1. Unit 2. Day 7.

2. Our Rational Number Story
1. Rational numbers can be written as: 𝑝 𝑞 [𝑝 & 𝑞 𝑎𝑟𝑒 𝑖𝑛𝑡𝑒𝑔𝑒𝑟𝑠]
2. Simplifying rational numbers (fractions) makes them easier to work with and to understand
3. Change rational numbers: fraction  decimal
Terminating Decimals:
0.64
RATIONAL
Repeating Decimals:
0. 81
RATIONAL
Non-terminating, non-repeating decimals:
IRRATIONAL …
4. Compare/Order Fractions

3. Today’s Lesson
Mixed number  improper fraction
Ordering collection of fraction/decimals/mixed

4. Improper Fractions
4 4
5 4
6 4
1 4
2 4
3 4
7 4
8 4
9 4
10 4
11 4
12 4
1 2
5 2
3 2 2 1 3

5. Improper Fractions
Mixed Number

6. Improper Fractions Mixed Number. 3 2 5 3
𝑅 1
13 4
3 1 4 4 13 = . 4 13 − 12 − 12 1 1 − 8 2 . 1
𝑅 4 1 8
9 5
1 4 5 = 5 9 5 9 . − − 5 5 4 4 − 40

7. Improper Fractions
Mixed Number

8. Improper Fractions Mixed Number
4 3 7
2 2 7
31 7
16 7 = =
3 4 5
5 5 6
19 5
35 6 = =

10. Today’s Lesson
Mixed number  improper fraction
Ordering collection of fraction/decimals/mixed

11. Example A: Replace each with <, >, or = to make a true sentence.
−2 7 9
− 25 9
− 17 6
− 17 6
>
− 50 18
− 51 18
> 9 6 : 9 , 18 , 27 , 36 , 45 , 54 : 6 , 12 , 18 , 24

12. Example B*: Replace each with <, >, or = to make a true sentence.
− 19 6
− 19 6
−3 1 4
− 13 4
>
− 38 12
− 39 12
> 6 4 : 6 , 12 , 18 , 24 , 30 , 36 : 4 , 8 , 12 , 16

13. Example C: Order the numbers from least to greatest.
−3 1 4 , −0.76, − 7 8 , − 5 6 , −3.2
−0.76
−3.2
−3 1 4
− 7 8
− 5 6
−3.2
−0.76 . . .
−0.875 8 7 2 5 5
−3.25 3
−0.8 3 8 3 3 . . . 4
1 3 8 7 6 5 − − 64 −
1 2 48 1 6 2 − − 56 − 8 18 2 2 4 − − − 40 18 20 2

14. Example C: Order the numbers from least to greatest.
−3 1 4 , −0.76, − 7 8 , − 5 6 , −3.2
− 13 4 −
− 7 8
− 5 6
− 32 10
− 2∙2∙19 2∙2∙5∙5
− 2∙2∙2∙2∙2 2∙5 − − − − −
−3 1 4
− 7 8
− 5 6
−3.2
−0.76
− 19 25
− 16 5