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1-3 Algebraic Expressions 1-3 Algebraic Expressions

1-3 Algebraic Expressions - PowerPoint Presentation

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1-3 Algebraic Expressions - PPT Presentation

Evaluate and simplify algebraic expressions by substituting and using order of operations How to You will need to translate words into mathematical operations What are some words or phrases for ID: 605663

variables equation expressions equations equation variables equations expressions algebraic operations solution true expression equal statement solve solving distribute save

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Slide1

1-3 Algebraic Expressions

Evaluate and simplify algebraic expressions by substituting and using order of operations.Slide2

How to…

You will need to translate words into mathematical operations.

What are some words or phrases for:

Addition

Subtraction

Multiplication

DivisionSlide3

Practice

Ex: The

product of 9 and

b

9b

26 less than

12 (**when you see “less than” notice that the first number goes last)

12 - 26

You try:

The quotient of 6 and 3

6 more than twice the points

T

wo times the sum of a and bSlide4

Modeling a Situation

You start with $20 and save $6 each week. What algebraic expression models the total amount you save?

What do we know?

How can we make an algebraic expression using what we know?

20 + 6wSlide5

Evaluate an Algebraic Expression

Replace variables with values

Use order of operations to simplify

Ex: q + r – 15 if q = 21 and r = 18

21 + 18 -15

39 – 15

24Slide6

Simplifying Expressions

Combine like terms

Use commutative property

Combine

If there is any distributing to be done

distribute FIRST!

 Slide7

1-4 Solving Equations

Solve problems by writing equations.Slide8

Equation

An equation is a statement that two expressions are equal.

Equations have an equal sign, expressions do not.Slide9

Properties of Equality

Reflexive

:

a = a

Ex: 5 = 5

Symmetric

: If

a = b,

then

b = a

Ex: If ½ = 0.5, then 0.5 = ½

Transitive: If a = b and b = c, then a = cEx: If 2.5 = and , then Substitution: If a = b, then you can replace a with b and vice versa.Ex: If a = b and 9 + a = 15, then 9 + b = 15 Slide10

Solving

A

solution of an equation

is a value that makes the equation true.

To find a solution, use

inverse operations

to “undo” the equation.

Must be done to BOTH sides of the equation.

If there is distributing to do, do it first.

Next, undo any addition or subtraction.

Last, undo multiplication or division.

Ex: distribute add 27 subtract 3y divide by 3 Slide11

No Solution or Identities

Equations have

no solution

if all variables cancel and the statement is false.

Ex: 4 = 5 (there are no variables and we know that 4

5)

Equations have

infinitely many solutions

or are

identities

if all variables cancel and the statement is true.

Ex: 0 = 0 (notice the answer is not zero. We know that it is true that 0 = 0 so the equation is an identity) Slide12

Literal Equations

An equation that uses at least 2 different variables.

You solve for a variable “in terms of” the other variables.

Isolate one of the variables and get all others to the opposite side of the equal sign.

You Try:

The equation

relates temperatures in degrees Fahrenheit

F

and degrees Celsius

C

. What is

F in terms of C? multiply by the reciprocal add 32 Slide13

Assignment

Odds p.22 #13-21

p.30 #21-33