(7) Lesson 4.2 - Compare and order Rational Numbers

1. Course 2, Lesson 4-2
Write each fraction or mixed number as a decimal. Use bar notation if
the decimal is a repeating decimal.
1.
2.
3.
Write each decimal as a fraction or mixed number in simplest form.
4. 1.2
5. 0.15
6. What is 2.65 as a fraction in simplest form?
32
5
1
9
5
8

2. Course 2, Lesson 4-2
ANSWERS
1. 2.6
2. 0.625
3.
4.
5.
6.
0.1
1
1
5
3
20
13
2
20

3. WHAT happens when you add,
subtract, multiply, and divide
fractions?
The Number System
Course 2, Lesson 4-2

4. Course 2, Lesson 4-2 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of
Chief State School Officers. All rights reserved.
The Number System
• 7.NS.2 Apply and extend previous understandings of
multiplication and division and of fractions to multiply and divide
rational numbers.
• 7.NS.2b Understand that integers can be divided, provided that
the divisor is not zero, and every quotient of integers (with non-zero
divisor) is a rational number. If p and q are integers, then –(p/q) =
(–p)/q = p/(–q). Interpret quotients of rational numbers by describing
real-world contexts.

5. The Number System
• 7.EE.3 Solve multi-step real-life and mathematical problems posed
with positive and negative rational numbers in any form (whole
numbers, fractions, and decimals), using tools strategically. Apply
properties of operations to calculate with numbers in any form; convert
between forms as appropriate; and assess the reasonableness of
answers using mental computation and estimation strategies.
Mathematical Practices
1 Make sense of problems and persevere in solving them.
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.
Course 2, Lesson 4-2 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of
Chief State School Officers. All rights reserved.

6. • To compare rational numbers
• To order rational numbers
Course 2, Lesson 4-2
The Number System

7. Course 2, Lesson 4-2
The Number System
• rational number
• common denominator
• least common denominator

8. 1
Need Another Example?
2
3
Step-by-Step Example
1. Fill in the with <, >, or = to make –1 –1
a true sentence.
Graph each rational number on a number line.
Mark off equal-size increments of between –2 and –1.
The number line shows that –1 < –1 .

9. Answer
Need Another Example?
Fill in the with <, >, or = to make
–3 –3 a true sentence.
>

10. 1
Need Another Example?
2
3
4
Step-by-Step Example
2. Fill in the with <, >, or = to make
a true sentence.
The LCD of the denominators 12 and 18 is 36.
Since > , > .

11. Answer
Need Another Example?
Fill in the with <, >, or = to make
a true sentence.
<

12. 1
Need Another Example?
2
3
4
Step-by-Step Example
3. In Mr. Huang’s class, 20% of students own roller shoes.
In Mrs. Trevino’s class, 5 out of 29 students own roller
shoes. In which class does a greater fraction of students
own roller shoes?
Express each number as a decimal and then compare.
More students in Mr. Huang’s class own roller shoes.
20% = 0.2 = 5 ÷ 29 ≈ 0.1724
Since 0.2 > 0.1724, 20% > .

13. Answer
Need Another Example?
In a football game, the quarterback completed 11
out of 19 passes. The next week, he completed
60% of his passes. During which game did he
complete the greater fraction of his passes?
the second game

14. 1
Need Another Example?
2
3
Step-by-Step Example
4. Order the set {3.44, π, 3.14, 3.4 } from least to greatest.
Line up the decimal points and compare using place value.
So, the order of the numbers from least to greatest is
3.14, π, 3.44, and 3.4.
3.140
Since 0 < 1, 3.14 < π.
Annex a zero.
3.1415926… π ≈ 3.1415926…
3.440 Annex a zero.
3.444... 3.4 = 3.444…
Since 0 < 4, 3.44 < 3.4.

15. Answer
Need Another Example?
Order the set , 0.6, 0.72, and from least
to greatest.
0.6, , , 0.72

16. 1
Need Another Example?
2
3
Step-by-Step Example
5. Nolan is the quarterback on the football team. He completed
67% of his passes in the first game. He completed 0.64, , and
69% of his passes in the next three games. List Nolan’s completed
passing numbers from least to greatest.
Express each number as a decimal and then compare.
Nolan’s completed passing numbers from least to greatest are
, 0.64, 67%, and 69%.
67% = 0.67 0.64 = 64% = 0.6 69% = 0.69

17. Answer
Need Another Example?
Maddie is a guard on the basketball team. She
made 70% of her field goals in the first game.
She made 0.62, , and 66% of her field goals in
the next three games. List Maddie’s made field
goal statistics from least to greatest.
0.62, 66%, 70%,

18. How did what you learned
today help you answer the
WHAT happens when you add,
subtract, multiply, and divide fractions?
Course 2, Lesson 4-2
The Number System

19. How did what you learned
today help you answer the
WHAT happens when you add,
subtract, multiply, and divide fractions?
Course 2, Lesson 4-2
The Number System
Sample answers:
• In this lesson I learned to graph rational numbers on a
number line, find common denominators when
comparing fractions, and use place value when
ordering rational numbers.

20. Explain how you
would compare
each pair of fractions.
and
and
Ratios and Proportional RelationshipsThe Number System
3
8
 3
18
5
6
 5
22
Course 2, Lesson 4-2