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Interactive Study Guide for Students: Pre-Algebra
Chapter 5: Rational Numbers
Section 1: Writing Fractions as Decimals
Writing Fractions as Decimals
Any fraction
Examples
a
, where b  0 , can be written as a decimal by
b
1. Write
3
as a decimal.
8
dividing the _______________ by the ________________.
So
a
= a  b . If the division ends, or ______________, when the
b
remainder is _________, the decimal is a ______________ decimal.
A _____________number, such as 2
1
as a decimal.
2
3
, is the sum of the whole
4
number and a fraction. Mixed numbers can also be written as a
decimal. 2
2. Write 3
3
3
=2+
= 2 + 0.75 = 2.75
4
4
Not all fractions can be written as a terminating decimal. This is
called a ______________ __________. You can use ______
_______________ to indicate that the 6 repeats forever.
3.Write 
4. Write
Example:
6
as a decimal.
11
2
as a decimal.
15
2
 0.66666666... = 0. 6
3
The ____________ of a repeating decimal is the digit or digits that
repeat.
Compare Fractions and Decimals
It may be easier to compare numbers when they are written as
_________________.
Compare with <, >, or =
5.
3
5
6. 1
7.
1
20
0.75
1.01
13
17
of the girls and
of
20
25
the boys make their own
breakfast. Which is greater?
Interactive Study Guide for Students: Pre-Algebra
Chapter 5: Rational Numbers
Section 2: Rational Numbers
Write Rational Numbers as Fractions
Examples
A number that can be written as a fraction is called a _____________
number.
Write as a fraction in simplest
form:
Examples: 0.75 
3
4
 0. 3  
1
3
28 
28
1
1 5
1 
4 4
Terminating decimals are rational numbers because they can be
written as a fraction with a denominator of __, ___, _____, and so on.
1. 5
2
3
2. -3
3. 0.48
Repeating decimals can be written as a fraction also. The shortcut:
just place the period (the repeating part) over digits of __.
4. 6.375
13
Example: 0. 1 3 =
99
Identify and Classify Rational Numbers
All rational numbers can be written as terminating or repeating
decimals. Decimals that are neither repeating nor terminating are
called ______________ because they cannot be written as fractions.
Examples:   3.141592654...
5. 0. 8
Identify all sets to which each
number belongs.
4.232232223…
6. -6
Rational numbers
7. 2
4
5
8. 0.9141141114…
Interactive Study Guide for Students: Pre-Algebra
Chapter 5: Rational Numbers
Section 3: Multiplying Rational Numbers
Multiply Fractions
To ___________ fractions, multiply the ____________ and then
multiply the _______________.
a c ac
1 2 2
 
b, d  0 example:  
b d bd
3 5 15
Examples
Find the product, then write it
in simplest form
1.
2 3
 =
3 4
2.
4 1
 
7 6
You can either ________ then _________, or simplify ________, and
then multiply.
Change ____________ fractions to ___________ fractions first before
multiplying.
A fraction that contains one or more variables in the numerator or the
denominator is called and ________________ ________________.
3. 
5 3
 
12 8
2
5
4. 1  2
1

2
2a b 2
5.


b d
Dimensional Analysis
You can use __________________ ____________ to compute
problems with units. The easiest way to do this is by using the
____________ method.
6. The landing speed of the
space shuttle is about 216
mph. How far does the
shuttle travel in
landing?
Interactive Study Guide for Students: Pre-Algebra
Chapter 5: Rational Numbers
Section 4: Dividing Rational Numbers
1
hour during
3
Divide Fractions
Examples
Two numbers whose product is 1 are called ________________
______________ or ______________.
Example:
1 3
 1
3 1
Dividing by 2 is the _______ and multiplying by
Example: 12  2  6 12 
1
.
2
1 12

6
2 2
So when we divide by a fraction, we can flip it (write the
_____________) and multiply.
Find the multiplicative inverse
of each number.
1. 
3
8
2. 2
1
5
Find the quotient and write it
in simplest form.
3.
1 5
 
