Transcript Powerpoint of Notes

LESSON 4-5
Warm Up
ALGEBRA READINESS
LESSON 4-4
Warm Up
ALGEBRA READINESS
“Comparing and Ordering Rational
Numbers” (4-5)
How do you
order rational
numbers?
To order rational numbers, put them all into decimal form. Then, put the
decimals in order by: 1. graphing them on a number line, or 2. changing them
to decimal form and lining the numbers up vertically by the decimal points,
adding zeroes in blank spaces, and comparing the place values from the left
(largest place values) to the right (smallest place values) [In the result of a tie, go
to the next largest place value until there is no longer a tie].
Example:
Write each fraction as a decimal by
dividing the bottom into the top.
Graph each
decimal on a
number line.
Change the decimals back to their
original form.
ALGEBRA READINESS
Comparing and Ordering Rational Numbers
LESSON 4-5
Additional Examples
Order –0.175, 2 , – 5 , 1.7, –0.95 from least to greatest.
3
8
Write each fraction as a decimal.
2
3
–
0.667
5
= –0.625
8
Then graph each decimal on a number line.
The number line shows that –0.95 < –0.625 < –0.175 < 0.667 < 1.7
So, –0.95 < – 5 < –0.175 < 2 < 1.7.
8
3
Turn the decimals that were changed
back into fractions (original form).
ALGEBRA READINESS
“Comparing and Ordering Rational
Numbers” (4-5)
How do you
compare
fractions?
To compare fractions, you can compare the numerators (number of parts) if the
denominator (size of the parts) are equal. So, if the denominators aren’t the
same, you need to change one or more of the fractions into equivalent fractions
with a common denominator.
Method 1: One way you find a common denominator is to multiply the two
original denominators.
2
3
Example: Recipe A uses 3 cups sugar and Recipe B uses 4 cups sugar.
Which recipe uses more sugar?
3 • 4 = 12
2 • 4 = 8_
3 • 4 = 12
3 • 3 = 9_
4 • 3 = 12
Since
Multiply the denominators together to find a
common denominator
Write equivalent fractions with a denominator of
12 (Hint: Notice that you multiply the each
fraction by the other fractions denominator)
8
9

, then 3  2 , so Recipe B uses more sugar.
12
12
4
3
ALGEBRA READINESS
“Comparing and Ordering Rational
Numbers” (4-5)
Method 2: Another way to find a common denominator is to use the Least Common
Denominator (LCD). The advantage of this method is that you will not need to reduce
the answer later.
What is the “least
common
multiple” (LCM)
and “least
common
denominator”
(LCD)?
Least Common Multiple (LCM): the smallest multiple shared by all of the numbers
Least Common Denominator (LCD): the LCM of two or more denominators (in
other words, the smallest common denominator)
Example:
List the multiples of each denominator
until you find a multiple that is shared
by both numbers (LCM). LCM = 36
Rewrite the fractions into equivalent
fractions with a denominator of 36
(The LCD is 36). Then, compare the
numerators.
5
Since 16  15 , then 4 
,.
12
36 36
9
ALGEBRA READINESS
Comparing and Ordering Rational Numbers
LESSON 4-5
Additional Examples
The Eagles won 7 out of 11 games, while the Seals
won 8 out of 12 games. Which team has the better record?
A common denominator of 11 and 12 is 11 • 12, or 132.
7
7 • 12
84
Eagles: 11 = 11 • 12 = 132
8 • 11
88
8
Seals: 12 = 12 • 11 = 132
Because
Write equivalent fractions with a
denominator of 132.
84
88
7
>
, 8 >
. The Seals have the better record.
132 12
132
11
ALGEBRA READINESS
Comparing and Ordering Rational Numbers
LESSON 4-5
Additional Examples
Compare
5
7
and 12 using their LCD. Use <, =, >.
18
List multiples of each denominator to find their LCD.
Multiples of 18: 18, 36
Multiples of 12: 12, 24, 36
Stop when you find a multiple that
is shared by both numbers.
The LCM of 18 and 12 is 36. So the LCD of the fractions is 36.
14
7
7•2
= 36
=
18
18 • 2
5
5•3
15
=
=
12
12 • 3
36
Use the LCD to write equivalent fractions.
15
14
so 5 > 7 .
>
,
36
36
12
18
ALGEBRA READINESS
Comparing and Ordering Rational Numbers
LESSON 4-5
Lesson Quiz
Compare. Use <, >, or =.
1. 5
<
3. 15
=
12
50
8
15
2. 4
>
36
120
4. 7
= 0.35
5
20
8
11
5. Order 0.17, 1 , –0.3, 0, and – 1 from least to greatest.
5
4
–0.3, – 1 , 0, 0.17, 1
4
5
6. A survey found that 75 out of 125 men and 88 out of
136 women prefer comedy films over action films. Which
group prefers comedy over action films more?
women
ALGEBRA READINESS