1. Take out homework and have it ready to be checked!!!
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2. Objective: Compare and order Rational numbers

3. Least Common Denominator
Vocabulary:
Rational Numbers
Irrational Number
Common Denominator
Least Common Denominator

4. What is a rational number???
any number that can be expressed as a fraction
Ex. Fractions, decimals, %’s, and
integers (whole #’s that are + and -)

5. Examples of Rational Numbers-5
-1.444…
20%
Integers
0.8 -3 5
-27 1 2
-35
Whole Numbers 6
2.22 1 3 35
1.3

6. a number that does not terminate AND does not repeat
Irrational Number:
a number that does not terminate AND does not repeat

7. Pi (π) is an irrational number…

8. A common number that both denominators fit into
Common Denominator:
A common number that both denominators fit into
Examples

9. Comparing Rational Numbers
Which is greater, or ? 7 9 2 9
When two fractions have the same denominator, just compare the numerators. 7 9 2 9
>
because 7 > 2.

10. the smallest number that both denominators will fit into.
Least Common Denominator (LCD):
the smallest number that both denominators will fit into.
Examples

11. Which is greater, or ? 3 4 4 5
When two fractions have different denominators, find the LCD, then compare.

12. Which is greater, or ? What’s the LCD of both fractions? 3 4 4 5
The LCD of the denominators 4 and 5 is 20.
Answer:

14. Compare the Following Fractions
<
>
<

15. Additional Example 1A: Comparing Fractions
Course 2
2-11
Comparing and Ordering Rational Numbers
Additional Example 1A: Comparing Fractions
Compare the fractions. Write < or >. 7 9 5 8
The LCM of the denominators 9 and 8 is 72. 7 9
7 · 8
9 · 8 56 72 =
Write equivalent fractions with 72 as the denominator. = 5 8
5 · 9
8 · 9 45 72 = =
Compare the numbers. 56 72
> 45
, and so 7 9
> 5 8

16. Ordering Rational Numbers
To put decimals in order, line up the decimal points and compare using place value.

17. Ordering Rational Numbers
Compare the decimals
>
0.427
0.425
0.427
Compare the numbers that are different… 7 > 5 so…
0.42 5

18. Additional Example 3: Ordering Fractions and Decimals
Course 2
2-11
Comparing and Ordering Rational Numbers
Additional Example 3: Ordering Fractions and Decimals 4 5
Order ,
0.93, and 0.9 from least to greatest.
Write as decimals with the same number of places. 4 5
= 0.80
0.93 = 0.93
0.9 = 0.90
Graph the numbers on a number line.
0.93
0.80 < 0.90 < 0.93
Compare the decimals in order. 4 5
From least to greatest, the numbers are 0.9, 0.93,

19. Insert Lesson Title Here
Course 2
2-11
Comparing and Ordering Rational Numbers
Insert Lesson Title Here
Lesson Practice
Compare the fractions. Write > or <. 1.
Compare the decimals. Write < or >.
and 0.312 3 7 4 10 5 8 2 3 or
> 2.
< or
> 5 6
4. Order , 0.8, from least to greatest.
0.8, 0.826, 5 6

20. Converting Fractions to Decimals
To convert a Fraction to a Decimal manually, follow these steps:
Step 1: Find a number you can multiply by the bottom of the fraction to make it 10, or 100, or 1000, or any 1 followed by 0s.
Step 2: Multiply both top and bottom by that number.
Step 3. Then write down just the top number, putting the decimal place in the correct spot (one space from the right for every zero in the bottom number)

21. Method #1: Converting with Proportions
Example # 1: Express 3/4 as a Decimal
Step 1: We can multiply 4 by 25 to become 100
Step 2: Multiply top and bottom by 25
= 75

22. Example # 1 continued….
Step 3: Write down 75 with the decimal place 2 spaces from the right (because 100 has 2 zeros);
Answer = 0.75
Can you explain what we just did?
Try to express ¼ as a decimal using method # 1.

23. Try to express ¼ as a decimal using method # 1.

24. Method #2: Convert by Dividing
Example #1: to write 5/8 as a decimal, we need to calculate 5 ÷ 8:
8 √ 5.000
So = as a decimal.
Try this example: write 4/5 as a decimal using division (method #2).

25. write 4/5 as a decimal using division (method #2)

26. Write 3/8 as a decimal using division (method 2)

27. Write 2/7 as a decimal using division (method 2)

28. Convert decimals to Percents
To convert a decimal to a percent
Step 1:Multiply the decimal Step 2: Move the decimal
by to the right two places.
0.45

29. Convert decimals to Percents
0.38
0.235
0.005
1.05
0.023