3 9
4.
5
6 
8
5.  7
6.
1
1
2 
2
10
3xy 2 x


4
8
Dimensional Analysis
___________________ _________________ is a very useful way to
solve division of fraction problems with units, especially in
_____________.
7. How many cheerleading
________________ Method Example: How many inches are there in
4 kilometers?
3
22 yds. Of fabric if each
4
7
uniform requires yd.?
8
__________________________________ = _____________
Interactive Study Guide for Students: Pre-Algebra
uniforms can be made with
Chapter 5: Rational Numbers
Section 5: Adding and Subtracting Like Fractions
Add Like Fractions
Examples
Fractions with the same denominator are called _________
____________. To add like fractions, add the numerators and write
the sum over the denominator. Always _________ fractions if
possible.
a c ac
 
b b
b
1 2 1 2 3

Example:  
5 5
5
5
Find the sum, simplify.
1.
3 5
 
7 7
2. 6
5 1
1 
8
8
For mixed fractions, add the whole numbers, then add the fractions,
then simplify.
1
1
2
1 1
2  4  2  4      6  7
2
2
2
2 2
Subtract Like Fractions
The rule to ___________ like fractions is similar to how we add like
fractions. Subtract the numerators and write the difference over the
denominator. Always _____________ fractions if possible.
a c ac
 
b b
b
Example:
1 2 1 2 1
1
 

or 
5 5
5
5
5
3.
9 13


20 20
4.
5 1
 
7 7
1
5. Evaluate
a-b if a=9 and
2
6
b=5 .
6
6.
Interactive Study Guide for Students: Pre-Algebra
Chapter 5: Rational Numbers
n 5n


8 8
Section 6: Least Common Multiple
Least Common Multiple
A __________________ of a number is the product of that number
and a whole number. Sometimes, number have some of the same
multiples. These are called ______________ ________________.
Example: 4: 0, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40
Examples
Find the LCM of the numbers.
1. 20, and 12
2. 24 and 32
6: 0, 6, 12, 18, 24, 30, 36, 42, 48, 54, 60
The _______________ of the nonzero multiples in common is called
the _____________ ______________ __________(LCM). The LCM of
4 and 6 is ____.
3. 18xy2 and 10y
When numbers are large, sometimes it is easier to use
________________ _________________, rather than list all of the
multiples.
Example:
108: 22333
=
240: 222235 =
2233
2435
Multiply the ________________ power of the numbers appearing in
either factorization.
24335 = 2160
Least Common Denominator
Find the LCD of the fractions.
The _____________ ______________ _________________ (LCD) of
two or more fractions is the LCM of the denominator.
One way to compare fractions is to write them using the LCD. We can
multiply the numerator and the denominator of a fraction by the
same number, because it is the same as multiplying the fraction by
___.
4.
5
11
and
9
21
5.
5
3
and
2
8ab
12b
6.
1
6
7
15
Interactive Study Guide for Students: Pre-Algebra
Chapter 5: Rational Numbers
Section 7: Adding and Subtracting Unlike Fractions
Add Unlike Fractions
Fractions with different denominators are called ____________
fractions. To add unlike fractions, use the LCM or any common
multiple and rename the fraction with a common denominator. Then
_______ and simplify.
Example:
1 2 1 5 2 3 5
6 11
      

3 5 3 5 5 3 15 15 15
Examples
1.
2.
1
2


4
3
3 7


8 12
To add mixed numbers, first write them as ____________ fractions,
then do the same thing.
2
9
1
1 5 13 5 3 13 2 15 26 41
5
2 4       


5
2
3 2 3 2 3 3 2 6
6
6
6
4.
Subtract Unlike Fractions
To __________ unlike fractions, use the LCM or any common multiple
and rename the fraction with a common denominator. Then _______
and simplify.
Example:


1
3
3. 1    2  
Example:
5 6
 
21 7
5. 6
1
1
4 
2
5
6 2 6 3 2 7 18 14 4
     


7 3 7 3 3 7 21 21 21
6. The length of a page in a
yearbook is
1 10 in., the top
margin is in. and3 the
2
bottom margin
is in. What
is the length of the4page
inside the margins?
Interactive Study Guide for Students: Pre-Algebra
Chapter 5: Rational Numbers
Section 8: Measures of Central Tendency
Mean, Median, and Mode
Examples
When you have a list of numerical data, it is often helpful to use one
or more numbers to represent the whole set. These numbers are
called ______________ of _____________ _________________. We
will study three types; __________, ______________ and
__________.
Height of BB plyrs. (cm)
Mean: think ___________; the _____ of the data _____________ by
the number of items in the data.
Median: think _________; the _________ number of the ordered
data, or the mean of the middle two numbers. To find the median,
list the numbers from least to __________.
Mode: think ____________; the number or numbers that occur most
often.
A number in the set of data that is much greater or much less than
the rest of the data is called an ___________________
____________. An extreme value can affect the mean of the data.
Vegetable
Calorie
Vegetable
Calorie
Asparagus
14
Cauliflower
10
Beans
30
Celery
17
Bell pepper
20
Corn
66
Broccoli
25
Lettuce
9
Cabbage
17
Spinach
9
Carrots
28
Zucchini
17
Analyze Data
You can use measures of central tendency to analyze data.
130
154
148
155
172
153
160
162
140
149
151
150
1. Find the mean.
2. Find the median.
3. Find the mode.
Make a line plot of the values
2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5,
5, 5, 5, 6, 6, 7, 7, 7, 8, 8, 8, 9,
9, 10, 11
4. Find the mean.
5. Find the median.
6. Find the mode.
The table at the left shows the
number of calories per serving
of each vegetable.
7. Find the mean median and
mode of the calories in
vegetables.
8. Identify an extreme value
and show the mean with it
and without it.
8. A sports store pays their
employees 7, 24, 7, 6, 8, 8, 8,
6 dollars. An extreme sports
store pays 8, 9, 10, 10, 9, 8,
10. Where would you work?
Interactive Study Guide for Students: Pre-Algebra
Chapter 5: Rational Numbers
Section 9: Solving Equations with Rational Numbers
Solve Addition and Subtraction Equations
Examples
You can solve rational number equations the same way you solved
equations with integers.
1. 2.1 = t – 8.5
2. x +
3
2
=
5
3
Solve Multiplication and Division Equations
We solve rational algebraic equation basically the same way as we
solved integers equations, except for one time: when the variable is
being multiplied by a _______________. To solve an equation like
this:
1
x4
2
3. -3y = 1.5
4.
5=
1
y
4
Multiply both sides by the ______________ of the fraction.
2 1
2
 x  4
1 2
1
so x  8
5.
2
x=7
3
Interactive Study Guide for Students: Pre-Algebra
Chapter 5: Rational Numbers
Section 10: Arithmetic and Geometric Sequences
Arithmetic Sequences
Examples
A ___________________ is an ordered list of numbers. An
__________________ sequence is a sequence in which the difference
between any two consecutive terms is the same. So, you can find the
next term in the sequence by adding the same number to the
previous term.
20,
30,
40,
50,
60,
State whether the seq. is
arithmetic. If it is, state the
common difference and write
the next three terms.
1. 8, 5, 2, -1, -4, …
____
2. 1, 2, 3, 7, 11, …
Terms
The difference is called the ________ ________
Geometric Sequence
A _________________ ________________ is a sequence in which the
quotient of any two consecutive terms is the same. You can find the
next term in the sequence by ________________ the previous term
by the same number.
State whether the seq. is
geometric. If it is, state the
common ratio and write the
next three terms.
3. -2, 6, -18, 54, …
4. 20, 10, 5,
1,
4,
16,
64,
256, ,,,
The quotient is called the ______________ ________.
5 5
, ,…
2 2