Evaluating Evaluating ExpressionsExpressionsEvaluating Evaluating

ExpressionsExpressions

R. PortteusR. Portteus

Order of Operations Review

How do you follow the order of operations?

Order of Operations1. ( )2. Exponents Ex. 3² = 3 x 3 = 93. x or ÷, from Left to Right4. + or ─, from Left to Right

Order of Operations ReviewOrder of Operations ReviewOrder of Operations ReviewOrder of Operations Review

20 ÷ 4 x 220 ÷ 4 x 233 + (5 - 8) + (5 - 8) = =

A.A.4343 B. 27B. 27

C. 1C. 1 D. 37D. 37

20 ÷ 4 x 220 ÷ 4 x 233 + (5 - 8) + (5 - 8) = =

A.A.4343

B.B.2727

C.C.11

D.D.3737

20 ÷ 4 x 23 + (5 - 8) = 20 ÷ 4 x 23 + (-3) = 20 ÷ 4 x 8 + (-3) = 5 x 8 + (-3) = 40 + -3 = 37

Evaluating Expressions• Vocabulary:

– Variable – A symbol, usually a letter of the alphabet, such as the letter n, that is used to represent a number.

– Variable expression (A.K.A. - Algebraic Expression) – An expression, such as n – 5, that consists of one or more numbers and variables along with one or more arithmetic operations. (Note: No equal sign)

– Evaluate a Variable Expression – write the expression, substitute a number for each variable, and simplify the result.

How do you describe a variable expression?

Variable Expression

Meaning Operation

5x, 5·x, (5)(x) (same as x·5)

5 times x Multiplication

5 divided by x

Division

5 + x (same as x + 5)

5 plus x Addition

5 – x 5 minus x subtraction

xx

5,5

Journal Reflection

• Evaluate Expressions Video

• Write your reflection from the video.

Journal Reflection

• Let’s watch a short video

Write your reflection from the video.

How do we evaluate expressions for each math operation, + - x ÷ ?

Substitute 4 for n. Simplify

Simplify (means to solve the problem or perform as many of the indicated operations as possible.)

Simplify (means to solve the problem or perform as many of the indicated operations as possible.)

Solution:Solution: Substitute 4 for n. Simplify

Solution:Solution:

Evaluate a Variable Expression with each operation

• Example 1: Evaluate each expression when n = 4.a. n + 3

n + 3 = 4 + 3 = 7

b. n – 3n – 3 = 4 – 3 = 1

Substitute 8 for x. Simplify

Solution:Solution:

Solution:Solution:

Using parenthesis is the preferred method to show multiplication. Additional ways to show multiplication are 5 · 8 and 5 x 8.

Using parenthesis is the preferred method to show multiplication. Additional ways to show multiplication are 5 · 8 and 5 x 8.

Substitute 8 for x. Simplify

Recall that division problems are also fractions – this problem could be written as:

Recall that division problems are also fractions – this problem could be written as:

44

2; 4

8

4

xx

because

x

Evaluate an Algebraic Expression

• Example 2: Evaluate each expression if x = 8.a. 5x

5x = 5(8)= 40

b. x ÷ 4x ÷ 4 = 8 ÷ 4= 2

Let’s go to the next level!

What if an expression has more than one variable?

How do I evaluate expressions with more than one variable?

Substitute 4 for x; 6 for y. simplify

Solution:Solution:

Evaluating Expressions with more than one variable• Example 3: Evaluate each expression

if x = 4, y = 6, and z = 24.a. 5xy

5xy = 5(4)(6)= 120

b.

= 4

Solution:Solution:

y

z

6

24

y

z

Substitute 24 for z; 6 for y. Simplify.

A

A

A

A

A

A

Now You Try… Evaluate each expression given that

a = 6, b = 12, and c = 3.

1. 4ac2. a ÷ c3. a + b + c4. ba5. b – c6. c ÷ b

Substitute the value for a = 6 and c = 3 into the problem and multiply

Substitute the value for a = 6 and c = 3 into the problem and multiply

Click to return to “You try it” slide

Click to return to “You try it” slide

You Try #1Evaluate each expression given that a = 6, b = 12, and c = 3.1. 4ac

4ac = 4(6)(3)= (24)(3)= 72

Substitute the value for a = 6 and c = 3 into the problem and divide

Substitute the value for a = 6 and c = 3 into the problem and divide

Click to return to “You try it” slide

Click to return to “You try it” slide

You Try #2Evaluate each expression given that a = 6, b = 12, and c = 3.2. a ÷ c

a ÷ c = 6 ÷ 3= 2

Substitute the value for a = 6, b=12, and c = 3 into the problem, then add.

Substitute the value for a = 6, b=12, and c = 3 into the problem, then add.

Click to return to “You try it” slide

Click to return to “You try it” slide

You Try #3Evaluate each expression given that a = 6, b = 12, and c = 3.3. a + b + c

a + b + c = 6 + 12 + 3= 18 + 3= 21

Substitute the value for b=12 and a = 6 into the problem, then multiply.

Substitute the value for b=12 and a = 6 into the problem, then multiply.

Click to return to “You try it” slide

Click to return to “You try it” slide

You Try #4Evaluate each expression given that a = 6, b = 12, and c = 3.4. ba

ba = (12)(6)= 72

Substitute the value for b=12 and a = 3 into the problem, then subtract.

Substitute the value for b=12 and a = 3 into the problem, then subtract.

Click to return to “You try it” slide

Click to return to “You try it” slide

You Try #5Evaluate each expression given that a = 6, b = 12, and c = 3.5. b - c

b – c = 12 – 3= 9

Substitute the value for c=3 and b = 12 into the problem, then Divide

Note: It is better to rewrite this division problem as a fraction.

This fraction can now be reduced to its simplest form.

Substitute the value for c=3 and b = 12 into the problem, then Divide

Note: It is better to rewrite this division problem as a fraction.

This fraction can now be reduced to its simplest form.

Divide both numerator and denominator by the GCF = (3) to reduce this fraction.

Divide both numerator and denominator by the GCF = (3) to reduce this fraction.

It is OK to have a fraction as an answer.

It is OK to have a fraction as an answer.

Click to return to “You try it” slide

Click to return to “You try it” slide

You Try #6Evaluate each expression given that a = 6, b = 12, and c = 3.6. c ÷ b

12

3

b

cbc

4

1

3

3

12

3

SummaryTo evaluate expressions:1.Replace a variable with a number2.Follow order of operations to find the solution.3.Follow the algorithms for integers.

Exit Ticket

5 x 6 = 30 9 x 5 = 45

2(8) – 4 = 18/3 + 18 = 16 – 4 = 12 6 + 18 = 24

3 x 4 = 12 10 ÷ 2 + 10 = 5 + 10 = 15

9(4) – 25 = 36 – 25 = 11

9 x 9 = 81

56/8 – 5 = 7 – 5 = 2

14 + 3(6) = 14 + 18 = 32

Homework

• Homework Evaluate Expressions 3 Terms Add/Subtract A and B here