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LESSON 1.4 EVALUATING EXPRESSIONS
Homework Check & REVIEW
Class work and Homework
1.Exercise 1.3.1
2.Pages 5-7
3.P. 14 – 16 Q # 1 - 9
By the end of this lesson, you will be able to:
Understand the meaning of the term “operations”
Understand the meaning of other words related to addition, subtraction, multiplication, division and equal.
Understand what “BEDMAS” stands for.
Apply BEDMAS to expressions with multiple operations.
We have to be able to “translate” words into expressions
What words indicate a particular operation?
Add Subtract SumPlus
More thanIncrease(d) by
PerimeterDeposit
GainGreater than
Up (flights of stairs)Total
MinusTake awayDifference
Reduce(d) byDecrease(d) by
WithdrawalLess than
Fewer (than)Loss of
We have to be able to “translate” words into expressions
What words indicate a particular operation?
Multiply Divide
TimesProduct
OfTwice (×2), double (×2), triple (×3), etc.
Half (×½), Third (×⅓), Quarter (×¼)Area (by)
Percent (of)Square (times itself 2 times)Cube (times itself 3 times)
… to the power of ___(times itself ___ times)
Split into __ partsCost eachQuotient
One-half (÷2), Third (÷3), Quarter (÷4)
IntoPer
Percent (out of 100)
1.FIRST – replace the variables with the known (given) value.
2.THEN – follow the Order of Operations.
To EVALUATEEVALUATE means to FIND THE VALUE OF THE EXPRESSIONEXPRESSION when the value of the variables are known.
An expression is NOT an equation because it DOES NOT have an
equal sign.There are 2 types of expressions.
5 + 84 Numerical3x + 10
AlgebraicNotice there are no equal signs in
these expressions so they are not equations!
A numerical expression contains only
numbers and symbols and NO LETTERS. 5 times 3 plus 8
(5•3) + 8
An algebraic expression contains
only numbers, symbols, and variables. It is sometimes referred to as a variable expression. The product of 3 and x 3xThe sum of m and 8 m + 8The difference of r and 2 r - 2
What is a variable?
A variable represents an unknown value.
1) 4 + x 2) 10 – ?
3) 5y 4) 20
A variable can be any letter of the alphabet since it represents an unknown.
Word Phrases for multiplication are:
The product of 5 and a number c
Seven times a number t
6 multiplied by a number d
5 • c or 5c
7 • t or 7t
6 • d or 6d
The Placement rule for multiplication is:
The product of 5 and a number c
Seven times a number t
6 multiplied by a number d
5 • c or 5c
7 • t or 7t
6 • d or 6d
Always write the variable AFTER the number.
Evaluate means to find the value of an algebraic expression by substituting numbers in for
variables.
m = 26 + m ?6 + 2
8
Evaluate means to find the value of an algebraic expression by substituting numbers in for variables.
r = 37 + r ?7 + 3
10
Evaluate the variable expression when n = 6.
1) n 8 2) n 26 8
14
6 24
Evaluate just means solve by substitution.
Evaluate the variable expression when n = 6.
Evaluate just means solve by substitution.
3) 3n 4) n6
3 6
1866
1
Evaluate the algebraic expression when n = 8.
1) 56n
2) 20 n
568
7
20 8
12
Evaluate the expression if a = 3 and b = 4.
1) 3a b 2) 2b a3 43
9 413
2 34 8 3
5
Evaluate the expression if a = 3 and b = 4.
3) 2ab 4) 5 ab2 43
6 45 43 5 12
1724
Evaluate the expression if x = 5 and y = 3.
1)3xy
33
5
1535
2) 2 2x y2 25 3
25 9
34
An expression is NOT an equation because it does not have an equal sign. There are 2 types of expressions.
NUMERICAL EXPRESSION: Contains only numbers and symbols. Example: 5 • 3 + 4
ALGEBRAIC EXPRESSION: Contains numbers, symbols, and variables. Also known as a variable expression. Example: m + 8
A VARIABLE is a letter or symbol that represents a number. Example: x
TYPES OF EXPRESSIONS #1
#2
Show the substitution. Show your work down.
Circle your answer.
Show your work one step at a time down. No equal signs!
Evaluate means solve.
Evaluate if x = 3 and y = 4 2
2 x y22(3 4)
22(7)2(49)
98
Evaluating Expressions
1) Replace each letter in the 1) Replace each letter in the expression with the assigned expression with the assigned value. value. First, replace each letter in the expression with the value that has been assigned to it. To make your calculations clear and avoid mistakes, always enclose the numbers you're substituting inside parentheses. The value that's given to a variable stays the same throughout the entire problem, even if the letter occurs more than once in the expression.
However, since variables "vary", the value assigned to a particular variable can change from problem to problem, just not within a single problem.
2) Perform the operations 2) Perform the operations in the expression using in the expression using the correct order of the correct order of operations.operations.Once you've substituted the value for the letter, do the operations to find the value of the expression. Don't forget to use the correct order of operations (BEDMAS): first do any operations involving exponents, then do multiplication and division, and finally do addition and subtraction!
I can explain what an expression is and provide an example.
I can explain the types of expression
I can explain the difference between the types of expressions.
I can describe the meaning of a variable.
I can look at an expression and provide a phrase for it.
I can make an expression from a word phrase.
I can explain the placement rule of multiplication.
I can explain the meaning of “substitution”.
I am able to solve an algebraic expression when given the value of a given variable(s).
I am able to replace each letter in the expression with the assigned value.
I am able to perform the operations in the expression using the correct order of operations.
I can write a variable expression that models a real life situation.