Download Section 5.1, “Rational Numbers”

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Copy HW in your planner.
– Text p. 222, #20-60 evens
Open your notebook to a new page and
put the following heading on the top of the
page. Section 5.1 “Rational Numbers”
Chapter 5 “Rational Numbers and
Equations”
Section 5.1 “Rational Numbers”
Section 5.2 “Adding and Subtracting Like Fractions”
Section 5.3 “Adding and Subtracting Unlike Fractions”
Section 5.4 “Multiplying Fractions”
Section 5.5 “Dividing Fractions”
Section 5.6 “Using Multiplicative Inverses to Solve Equations”
Section 5.7 “Equations and Inequalities with Rational Numbers”
Objective
SWBAT write decimals as fractions.
SWBAT write fractions as decimals.
WHOLE NUMBER
a number that is whole (no
decimal) and positive.
0, 1, 2, 3, …
INTEGER
all whole numbers and their
opposites.
… -3, -2, -1, 0, 1, 2, 3, …
Section 5.1, “Rational Numbers”
A RATIONAL NUMBER is a number that can be
written as a quotient of two integers (a fraction).
Numbers that cannot be written as a fraction are
called IRRATIONAL.
RATIONAL NUMBERS
1
2
3

5
12
1
3
1
4
IRRATIONAL NUMBERS
2
3
5

“Rational Numbers”
Rational Numbers
Integers
Integers
-3,-2,-1, 0,1,2,3…
Whole Numbers
Whole Numbers
0,1,2,3,4,5…
Rational Numbers
numbers that can
represented as a
ratio or fraction
a
,b  0
b
D
F
Writing Decimals as Fractions
Decimal numbers can be one of the following:
1) terminating
rational
0.375 
3
8
2) repeating (follows a pattern)
rational
0.454545...  0.45 
5
11
3) nonrepeating (goes on forever without a pattern)
irrational
2.23606797749...  5
D
F
Writing Decimals as Fractions
Write the following decimal as fraction.
0.45
How do you say this?
45
100
“Forty-five hundredths”
45
100
Simplify
335
2 255
9

20
D
Writing Decimal Numbers As
F
Mixed Numbers
Rewrite the decimal number as a sum.
Write the decimal as a fraction.
1.375
+
Simplify
375
1000
“Three hundred
seventy-five
thousandths”
1
+
3
8
3 125
8 125
3

8
3
1
8
D
Writing Decimal Numbers As
F
Mixed Numbers
-3.2+
Rewrite the decimal number as a sum.
Write the decimal as a fraction.
Simplify
2
10
“Two-tenths”
-3
+
1
5
2 1
25
1

5
1
-3
5
D
F
Writing Decimals as Fractions
Write the following decimal as a fraction.
0.09
For repeating decimals use the following strategy:
0.090909…
If there are two repeating digits in the decimal, place the digits over 99.
09
99
Simplify, if
possible
33
3  3 11
1

11
If there is one repeating digit in the decimal, place the digit over 9.
If there are three repeating digits in the decimal, place the digits over 999.
D
F
Writing Decimals as Fractions
Write the following decimal as a fraction.
0.162 For repeating decimals use the following strategy: 0.162162…
If there are three repeating digits in the decimal, place the digits over 999.
162
999
Simplify,
If possible
2 3333
3  3  3  37
6

37
F
D
Writing Fractions as Decimals
7
Rewrite the fraction
as a decimal.
8
A fraction is the quotient of two integers
7
8
This means 7 divided by 8.
7 8
0 87 5
8 7 .0 0
64
6
56
4
40
Finished
F
D
Writing Mixed Numbers as
Decimals
3
18
Rewrite the mixed number as a sum.
Write the fraction as a decimal.
“3 ÷ 8”
+
1
+
0.375
1.375
F
D
Writing Fractions as Decimals
When writing a fraction as a decimal, think of the fraction as a division
expression. Then divide the numerator by the denominator.
4
=
5
4  5 = 0.8
3
1
= 1  (3  16) = 1.1875
16
2
=
0.2222222…
= 2 9
= 0.2
9
F
D
Using a Number Line
Plot the numbers on a number line. Then order them from least to greatest.
2
5 3
, 0.2, 0.67, ,
5
8 2
0.4, 0.2, 0.67, 0.625, 1.5
0
0.2
0.4
0.5 0.625 0.67
1
In order them from least to greatest.
2 5
3
0.2, , , 0.67,
5 8
2
1.5
Homework
– Text p. 222, #20-60 evens