This document provides a lesson on adding and subtracting rational numbers. It begins with a warm up problem and example of adding decimals. It then teaches how to add and subtract rational numbers with like denominators by adding or subtracting the numerators and keeping the denominator. Several examples are provided using number lines and evaluating expressions. The document ends with a two part lesson quiz to assess understanding.

1. Pre-Algebra
3-2
Adding and Subtracting
Rational Numbers3-2
Adding and Subtracting
Rational Numbers
Pre-Algebra
Warm UpWarm Up
Problem of the DayProblem of the Day
Lesson PresentationLesson Presentation

2. Pre-Algebra
3-2
Adding and Subtracting
Rational Numbers
Problem of the Day
Four sprinters run a race. In how many
different ways can they arrive at the finish
line, assuming there are no ties?

3. Pre-Algebra
3-2
Adding and Subtracting
Rational Numbers
Problem of the Day
Four sprinters run a race. In how many
different ways can they arrive at the finish
line, assuming there are no ties?
24

4. Pre-Algebra
3-2
Adding and Subtracting
Rational Numbers
Learn to add and subtract decimals and
rational numbers with like denominators.

5. Pre-Algebra
3-2
Adding and Subtracting
Rational Numbers
The 100-meter dash is measured in
thousandths of a second, so runners
must react quickly to the starter pistol.
If you subtract a runner’s reaction time
from the total race time, you can find the
amount of time the runner took to run
the actual 100-meter distance.

6. Pre-Algebra
3-2
Adding and Subtracting
Rational Numbers
In August 2001 at the World University
Games in Beijing, China, Jimyria Hicks ran
the 200-meter dash in 24.08 seconds. Her
best time at the U.S. Senior National Meet in
June of the same year was 23.35 seconds.
How much faster did she run in June?
She ran 0.73 second faster in June.
24.08
–23.35
0.73
Align the decimals.
Additional Example 1: Sports Application

7. Pre-Algebra
3-2
Adding and Subtracting
Rational Numbers
Tom ran the 100-meter dash in 11.5 seconds
last year. This year he improved his time by
0.568 seconds. How fast did Tom run the
100-meter dash this year?
Try This: Example 1
Tom ran the 100-meter dash in 10.932 seconds
this year.
Subtract 0.568 from 11.5 to determine the new time.
10.932
–0.568
11.5 Add 2 zeros so the
decimals align.
00

8. Pre-Algebra
3-2
Adding and Subtracting
Rational Numbers
A. 0.3 + (–1.2)
Move right 0.3 units.
0.4–1.0 –0.4 0
From 0.3, move left 1.2 units.
–1.2
0.3
Use a number line to find the sum.
Additional Example 2A: Using a Number Line to Add
Rational Decimals
–1.4
You finish at –0.9, so 0.3 + (–1.2) = –0.9.

9. Pre-Algebra
3-2
Adding and Subtracting
Rational Numbers
0
1
5
+
2
5
1
5
2
5
1
5
3
5
2
5
Use a number line to find the sum.
Additional Example 2B: Using a Number Line to Add
Rational Decimals
Move right units.
1
5
B.
4
5
1
You finish at , so
1
5
+
2
5
3
5
= .
3
5
From , move right units.
1
5
2
5

10. Pre-Algebra
3-2
Adding and Subtracting
Rational Numbers
A. 1.5 + (–1.8)
Move right 1.5 units.
1.6–0.4 0 0.8
From 1.5, move left 1.8 units.
–1.8
1.5
Use a number line to find the sum.
Try This: Example 2A
You finish at –0.3, so 1.5 + (–1.8) = –0.3.
0.4 1.4

11. Pre-Algebra
3-2
Adding and Subtracting
Rational Numbers
0
3
8
+
1
8
3
8
1
8
1
8
3
8
1
4
1
2
5
8
B.
Try This: Example 2B
Use a number line to find the sum.
Move right units.
3
8
From , move right units.
3
8
1
8
You finish at ,
which simplifies to .
1
2
4
8

12. Pre-Algebra
3-2
Adding and Subtracting
Rational Numbers
ADDING AND SUBTRACTING WITH
LIKE DENOMINATORS
Words Numbers
To add or subtract
rational numbers
with the same
denominator, add or
subtract the
numerators and keep
the denominator.
= , or ––2
7
2
7
4
7
+ – =
2 + (–4)
7
2
7

