Course 3 2-3 Adding and Subtracting Rational Numbers 2-3 Adding and Subtracting Rational Numbers...
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Course 3 2-3 Adding and Subtracting Rational Numbers 2-3 Adding and Subtracting Rational Numbers Course 3 Warm Up Problem of the Day Lesson Presentation
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Course 3
2-3 Adding and Subtracting Rational Numbers
2-3 Adding and Subtracting Rational Numbers
Course 3
Warm Up
Problem of the Day
Lesson Presentation
Course 3
2-3 Adding and Subtracting Rational Numbers
Warm UpDivide.
1. 2.
3. Write each decimal as a fraction in simplest form.
4. 1.15 5. –0.22
21
14
24
56
12
30
2 5
1 1 2
3 7
1 3 20
– 11 50
Course 3
2-3 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
Course 3
2-3 Adding and Subtracting Rational Numbers
Learn to add and subtract decimals and rational numbers with like denominators.
Course 3
2-3 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
Write the numbers so that the decimals line up.
Additional Example 1: Sports Application
Course 3
2-3 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?
Check It Out: 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 two zeros so
the decimals align.00
Course 3
2-3 Adding and Subtracting Rational Numbers
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.
Course 3
2-3 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
4 5
1
You finish at , so
1 5
+ 2 5
3 5
= .
3 5
From , move right units.1 5
2 5
Course 3
2-3 Adding and Subtracting Rational Numbers
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.
Check It Out: Example 2A
You finish at –0.3, so 1.5 + (–1.8) = –0.3.
0.4 1.4
Course 3
2-3 Adding and Subtracting Rational Numbers
0
3 8
+1 8
3 8
1 8
1 8
3 8
1 4
1 2
5 8
Check It Out: 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
Course 3
2-3 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 – –3 5
3 5
4 5
+ – =1 + (–4)
51 5
Course 3
2-3 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
Course 3
2-3 Adding and Subtracting Rational Numbers
Remember!
Subtracting a number is the same as adding its opposite.
Course 3
2-3 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. Write each answer in simplest form
6 7
+ –3 7
A.
B.
Course 3
2-3 Adding and Subtracting Rational Numbers
= 1 9
5 9
+ – 4 9
5 + (–4) 9
=5 9
+ –4 9
Check It Out: Example 3
Subtract numerators. Keep the denominator.
1 5
– – 3 5
1 5
– – 3 5
= – 4 5
–1 – 3 5
=
Add or subtract. Write each answer in simplest form
A.
B. can be written as . – 4 9
–4 9
Course 3
2-3 Adding and Subtracting Rational Numbers
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
Course 3
2-3 Adding and Subtracting Rational Numbers
4 5= 3
+ 7 10
31 10
Add numerators, keep the denominator.
7 + 31 10
Simplify.
+ m for m = 37 10
1 10
38 10
=
+ 3 7 10
1 10
Substitute 3 for m.1 10
3(10) + 1 103 = =
31 10
1
10
Evaluate the expression for the given value of the variable.
Additional Example 4B: Evaluating Expressions with Rational Numbers
Course 3
2-3 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
Check It Out: Example 4A
Evaluate the expression for the given value of the variable.
Course 3
2-3 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 = =
47 8
7 8
Check It Out: Example 4BEvaluate the expression for the given value of the variable.
1 2= 6
Course 3
2-3 Adding and Subtracting Rational Numbers
Add or subtract.
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.
Course 3
2-3 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
