Transcript Writing Decimals as Fractions

Do Now 2/1/10
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Take out HW from Friday
 Text p. 258, #8-40 evens, & 11
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Copy HW in your planner.
 Text p. 262, #2-34 evens
 Chapter 5 TEST Tuesday
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Be ready to copy Problem of the Week #1.
Homework
Text p. 258, #8-40 evens & #11
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8) -0.0875
10) 4.02
11)  263 , 5.24, 5.3 , 134 , 5 9
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12) -1/3
14) 3 1/3
16) 3/8
18) -9/34
20) 7 27/28
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25
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25
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20
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22) -1 1/3
24) 2 5/17
4
26) a
9
 4n 7
5
28)
30) -1 5/6
32) 8 1/3
34) -1 1/8
36) 1/2
38) 2/9
40) -17/21
Objective
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SWBAT review writing fractions as decimals and
vice versa, adding and subtracting like and unlike
fractions, multiplying fractions, dividing
fractions, and solving equations and inequalities
with rational numbers.
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.
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
Writing Decimals as Fractions

Write the following decimal as fraction.
0.45
How do you say this?
“Forty-five hundredths”
45
100
Simplify
335
2 255
9

20
Writing Decimal Numbers As 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
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.
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
Section 5.2 “Adding and Subtracting Like Fractions”
Adding Fractions with Common Denominators
To ADD fractions with common denominators, add their
numerators together.
Add the numerators
a b ab
 
c c
c
2 3

7 7
2 3 5
 
7 7 7
Section 5.2 “Adding and Subtracting Like Fractions”
Subtracting Fractions with Common Denominators
To SUBTRACT fractions with common denominators,
subtract their numerators.
Subtract the numerators
a b a b
 
c c
c
5 1

6 6
4 2
 
6 3
Section 5.3 “Adding and Subtracting Unlike Fractions”
Fractions with Different Denominators
To ADD or SUBTRACT fractions with different
denominators follow these steps:
1. Rewrite the fractions using a common denominator.
2. Add or subtract the numerators.
What is the common
denominator?
2 1

5 7
2 2  7 14


5 5  7 35
1 1 5 5


7 7  5 35
14 5 19


35 35 35
“Adding and Subtracting Mixed Numbers”
Mixed Numbers with Different Denominators
To ADD & SUBTRACT mixed numbers do the following:
1. Write the fractions as improper fractions
2. Write fractions using the LCD.
3. Add or subtract the numerators
4. Simplify if necessary
Try It Out
1 3
4 1
4 8
1. Improper fractions
17 11

4 8
2. Write fractions using LCD.
34 11

8 8
3. Simplify
23

8
7
2
8
5w 7 w
Simplify the Expression. 

12
9
Find the LCD for 12 and 9.
LCD = 36
Rewrite equivalent fractions using the LCD.
5w ?


12 36
7w ?

9 36
5w  5w  3  15w



12
12  3
36
7 w 7 w  4 28w


9
94
36
 15w 28w 13w


36
36
36
Section 5.4, “Multiplying Fractions”
Multiplying Fractions
To multiply fractions:
1. Rewrite fractions as improper fractions (when necessary)
2. Multiply the numerators and denominators.
3. Simplify if necessary.
a c ac
 
b d bd
3 4 12
 
5 7 35
Section 5.5, “Dividing Fractions”
Dividing Fractions
To divide fractions:
1. Rewrite fractions as improper fractions (when necessary)
2. Write the reciprocal of the second fraction.
3. Multiply the numerators and denominators.
4. Simplify if necessary.
a c a d ad
   
b d b c bc
3 4 3 7 21 1
    1
5 7 5 4 20 20
Section 5.6, “Using Multiplicative
Inverses to Solve Equations”
Multiplicative Inverse Property
To solve an equation that has a fractional
coefficient, you can multiply each side of the
equation by the fraction’s multiplicative inverse.
MULTIPLICATIVE
INVERSE
= RECIPROCAL
4
x  12
7
Solve for x.
7 4
7
  x  12  
4 7
4
Multiply each side of the equation
by the MULTIPLICATIVE INVERSE of 4/7
7
1x  12 
4
Multiply
-3
 12  7
1x 
1 4 1
Divide (cancel) common factors
x  21
Section 5.7, “Equations and Inequalities
with Rational Numbers”
Another way to solve an equation with fractions is
to clear fractions by multiplying the WHOLE
EQUATION by the LCD of the fractions.
The resulting equation is equivalent to the original
equation WITHOUT fractions.
Solving Equations by Clearing Fractions
11
4 1
 x 
15
5 3
15
Find LCD of all fractions in the
equation, then multiply the whole
equation by the LCD.
4 1
 11

x

 

5 3
 15
15
11
 x
15
15
4
 
5
11x  12  5
15
11x  7
x
Use distributive property and simplify
each term of the equation.
Two-step equation. Solve for x.
11x  1212  512
 11
7
x
 11
 11
1
3
7
11
Solving Equations by Clearing Decimals
2.3  5.14  0.8m
Look for the greatest number of decimal
places. Then multiply the WHOLE
EQUATION by that power of 10.
100 2.3  5.14  0.8m
100 2.3 100  5.14 100  0.8m
230  514  80m
230(514)  514 514  80m
 284  80m
 284 80m

80
80
m  3.55
Use distributive property and
simplify each term of the equation.
Two-step equation. Solve for m.
BLUFF!
Homework

Text p. 262, #2-34 evens
 Chapter
5 TEST tomorrow!!