do now 1/12/10 copy hw in your planner. –text p. 222, #20-60 evens open your notebook to a new...
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Do Now 1/12/10Do Now 1/12/10
Copy HW in your planner.Copy HW in your planner.– Text p. 222, #20-60 evensText p. 222, #20-60 evens
Open your notebook to a new page and put the Open your notebook to a new page and put the following heading on the top of the page. following heading on the top of the page. Section Section 5.1 “Rational Numbers”5.1 “Rational Numbers”
Chapter 5 “Rational Numbers and Chapter 5 “Rational Numbers and Equations”Equations”
Section 5.1 “Rational Numbers”Section 5.1 “Rational Numbers”
Section 5.2 “Adding and Subtracting Like Fractions”Section 5.2 “Adding and Subtracting Like Fractions”
Section 5.3 “Adding and Subtracting Unlike Fractions”Section 5.3 “Adding and Subtracting Unlike Fractions”
Section 5.4 “Multiplying Fractions”Section 5.4 “Multiplying Fractions”
Section 5.5 “Dividing Fractions”Section 5.5 “Dividing Fractions”
Section 5.6 “Using Multiplicative Inverses to Solve Equations”Section 5.6 “Using Multiplicative Inverses to Solve Equations”
Section 5.7 “Equations and Inequalities with Rational Numbers”Section 5.7 “Equations and Inequalities with Rational Numbers”
ObjectiveObjective
SWBAT write decimals as fractions.SWBAT write decimals as fractions.
SWBAT write fractions as decimals.SWBAT write fractions as decimals.
WHOLE NUMBERWHOLE NUMBERa number that is whole (no a number that is whole (no
decimal) and positive.decimal) and positive.
0, 1, 2, 3, …0, 1, 2, 3, …
Remember This???
INTEGERINTEGERall whole numbers and all whole numbers and
their opposites.their opposites.
… … -3, -2, -1, 0, 1, 2, 3, …-3, -2, -1, 0, 1, 2, 3, …
Remember This???
Remember This???
Section 5.1, “Rational Numbers”Section 5.1, “Rational Numbers”
A A RATIONAL NUMBER RATIONAL NUMBER is a number that can be is a number that can be written as a quotient of two integers (a fraction). written as a quotient of two integers (a fraction). Numbers that cannot be written as a fraction are Numbers that cannot be written as a fraction are called called IRRATIONALIRRATIONAL..
RATIONAL NUMBERSRATIONAL NUMBERS IRRATIONAL NUMBERSIRRATIONAL NUMBERS
2
1
5
3
1
12
4
31 2 3 5
““Rational Numbers”Rational Numbers”
Rational NumbersRational Numbers
IntegersIntegers
Whole NumbersWhole Numbers 0,1,2,3,4,5…0,1,2,3,4,5…
IntegersIntegers-3,-2,-1, 0,1,2,3…-3,-2,-1, 0,1,2,3…
Rational NumbersRational Numbers numbers that cannumbers that canrepresented as a represented as a ratio or fractionratio or fraction
0, bb
a
Whole NumbersWhole Numbers
Writing Decimals as FractionsWriting Decimals as Fractions
Decimal numbers can be one of the following: Decimal numbers can be one of the following: 1) terminating1) terminating
2) repeating 2) repeating (follows a pattern)(follows a pattern)
3) nonrepeating 3) nonrepeating (goes on forever without a (goes on forever without a pattern)pattern)
5...92360679774.2
11
545.0...454545.0
8
3375.0
rational
rational
irrational
D FD F
Writing Decimals as FractionsWriting Decimals as Fractions
Write the following decimal as fraction.Write the following decimal as fraction.
100
450.450.45 How do you say this?How do you say this?
““Forty-five hundredths”Forty-five hundredths”
SimplifySimplify
100
45
5522
533
20
9
D FD F
Writing Decimal Numbers As Writing Decimal Numbers As Mixed NumbersMixed Numbers
Rewrite the decimal number as a sum.Rewrite the decimal number as a sum.
Write the decimal as a fraction. Write the decimal as a fraction.
11
““Three hundred Three hundred seventy-five seventy-five thousandths”thousandths”
.375.37511 ++
3388++11
3388
SimplifySimplify
1000
375
1258
1253
8
3
D FD F
Writing Decimal Numbers As Writing Decimal Numbers As Mixed NumbersMixed Numbers
Rewrite the decimal number as a sum.Rewrite the decimal number as a sum.
Write the decimal as a fraction. Write the decimal as a fraction.
-3-3
““Two-tenths”Two-tenths” .2.2-3-3 ++
1155++-3-3
1155
SimplifySimplify
10
2
52
12
5
1
D FD F
Writing Decimals as FractionsWriting Decimals as Fractions
Write the following decimal as a fraction.Write the following decimal as a fraction.
0.090.09 For repeating decimals use the following strategy: For repeating decimals use the following strategy:
Simplify, if Simplify, if possiblepossible
99
09
1133
33
11
1
If there are two repeating digits in the decimal, place the digits over 99. If there are two repeating digits in the decimal, place the digits over 99.
0.090909…0.090909…
If there is one repeating digit in the decimal, place the digit over 9. 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. If there are three repeating digits in the decimal, place the digits over 999.
D FD F
Writing Decimals as FractionsWriting Decimals as Fractions
Write the following decimal as a fraction.Write the following decimal as a fraction.
0.1620.162 For repeating decimals use the following strategy: For repeating decimals use the following strategy:
Simplify,Simplify,If possibleIf possible
999
162
37333
33332
37
6
0.162162…0.162162…
If there are three repeating digits in the decimal, place the digits over 999. If there are three repeating digits in the decimal, place the digits over 999.
D FD F
Writing Fractions as Decimals Writing Fractions as Decimals
8
7Rewrite the fraction as a Rewrite the fraction as a decimal.decimal.
8
7 This means 7 divided by 8.This means 7 divided by 8.
A fraction is the quotient of two integersA fraction is the quotient of two integersRemember
87
780
64 6
87
Finished
.00
56 4
05
40
F DF D
Writing Mixed Numbers as Writing Mixed Numbers as DecimalsDecimals
Rewrite the mixed number as a sum.Rewrite the mixed number as a sum.
Write the fraction as a decimal. Write the fraction as a decimal.
1.371.3755
““3 3 ÷ 8÷ 8””
33 8811
++0.3750.375++11
F DF D
54 5
4=
Writing Fractions as DecimalsWriting Fractions as Decimals
)163(1 16
31 =
When writing a fraction as a decimal, think of the fraction as a division expression. Then divide the numerator by the denominator.
= 0.8= 0.8
= 1.1875= 1.1875
92 9
2= = 0.2222222…= 0.2222222…
= 0.2= 0.2
F DF D
0 0.5 1
Plot the numbers on a number line. Then order them from least to greatest.
2
3,
8
5,67.0,2.0,
5
2
1.5
5.1,625.0,67.0,2.0,4.0
0.40.2 0.670.625 1.5
2
3,67.0,
8
5,
5
2,2.0
In order them from least to greatest.
Using a Number LineUsing a Number LineF DF D
HomeworkHomework– Text p. 222, #20-60 evensText p. 222, #20-60 evens