Adding and Subtracting Rational Numbers

1
Adding and Subtracting
Rational Numbers

• 3.2

2
Warm Up
Divide. 1. 2.
3. Write each
decimal as a fraction in simplest form. 4. 1.15
5. 0.22
3
Learn to add and subtract decimals and rational
numbers with like denominators.
4
Example Sports Application
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?
Align the decimals.
0.73
She ran 0.73 second faster in June.
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Example
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?
Subtract 0.568 from 11.5 to determine the new
time.
Add 2 zeros so the decimals align.
11.5
00
0.568
10.932
Tom ran the 100-meter dash in 10.932 seconds this
year.
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Example Using a Number Line to Add Rational
Decimals
Use a number line to find the sum.
A. 0.3 (1.2)
Move right 0.3 units.
From 0.3, move left 1.2 units.
1.2
0.3
0.4
0
0.4
1.0
1.4
You finish at 0.9, so 0.3 (1.2) 0.9.
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Example Using a Number Line to Add Rational
Decimals
Use a number line to find the sum.
1 5
2 5

B.
3 5
2 5
4 5
1 5
0
1
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Try This
Use a number line to find the sum.
A. 1.5 (1.8)
Move right 1.5 units.
From 1.5, move left 1.8 units.
1.8
1.5
0
0.8
1.6
0.4
1.4
0.4
You finish at 0.3, so 1.5 (1.8) 0.3.
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Try This
Use a number line to find the sum.
3 8
1 8

B.
3 8
1 4
1 2
5 8
1 8
0
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Key Concept
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Key Concept
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.
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Example Adding and Subtracting Fractions with
Like Denominators
Add or subtract.
Subtract numerators. Keep the denominator.
A.
6 7
3 7
B.

13
Try This
Add or subtract.
Subtract numerators. Keep the denominator.
A.
5 9
4 9
B.

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Example Evaluating Expressions with Rational
Numbers
Evaluate the expression for the given value of
the variable.
A. 12.1 x for x 0.1
12.1 (0.1)
Substitute 0.1 for x.
12.2
Think 12.1 (0.1) 12.1 0.1
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Example Evaluating Expressions with Rational
Numbers
Evaluate the expression for the given value of
the variable.
B.
Add numerators, keep the denominator.
Simplify.
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Try This
Evaluate the expression for the given value of
the variable.
A.
52.3 y for y 7.8
52.3 (7.8)
Substitute 7.8 for y.
Think 52.3 (7.8) 52.3 7.8
60.1
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Try This
Evaluate the expression for the given value of
the variable.
B.
Add numerators, keep the denominator.
Simplify.
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Lesson Quiz Part 1
Simplify.
1. 1.2 8.4
7.2
0.3
2. 2.5 (2.8)
3 4
5 4
3.



Evaluate.
4. 62.1 x for x 127.0
64.9
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Lesson Quiz Part 2
5.
Sarahs best broad jump is 1.6 meters, and Jills
best is 1.47 meters. How much farther can Sarah
jump than Jill?
0.13m