1. Fractions and Decimals

2. Greatest Common Factor
The largest factor shared by two or more numbers.

3. Rainbow Method Find the factors of 12 and 18.
12: 1, 2, 3, 4, 6, GCF:6
18: 1, 2, 3, 6, 9, 18

4. House Method Find the GCF of 12 and 18. 12 18 1x12 1x18 2x6 2x9
1x x18
2x x9
3x x6
GCF = 6

5. Prime Factorization Create factors trees. 12 18 1 x 12 1 x 18
1 x x 18
2 x x 9
2 x x 3
GCF= 2 X 3= 6

6. Simplifying Fractions
Step 1: Find the GCF
Step 2: Divide the numerator and the denominator by the GCF
12 /6 = 2
18 /6= 3

7. Mixed Numbers and Improper Fractions
A mixed number is the sum of a whole number and a fraction.

8. PROPER FRACTIONS
large
Small

9. IMPROPER FRACTIONS
large small

10. MIXED NUMBERS
fraction
whole number

11. Mixed Numbers

12. Improper Fractions

13. 2
2 x 2 + 1 = = 2 2 2

14. 2 2 3 2 = 3 3 -6 2

15. Express the mixed number as an improper fraction.= = 5

16. Express the improper fraction as a mixed number.6 = =
-18 1

17. Least Common Multiples
LCM OR LCD

18. Least Common Multiple (LCM)
The least common multiple is the smallest number that is common between two lists of multiples.

19. EXAMPLE: Find the LCM of 12 and 18
The multiples of 12:
12 x 1 = 12
12 x 2 =24
12 x 3 = 36
12 x 4 = 48
12 x 5 =60
The multiples of 18:
18 x 1 = 18
18 x 2 = 36
18 x 3 = 54
18 x 4 = 72
18 x 5 = 90

20. 12, 24, 36, 48, 60
18, 36, 54, 72, 90
The first number you see in both lists is 36.
The least common multiple of 12 and 18 is 36.

21. Example 2: Find the LCM of 9 and 10
9, 18, 27, 36, 45, 54, 63, 72
81, 90, 99
10, 20, 30, 40, 50, 60, 70, 80
90, 100, 110
If you don’t see a common multiple, make each list go further.
The LCM of 9 and 10 is 90

22. What is the Least Common Multiple of 6 & 8
6 = 6, 12, 18, 24, 30, 36
8 = 8, 16, 24, 32, 40, 48

23. Draw a picture
Use >, <, or =.
<

24. Use >, <, or =.
“Butterfly” method 9
< 10
<

25. “Butterfly” method
Use >, <, or =. 12 10
>
>

26. To order fractions you can draw a picture or use the Least Common Denominator (LCD) or (LCM).

27. Order :
least to greatest
Draw a picture

28. Order the fractions from least to greatest., ,

29. One way to compare or order fractions is to express them with the same denominator.

30. The Least Common Denominator is the Least Common Multiple of the denominators.
LCD = LCM

31. List the fractions in order from greatest to least.
Use LCD
List the fractions in order from greatest to least.

32. Step 1: Find the LCM of the denominators
Use LCD
Step 1: Find the LCM of the denominators

33. Find the LCD:
6: 6, 12, 18, 24, 30, 36, 42, 48…
12: 12, 24, 36, 48 …
9: 9, 18, 27, 36, 45 …
3: 3, 6, 9, 12, 15, 18, 21, 24,
27, 30, 33, 36 …
LCD = 36

34. 6 21 36 36 20 24 36 36 Step 2: Write equivalent fractions. x 6 x 3 x 6

35. Step 3: Compare the numerators
G L 21 6 36 36 24 20 36 36

36. In order from greatest to least:
Use LCD
In order from greatest to least: