Unit 3 ­ Rational Numbers
Focus this unit...
1. Compare and order rational numbers in fraction
and decimal form
2. Solve problems by adding, subtracting, multiplying and dividing
3.
rational numbers.
Apply the order of operations with rational numbers with and
without technology
What is a rational Number?
Any number that can be written in the form of...
(a and b must be integers)
and b≠0
Set of Rational Numbers includes all fractions and all decimals that terminate or repeat...
can be written in fraction form
repeating decimal
terminating decimal
1
** Not all numbers can be written as fractions...
and are numbers that cannot be For example
written in fraction form so...
these are called Irrational Numbers
Irrational Numbers are non­terminating, non­repeating decimals
ie:
= 3.14...."never ending"
2
Review...Equivalent Fractions
are equivalent fractions
x 3
if we multiply or divide the numerator or denominator by the same number, we can find equivalent fractions
x 3
an equivalent fraction to...
x 2
x 2
an equivalent fraction to...
÷ 3
÷ 3
Find equivalent fractions for each of the following...
3
Comparing Fractions...
decide if one fraction is greater than >
<
less than
=
or equal to another fraction
write an equivalent fraction for
>
>
>
Pull
<
Pull
Discover, using equivalent fractions, if one fraction is >, < or = to the other
Answer
Pull
Equivalent fraction
4
Common Denominators
to look for a common denominator, look for the least common multiple for the denominators...
Multiples of the denominators
2 and 3
2, 4, 6, 8, 10...
3, 6, 9, 12...
Common Denominator
Find equivalent fractions for both, with a denominator of 6
x 3
x 2
x 3
x 2
5
Converting Between Fractions and Decimals
Fractions ⇒ Decimals
Use a calculator
"repeating decimal"
Use a calculator
"terminating decimal"
Decimals ⇒Fractions
** Use Place Value
0.7 means 7 tenths
1 decimal = 1 zero or 10
place
0.23 means 23 hundredths
2 decimal = 2 zeros or
places
100 2.3 means 2 and 3 tenths
6
Section 3.1 ­ What is a Rational Number
Remember rational numbers include...
­
integers
­
positive and negative fractions
­
repeating decimals
­
terminating decimals
***NOTE: Negative fractions can be written as...
The negative sign can be written with either the numerator or the denominator But...
because when we divide two negative integers, the answer is positive.
So...
7
Finding a rational number between two given numbers...
a)
1.25 and ­3.26
Draw a number line and label the two points given
­5
­4
­3
­2
­1
0
1
2
4
3
5
A rational number between 1.25 and ­3.26 can be any number in the shaded region (yellow).
ex: ­2.5, ­1, 0.7, etc...
b)
­0.25 and ­0.26
>
<
­0.26
­0.25
Add zeros... ­0.25 = ­0.250, ­0.26 = ­0.260
­0.257
­0.253
>
<
­0.26
­0.255
­0.251
­0.25
8
Try these...
1.
5.6 and 5.7
>
<
Add zeros
>
<
2.
change to
equivalent
fractions
Draw a number line dividing it into quarters...
>
<
two numbers between
If we want more numbers between ­2/4 and 1/4, draw a number line and divide it into eighths.
How many numbers can you find between them???
9
Try...Find the rational numbers between...
Change fractions to equivalent fractions
>
<
2
3
4
Answer lies between these numbers
Possible answers include...
Find two rational numbers between
10
Ordering Rational Numbers in Decimal or Fraction Form...
Example: Using a number line order the following from least to greatest.
A B C D E F
a)
E
F CA
D
B
>
<
­4 ­3 ­2 ­1 0 1 2 3
Least to greatest ­ read numbers from left to right.
11
b)
Convert each fraction to a decimal...
A
B
Set up your decimals to have the same place value...
C
­2.500, ­1.250, ­0.375, 0.555, 0.700, 2.666
D
E
F
C
D
A BE
F
<
>
­3 ­2 ­1 0 1 2 3 4
List your answer...in the form they were in before you converted them to decimals
12
Try these...
1.
2.
Text Practice...
Page 101 ­ #'s 5 ­ 25, 27
Extra Practice 1
3.2 Adding Rational Numbers
13