arithmetic chapter 1. arithmetic 1.1 operations with rational numbers 1.2 exponents, base &...

ARITHMETIC

CHAPTER 1

ARITHMETIC

1.1 Operations with Rational Numbers1.2 Exponents, Base &

Decimals1.3 Estimation & Decimal Operations1.4 Equivalence, Order & Sequences1.5 Percents 1.6 Word Problems

1.1 Rational Numbers

Types of Numbers:

natural, whole, integers, rational, prime, composite, fractions, mixed

Addition Sign Rules: If same signs, add & keep the sign. If different signs, subtract smaller from larger and give sign of the larger.

Rational Numbers

Change mixed numbers to fractions.

Find Least Common Denominators

Addition continued

1.1 Adding & Subtracting

1.

=+9

1

2

12

18

2

18

92 +

Remember to find common denominators first.Did you forget the 2


=+−4

112

4

11- D.

4

3- C.

4

3 B.

4

13 .A

4

11

4

41 +−3.

It is subtraction! Subtract smaller from larger and give same sign as larger. (Thus result is negative)

We need to get 4/4 from 2: 2 = 1 and 4/4


)1(3

2- −−

3

1- D.

3

1 C. 1- B.

3

5- .A

13

2+−=4.

First let us change the -(-1) to a +1Remember: bigger minus smaller, sign bigger! (result must be positive)

1.1 Multiplying & Dividing

Multiplication & Division Rules of Signed Numbers:

Multiplication of Fractions db

a

d

c

b

a

x

c x x =

Division of Fractions c

d

b

a

d

c

b

ax=÷

If same signs, result is positive. If different signs, result is negative.

1.1 Multiplication & Division

€

13×1

1

5=

€

1

3 ×

5

6 2

15

11 D.

5

2 C.

4

1 B.

15

2 .A

5.1

1.1 Multiplication & Division

=⎟⎠

⎞⎜⎝

⎛−÷⎟⎠

⎞⎜⎝

⎛3

2

5

1-

3

10- D.

10

3- C.

10

3 B.

3

10 .A

€

1

5 ×

2

3

10

3=7.

Same signs means positive result!!

Remember to invert the second fraction!

1.2 Exponent; Base; Decimal

A. Definition of Exponents

B. Place Value & Base

Place value increases moving left of units place, and decreases moving right of units place.

...10

1

10

1

10

1

10

1.10101010...

43211234 U

n times) used is a(

x...xx aaaaan =

1.2 Examples

=)6)((7 43 )777( •• )6666( •••1.

1.2 Examples

5. Select the place value associated with the underlined digit 83,584.02

2323

10 D. 10 C. 10

1 B.

10

1 .A

1.3 Estimation & Operations

A. Estimating Sums, Averages or Products:

An estimate of the average is between the highest and lowest.

1.3 Estimation & Operations

B. Operations with Decimals: To add or subtract: line up dec. pts. To multiply: number of dec. places in the product is the sum of the number of dec. places in the factors. To divide: if divisor is whole number, bring decimal pt. up. If divisor is not, move decimal point as needed.

1.3 Estimation Examples 1. If a unit of water costs $1.82 and 40.435 units were used, which is a reasonable estimate? (Water is sold…)

A. $80,000 B. $800 C. $8000 D.$80

1.3 Estimation Examples 4. 500 students took an algebra test. All scored less than 92 but more than 63. Which of the following could be a reasonable estimate of the avg. score?

A. 96 B. 63 C. 71 D. 60

1.3 Decimal Examples

7. 14.22 - 1.761=

A.12.459

B.13.459

C.11.459

D.12.261

14.220-1.761

It is smaller than

14.22 - 1.22=13It is larger than

14.22 -2=12.22

C. 7.1344


10. 3.43 x 2.8

A. 0.9604 Estimate 3 x 3 = 9

B. 8.504

D. 9.604

Larger than 3 x 2.8 = 8.24


=÷0.0536.75 .

75.3605.0735

A. 735

12.

B. 73.5

C. 7.35D. 0.0735

Dividing by a number between0 and 1 will cause the result to be larger than original number

1.4 Equivalence; Order; Seq.

Rational numbers can be written as fractions, mixed numbers, dec. or %

%2525.4

1 ==Example

To compare two rational numbers, express them in the same way

A sequence of numbers is arranged according to some law. Look for the pattern to find the next number.

1.4 Equivalence Examples

1. 0.19=10019

100

19 D.

10

19 C.

10

91 B.

100

19 .A %

0.19 is not greater than 1

% “means divided by 100”19/100 %=0.19/100=0.0019


2. 350%=

A. 0.350

B. 3.50

C. 350.0

D. 3500


10092

A. 0.92

3.

B. 0.092

C. 9.2%

D. 0.92%

1.4 Order Examples

20

11

26

5

100 ~260

sm lgB. <

20

17 0.82

85.0100

85

5 x 20

5 x 17

20

17===

sm lg<

<

5.

8.

A. =

C. >

B. <A. =

C. >

1.4 Sequence Examples

10. Identify the missing term in the following geometric progression

€

−1,1

4,−

1

16,

1

64,−

1

256,_____

PATTERN: Multiply each denom. by 4 to get the nextSigns alternate

4

1 D.

1024

1- C.

1024

1 B.

2048

1 .A

256 x 4 = 1024Thus, positive

1.5 Percents

100#

p

original

difference=

Percent problems100

""

""

"" p

of

is=

Real-world problems with percent

R S T U V Method

Percent increase or decrease

1.5 Percent Examples

1. If 30 is decreased to 6, % decrease?

10030 .)(

24 .)( p

orig

diff=

5p = 400 p = 80

A. 8% B. 24% C. 20% D. 80%

5

4

1.5 Percent Examples

5. What is 120% of 30?

100

120

30=

x 10x = 360

x = 36

A. 0.25 B. 25 C. 36 D. 3.6

B. $380

Find the cost of renting this

1.6 Word Problems

1. A car rents for $180 per

A. $280

week plus $0.25 per mile.

car for a two week trip of 400miles for a family of 4.

D. $760C. $460

when divided by 14.

D. 53C. 48B. 18

multiple of 6 which leaves a

1.6 Word Problems

6. Find the smallest positive

A. 36

remainder of 6 when dividedby 10 and a remainder of 8

REMEMBER

MATH IS FUN

AND …

YOU CAN DO IT

arithmetic chapter 1. arithmetic 1.1 operations with rational numbers 1.2 exponents, base &...

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