pg 45 section 2.1 “basic assumptions”...

Name___________________________________ Period____ 1 pg 45 Section 2.1 “Basic Assumptions” Notes

This chapter develops rules for working with positive and negative numbers.

The two principal operations are addition and multiplication. Subtraction is related to addition and division is related to multiplication.

Simplify: a. 43 78 7+ +

Simplify: b. 6 47 92 8 3+ + + + c. 50 9 2 9⋅ ⋅ ⋅

Simplify: a. 7 9 5m+ + b. ( )( )( )2 3 4x y z

Simplify: c. 4 5 3y+ + d. ( )( )( )5 3 4a b c

Name the property illustrated.

a. ( ) ( )3 14 14 3=

b. ( )1 115 155 5

w w = ⋅

c. If 7 35m = , then 35 7m=

Name the property illustrated.

c. ( ) ( )74 99 1 74 99 1+ + = + +

d. 5 3 3 5+ = +

e. If 2 7w+ = and 7 5 2= + , then 2 5 2w+ = +

Name___________________________________ Period____ 2 Section 2.1 Assignment

Name___________________________________ Period____ 3 pg 49 Section 2.2 “Addition on a number line” Notes

Moves to the left on a number line represent negative numbers and moves to the right represent positive numbers.

Find the sum of 3 and 6− − :

Find the sum of ( )3 6+ − using a number line.

Find the sum of 3 6− + using a number line.

Give an addition statement illustrated by the diagram.

a.

Give an addition statement illustrated by the diagram.

b.

c.

Simplify: a. ( )0 7+ − b. 13.9 0+

Simplify: c. 95 0− + d. ( )0 47+ −

Simplify: a. ( )5 5+ − b. 21.7 21.7− +

Simplify: c. 11 11− + d. ( )0.025 0.025+ −

Simplify: a. ( )8 3− + − b. ( )2 5− + −

Simplify: a. ( ) ( )3 7 4 6a b+ − + + − b. ( )3 6 9 6y− + + + −

Name___________________________________ Period____ 5 pg 54 Section 2.3 “Rules of Addition” Notes

If their signs are the same: ADD and keep the sign

If their signs are different: SUBTRACT and keep the sign of the larger number.

Simplify:

a. ( )12 7− + − b. 15 8− + c. ( )16 3+ − d. 43 76+

Simplify:

e. ( )22 5− + − f. 17 20− + g. ( )11 23+ − h. 93 42+

Simplify:

a. ( ) ( )7 9 15 12+ − + + − b.

291379185462

−

−

Simplify:

a. ( ) ( )10 11 12 13 14+ − + + − + b.

12151026

−

−

An elevator started at the eighteenth floor. It then went down seven floors and up 9 floors. At what floor was the elevator then located?

A submarine descended to a level 230 m below the surface of the ocean. Later it ascended 95 m and then dove 120 m. What was the new depth of the submarine?

On five plays a football team lost 3 yards, gained 15, gained 8, lost 9, and lost 4. What was the net yardage on the play?

During an unusual storm, the temperature fell 8°C, rose 5°C, fell 4°C, an then rose 6°C. If the temperature was 32°C at the outset of the storm, what was it after the storm was over?

Name___________________________________ Period____ 7 pg 59 Section 2.4 “Subtracting Real Numbers” Notes

SUBTRACTING is the same thing as ADDING THE OPPOSITE.

Simplify:

a. 3 12− b. 7 1− − c. ( )4 10− − − d. ( )6y y− +

Simplify:

e. 9 15− f. ( )3 4− − − g. ( )6 17− − − h. ( )6y y− − − +

Whenever you see a sum like this: ( )9 2x+ − or ( )65 12− + − it is usually simplified like this:

9 2x− or 65 12− −

Simplify. a. 30− decreased by 19− b. The opposite of the difference between a and b

Simplify. c. 23− decreased by 2− d. The difference between 68− and 15, decreased by 30.

**When you find the opposite of a sum or a difference, you change the sign of each term of the sum or difference.

Simplify. a. ( )4x− − b. ( )5c n− − + − c. ( )2x y− −

Simplify. a. ( )14x− + b. ( )15r d− − − c. ( )5 8x− +

Evaluate each expression if 4, 5,and 1a b c= − = = − .

a. c a b− − b. ( )a c a b− − −

Name___________________________________ Period____ 9 pg 65 Section 2.5 “The Distributive Property” Notes

Either way you compute it, the total cost is the same.

Simplify using the distributive property.

a. ( )5 2x + b. ( )6 7 10y −

Simplify using the distributive property.

c. ( )5 3m− d. ( )4 8 9w+

The distributive property can make mental math easier.

