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ARITHMETIC
CHAPTER 1
ARITHMETIC
1.1 Operations with Rational
Numbers
1.2 Exponents, Base &
Decimals
1.3 Estimation & Decimal
Operations
1.4 Equivalence, Order &
Sequences
1.5 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
Addition
continued
Change mixed numbers to fractions.
Find Least Common Denominators
1.1 Adding & Subtracting
1.
1
1
2


2
9
9
2
2 
18 18
Remember to find common denominators first.
Did you forget the 2
1.1 Adding & Subtracting
3.
A.
1
 2 1 
4
1
3
4
4 1
1 1
4 4
B.
3
4
C.
3
4
D.
1
-1
4
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
1.1 Adding & Subtracting
4.
2
-  (1)
3
5
A. 3
2
  1
3
B. - 1
1
C.
3
1
D. 3
First let us change the -(-1) to a +1
Remember: bigger minus smaller, sign
bigger! (result must be positive)
1.1 Multiplying & Dividing
Multiplication & Division Rules of Signed
Numbers:
If same signs, result is positive.
If different signs, result is negative.
Multiplication of
Fractions
Division of
Fractions
a c axc
x 
b d bxd
a c
a d

 x
b d
b c
1.1 Multiplication & Division
5.
1 1
1 
3
5
2
A.

15
1
1
B.
4
1
6 2

3
5
2
C.
5
1
D. 1
15
1.1 Multiplication & Division
7.
 1  2
-    
 5  3
10
A.
3
3
B.
10
1
3

5
2
3
C. 10
3

10
10
D. 3

Same signs means positive result!!
Remember to invert the second fraction!
1.2 Exponent; Base; Decimal
A. Definition of
a n  axaxa...xa
(a is used n times)
Exponents
Place value increases
B. Place
Value & Base moving left of units place,
and decreases moving
right of units place.
1
1
1
1
...10 10 10 10 U .
...
1
2
3
4
10 10 10 10
4
3
2
1
1.2 Examples
1.
(7 )(6 ) 
3
4
( 7  7  7 ) ( 6  6  6  6)
1.2 Examples
5. Select the place value associated
with the underlined digit 83,584.02
1
A.
103
1
B.
10 2
C. 103
D. 10 2
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
14.220
-1.761
It is smaller than
C.11.459
14.22 - 1.22=13
It is larger than
D.12.261
14.22 -2=12.22
1.3 Decimal Examples
10. 3.43 x 2.8
A. 0.9604
B. 8.504
C. 7.1344
D. 9.604
Estimate 3 x 3 = 9
Larger than 3 x 2.8
= 8.24
1.3 Decimal Examples
12. 36.75 0.05 
A. 735
B. 73.5
C. 7.35
D. 0.0735
735 .
0.05 36.75
Dividing by a number between
0 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 %
Example
1
 .25  25%
4
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
19
100
1. 0.19=
A.
19
%
100
9
B. 1
10
19
C.
10
0.19 is not greater than 1
% “means divided by 100”
19/100 %=0.19/100=0.0019
19
D.
100
1.4 Equivalence Examples
2.
350%=
A. 0.350
B. 3.50
C. 350.0
D. 3500
1.4 Equivalence Examples
92
100
3.
A. 0.92
B. 0.092
C. 9.2%
D. 0.92%
1.4 Order Examples
100 5
5.
sm
8.
26
0.82
sm
<
<
11 ~260
20
lg
17
20
lg
17 17 x 5 85


 0.85
20 20 x 5 100
A. =
B. <
C. >
A. =
B. <
C. >
1.4 Sequence Examples
10. Identify the missing term in the
following geometric progression
1
1 1
1
1, ,
,
,
,_____
4 16 64
256
PATTERN:
Signs alternate
Thus,
positive

1
A.
2048
1
B.
1024
Multiply each denom.
by 4 to get the next
256 x 4 = 1024
1
1
C. D.
1024
4
1.5 Percents
Percent increase or
decrease
difference
p

original # 100
" is"
" p"
Percent problems

" of " 100
Real-world problems with percent
R
S
Method
T
U
V
1.5 Percent Examples
1. If 30 is decreased to 6, % decrease?
4
(diff .) 24
p

(orig .) 305 100
5p = 400
A. 8%
B. 24%
p = 80
C. 20%
D. 80%
1.5 Percent Examples
5. What is 120% of 30?
x 120

30 100
A. 0.25
B. 25
10x = 360
x = 36
C. 36
D. 3.6
1.6 Word Problems
1. A car rents for $180 per
week plus $0.25 per mile.
Find the cost of renting this
car for a two week trip of 400
miles for a family of 4.
A. $280
B. $380
C. $460
D. $760
1.6 Word Problems
6. Find the smallest positive
multiple of 6 which leaves a
remainder of 6 when divided
by 10 and a remainder of 8
when divided by 14.
A. 36
B. 18
C. 48
D. 53
REMEMBER
MATH IS FUN
AND …
YOU CAN DO IT