13. Pre-Algebra
3-2
Adding and Subtracting
Rational Numbers
ADDING AND SUBTRACTING WITH
LIKE DENOMINATORS
Words Algebra
To add or subtract
rational numbers
with the same
denominator, add or
subtract the
numerators and keep
the denominator.
=+
a
d
a + b
d
b
d

14. Pre-Algebra
3-2
Adding and Subtracting
Rational Numbers
Additional Example 3: Adding and Subtracting
Fractions with Like Denominators
Subtract numerators.
Keep the denominator.
2
9
– –
5
9
2
9
– –
5
9
= –
7
9
=
3
7
6
7
+ –
3
7
–2 – 5
9
=
6 + (–3)
7
=
can be written as .–
3
7
–3
7
Add or subtract.
6
7
+
–3
7
A.
B.

15. Pre-Algebra
3-2
Adding and Subtracting
Rational Numbers
=
1
9
5
9
+ –
4
9
5 + (–4)
9
=
5
9
+
–4
9
Try This: Example 3
Subtract numerators.
Keep the denominator.
1
5
– –
3
5
1
5
– –
3
5
= –
4
5
–1 – 3
5
=
Add or subtract.
A.
B. can be written as .–
4
9
–4
9

16. Pre-Algebra
3-2
Adding and Subtracting
Rational Numbers
A. 12.1 – x for x = –0.1
Substitute –0.1 for x.12.1 – (–0.1)
12.2 Think: 12.1 – (–0.1) =
12.1 + 0.1
Evaluate the expression for the given value of
the variable.
Additional Example 4A: Evaluating Expressions with
Rational Numbers

17. Pre-Algebra
3-2
Adding and Subtracting
Rational Numbers
4
5
= 3
+
7
10
31
10
Add numerators,
keep the denominator.
7 + 31
10
Simplify.
+ m for m = 3
7
10
1
10
38
10
=
+ 3
7
10
1
10
Substitute 3 for m.1
10
3(10) + 1
10
3 = =
31
10
1
10
B.
Evaluate the expression for the given value of
the variable.
Additional Example 4B: Evaluating Expressions with
Rational Numbers

18. Pre-Algebra
3-2
Adding and Subtracting
Rational Numbers
52.3 – y for y = –7.8
Substitute –7.8 for y.52.3 – (–7.8)
60.1
Think: 52.3 – (–7.8) =
52.3 + 7.8
Try This: Example 4A
A.
Evaluate the expression for the given value of
the variable.

19. Pre-Algebra
3-2
Adding and Subtracting
Rational Numbers
+
5
8
47
8
Add numerators,
keep the denominator.
5 + 47
8
Simplify.
+ m for m = 5
5
8
7
8
52
8
=
+ 5
5
8
7
8
Substitute 5 for m.7
8
5(8) + 7
8
5 = =
31
8
7
8
B.
Try This: Example 4B
Evaluate the expression for the given value of
the variable.
1
2
= 6

20. Pre-Algebra
3-2
Adding and Subtracting
Rational Numbers
Simplify.
1. –1.2 + 8.4
2. 2.5 + (–2.8)
3.
4. 62.1 + x for x = –127.0
3
4
+
5
4
–
Lesson Quiz: Part 1
Evaluate.

21. Pre-Algebra
3-2
Adding and Subtracting
Rational Numbers
Simplify.
1. –1.2 + 8.4
2. 2.5 + (–2.8)
7.2
–0.3
3.
4. 62.1 + x for x = –127.0
1
2
–
3
4
+
5
4
–
–64.9
Lesson Quiz: Part 1
Evaluate.

22. Pre-Algebra
3-2
Adding and Subtracting
Rational Numbers
Sarah’s best broad jump is 1.6 meters,
and Jill’s best is 1.47 meters. How much
farther can Sarah jump than Jill?
Lesson Quiz: Part 2
5.

23. Pre-Algebra
3-2
Adding and Subtracting
Rational Numbers
Sarah’s best broad jump is 1.6 meters,
and Jill’s best is 1.47 meters. How much
farther can Sarah jump than Jill?
Lesson Quiz: Part 2
5.
0.13 m