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Pre-Algebra
3-2 Adding and Subtracting Rational Numbers3-2 Adding and Subtracting
Rational Numbers
Pre-Algebra
Warm Up
Problem of the Day
Lesson Presentation
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?
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
Pre-Algebra
3-2 Adding and Subtracting Rational Numbers
Learn to add and subtract decimals and rational numbers with like denominators.
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.
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
0.73Align the decimals.
Additional Example 1: Sports Application
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.
10.932–0.56811.5 Add 2 zeros so the
decimals align.00
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.
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
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
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
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)
72 7
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
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.
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
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
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) + 1 103 = =
31 10
1
10
B.
Evaluate the expression for the given value of the variable.
Additional Example 4B: Evaluating Expressions with Rational Numbers
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.
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 85 = =
31 8
7 8
B.
Try This: Example 4B
Evaluate the expression for the given value of the variable.
1 2= 6
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.
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.
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.
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
