expressions by combining like terms. To combine like terms, work with the coefficients of the like terms

24
Combining Like Terms t + t + t+ t + t There are five variables which are like terms therefore we simply add them like we would if they were numbers. t + t + t+ t + t = 5t

25
Combining Like Terms 4t + 3t + t = (4+3+1)t = 8t 2t 2 + 8 – 5t 2 Rearrange the variables so that all like terms are side by side. 2t 2 – 5t 2 + 8 (notice that the sign in front of the number came with the number) 2t 2 – 5t 2 + 8 = -3t 2 + 8

26
Combining Like Terms 2t + 3t 2 – 2t –t 2 3t 2 – t 2 + 2t – 2t (collecting like terms) 2t 2 + 0 2t 2

27
Which figure below models the simplification of - 4x - 5 + 7x + 7 using these tiles? 1. 2. 3. 4.

28
Combining Like Terms 3x + 5 – 9x = -5 +3b – 7 – 5b = – 6x + 5 -5 – 7 = -12 3b – 5b = -2b – 2b - 12

29
Simplifying Algebraic Expressions Rewrite using as few symbols as possible Use the distributive property if necessary to remove parentheses. Combine like terms More often than not will have numbers and letters in the final answer.

30
Distributive Property or Distributive Property

31
Objective - To use the distributive property to simplify numerical and variable expressions. Order of Operations Distributive Property It works! Why use the distributive property?

32
Simplify using the distributive property. 1) 2) 3) 4) 5) 6)

33
Geometric Model for Distributive Property Two ways to find the area of the rectangle. 4 52 As a wholeAs two parts

34
Geometric Model for Distributive Property Two ways to find the area of the rectangle. 4 52 As a wholeAs two parts same

35
Scientific Notation A short-hand way of writing large numbers without writing all of the zeros.

36
The Distance From the Sun to the Earth 93,000,000

37
Step 1 Move decimal left Leave only one number in front of decimal

38
Step 2 Write number without zeros

39
Step 3 Count how many places you moved decimal If moved to left, make it positive If moved to right, make it negative Make that your power of ten

40
93,000,000 --- Standard Form 9.3 x 10 7 --- Scientific Notation

41
Practice Problem 1) 98,500,000 = 9.85 x 10 ? 2) 64,100,000,000 = 6.41 x 10 ? 3) 279,000,000 = 2.79 x 10 ? 4) 4,200,000 = 4.2 x 10 ? 5) 0.000013 = 1.3 x 10 ? Write in scientific notation. Decide the power of ten. 9.85 x 10 7 6.41 x 10 10 2.79 x 10 8 4.2 x 10 6 1.3 x 10 -5

42
Complete Practice Problems 1) 50,000 2) 7,200,000 3) 802,000,000,000 4) 0.000000000631 Write in scientific notation. 1) 5 x 10 4 2) 7.2 x 10 6 3) 8.02 x 10 11 4) 6.31 x 10 -10

43
Write in Standard Form 6.27 x 10 6 9.01 x 10 4 3.95 x 10 -3 6,270,000 90,100 0.00395 Positive exponent→ move to right Negative exponent → move to left

Similar presentations

© 2024 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google