Order of Operations 1.2 Algebra r of Operations

Order of Operations

Algebra 1.2

r of Operations

P lease

E xcuse

My

D ear

A unt

S haniqua

Parenthesis - Do all grouped operations first.

Exponents - Second

Multiplication and Division - Left to Right.

Addition and Subtraction - Left to Right.

Follow the correct order of operations to evaluate expressions.

Evaluate: Remember to use the correct Order of Operations.

2

1.

18 ? 5 ? 2

2.

2 ?12 ? 6 ? 2 ?

3.

2?3 ? 2?

10

3.

2 ?bd ? c ? ? a 2

Evaluate for a=3, b=4, c=5, d=10

1.

ab ? bc ? d

2.

c ? ad

a?b

?

Solve the following using the correct order of operations:

1.

3? 3?3? 3

6.

32 ?3?3?3

2.

3? 3? 3? 3

7.

3? 3?3?3

3.

(3 ? 3) ? 3 ? 3

8.

(3 ? 3 ? 3) ? 3

4.

3 ?3 ? 3 ?3

9.

3? 3?3?3

5.

(3 ? 3) ? (3 ? 3)

10.

32 ?3?3?3

?

Name________________________ Period _____

Order of Operations Practice

Algebra 1.2

When evaluating expressions, work using the correct order of operations:

P (Parenthesis) Do all grouped operations first.

E (Exponents) Do all operations involving exponents.

M D (Mult./Div.) Do all multiplication and division from left to right.

A S (Add./Sub.) Do all addition and subtraction last - from left to right.

Solve:

1.

( 9 ? 1) 2 ? 5

2.

15 ? 3 ? 2

3.

( 6 ? 3 )( 5 ? 2 )

4.

2 [ 4 ? ( 9 ? 2 )]

6.

(5 ? 2 ) 2

3

5.

7.

9.

6 ? ( 9 ? 1)

2

2 ? 6 ?3

5

3

(15 ? 3 ) ? 6

4

8.

10.

37 ? 2 2 ? 3

3

(5 ? 3 2 ? 3) 2

8

Name________________________ Period _____

Order of Operations Practice

Algebra 1.2

Evaluate for a=3, b=4, c=6

11.

c ? (2 a ? b)2

12.

b2 ? a2

13.

( a ? b )( c ? b ) 2

14.

2 [ c ? ( 3 b ? a )]

15.

c ? (b 2 ? a )

16.

6 (c ? b ) 2

a

17.

c ? b ?a

3

18.

b ? c2 ?a

19.

b (c ? a ) ? 3c

20.

a ? ab 2 ? c

Integer Addition

Algebra

1.4

notes:

Integers are positive and negative Whole Numbers like

-9 127 -90 -54 75

120 65

21 -78

-23 -11

70

Integers are NOT decimals or fractions.

Adding and subtracting integers can seem unnecessarily complicated.

Try the following practice problems first:

Practice:

1.

13 ? 31

2.

13 ? 31

3.

31? 13

4.

? 13 ? ( ? 31)

5.

? 31? 13

6.

? 31 ? ( ? 13)

7.

? 31? 13

8.

31 ? ( ? 13)

If you got all of these right, you already have a proven method for adding

and subtracting integers. Close your ears, sit quietly, and continue using

your own method. If you missed even one, pay close attention and take

notes.

notes:

Adding Integers:

Same Sign Sum

When adding integers with the same sign, find the sum and keep the

sign of both numbers.

1.

13 ? 11

2.

? 13 ? ( ?11)

3.

23 ? 2

4.

? 23 ? ( ?2)

Different Sign Difference

When adding integers with different signs, find the difference and

keep the sign of the ¡®bigger¡¯ number.

1.

? 13 ? 11

2.

13 ? (?11)

3.

23 ? ( ?2)

4.

? 23 ? 2

Mixed Review

Add:

1.

15 ? (?14)

2.

3 ? (?8)

3.

? 7 ? (?8)

4. 13 ?

5.

? 12 ? (?14)

6.

? 6 ? 11

7.

? 9 ? (?5)

8.

(?6)

23 ? (?23)

Subtraction

Algebra 1.4

Subtracting Integers:

SMATO Subtraction Means Add The Opposite

Subtracting Integers is more complicated than adding integers.

To subtract integers, change subtraction to addition and switch the sign

of the second number. Then, follow the two rules we have learned

for adding integers.

Examples: SMATO

Change to addition.

1.

? 11 ? 15

2.

? 21 ? 3

3.

8 ? (?14)

4.

? 30 ? (?5)

Practice: Change to addition, then solve.

1.

13 ? 25

4.

? 29 ? ( ? 6 )

2.

? 11 ? 15

5.

? 15 ? 23

3.

17 ? ( ? 26 )

6.

? 29 ? 21 ? ( ? 7 )

Adding and Subtracting Rationals:

Use the same rules for fractions and decimals as you would for integers:

Same Sign Sum, Different Sign Difference, SMATO.

Examples:

1

1

?

4 10

1.

?

4.

4 .25 ? ( ? 2 .75 )

2.

3.5 ? 4.9

3.

1 ? 7?

? ? ?? ?

3 ? 8?

5.

1

1

?1 ? 5

6

2

6.

? 1 . 4 ? 0 . 03

Practice:

1 2

?

2 3

1.

?

4.

? 6.2 ? (?2.1)

2.

? 1.9 ? 4.5

3.

4 ? 9?

? ?? ?

5 ? 10 ?

5.

1

1

?3 ?5

2

4

6.

2.9 ? (?1.05)

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