Simplify. a. 5 83⋅ = b. ( )6 9.5 = c. 18 24

=

Simplify. 75 17 25 17⋅ + ⋅

Simplify. 26 23 26 77⋅ + ⋅

Simplify. a. 8 6y y− b. 3 7 4n n n+ − c. 8( 1) 3n n− +

Simplify. a. 14 20m m− b. 8 2 10a a a− + c. ( )5 7 3n n+ −

Name___________________________________ Period____ 12 pg 70 Section 2.6 “Rules for Multiplication” Notes

Multiply: a. ( )4 7 b. ( )4 7− c. ( )4 7− d. ( )( )4 7− −

Multiply: a. ( )8 6 b. ( )8 6− c. ( )8 6− d. ( )( )8 6− −

State whether the expression names a positive number, a negative number, or zero.

a. ( )( )( )4 6 7 5− − − b. ( )( )( )( )( )2 8 7 5 6− − − − c. ( )( )( )( )9 3 0 5− −

State whether the expression names a positive number, a negative number, or zero.

a. ( )( )( )( )( )23 81 0 15 2− − − − b. ( )( )2 5 20− c. ( )( )( )2 3 12 1− −

Simplify: a. ( )( )3 4x y− − b. ( )4 5p p+ −

Simplify: a. ( )( )6 5m n− b. ( )6 11r r− −

Simplify: a. ( )2 3x y− − b. ( )3 4 2p p− −

Simplify: a. ( )6 5a b− − b. ( )5 3 2 9r r− −

Simplify: a. ( ) ( )2 2 7q w w q− + − − b. ( )3.4 1.6 1.9 3.6y s y s+ − − −

Name___________________________________ Period____ 14 pg 75 Section 2.7 “Problem Solving: Consecutive Integers” Notes

When you count by ones from any number in the set of integers you obtain consecutive integers.

{ }... 3, 2, 1,0,1,2,3...− − −

Natural order - listed in order from least to greatest.

An integer is represented with n.

a. Write the next three integers in natural order from n.

b. Write the integer that immediately precedes n.

c. Write an equation that states that the sum of four consecutive integers, starting with n, is 66.

An integer is represented with d.

a. Write the next four integers in natural order after d.

b. Write the integer that immediately precedes d.

c. Write an equation that states that the sum of three consecutive integers is 24.

Even integers: { }... 6, 4, 2,0,2,4,6...− − − Odd integers: { }... 5, 3, 1,0,1,3,5...− − −

If you count by twos beginning with an even integer you obtain consecutive even integers.

88+2=108+4 or 10+2=12 n, n+2, n+4…

If you count by twos beginning with an odd integer you obtain consecutive odd integers.

1717+2=1917+4 or 19+2=21 n, n+2, n+4…

Write an equation to represent the given relationship among integers.

a. The sum of two consecutive integers is 93.

b. The product of two consecutive even integers is 120.

c. The largest of three consecutive even integers is three times the smallest.

Write an equation to represent the given relationship among integers.

d. The sum of three consecutive integers is 192.

e. The product of two consecutive odd integers is 63.

f. Twice the smaller of two consecutive odd integers is seven more than the larger.

Solve over the given domain: The sum of three consecutive odd integers is 100 more than the smallest integer. What are the integers? Domain for the smallest integer: { }27,37,47

Name___________________________________ Period____ 16 pg 79 Section 2.8 “The reciprocal of a Real Number” Notes

Reciprocals - two numbers whose product is 1.

Multiplicative inverse - another name for reciprocal.

1 1 12 2 2

−− = =

−

State the reciprocal in simplest form.

a. 2− b. 0.25 c. 1 , 0ww

≠

Simplify: a. 1 14 7⋅−

b. 144

y ⋅ c. ( ) 163

ab − −

Simplify: a. 1 13 5⋅

− − b. 19

9m ⋅ c. ( ) 164

8gh −

Simplify: a. ( )1 42 33

m v− b. ( ) ( )1 18 10 15 32 3

u v u v+ − −

Simplify: a. ( )1 24 66

x y− − + b. ( ) ( )1 15 20 2 65 2

a b b a− + − −

Name___________________________________ Period____ 18 pg 83 Section 2.9 “Dividing Real Numbers” Notes

It is very important as you go throughout the year that you understand the following:

Dividing by 2 is the same thing as multiplying by12 .

Multiplying by 15 is the same thing as dividing by 5.

Divide: a. 246

b. 246− c. 24

6− d. 24

6−−

Rewrite each quotient as a product and then simplify.

a. ( ) 1093

− ÷ −

b. 313

−

−

Rewrite each quotient as a product and then simplify.

a. ( ) 5126

− ÷ −

b. 1612

−

Simplify: a. 459x

− b. 13

13w⋅

Simplify: a. 488a

− b. 6

6x

− ⋅

*************Important questions and answers about dividing real numbers*******************

14 10 14 102 2 2

x y x y+= +

pg 45 section 2.1 “basic assumptions”...

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