Transcript 2-3

Adding and Subtracting
2-3 Rational Numbers
Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
Adding and Subtracting
2-3 Rational Numbers
Warm Up
Divide.
1.
21
14
1 1
3.
24
56
3
7
2
2.
12
30
2
5
Write each decimal as a fraction in
simplest form.
11
3
–
1
4. 1.15
5. –0.22
50
20
Adding and Subtracting
2-3 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
Adding and Subtracting
2-3 Rational Numbers
Learn to add and subtract decimals and
rational numbers with like denominators.
Adding and Subtracting
2-3 Rational Numbers
Additional Example 1: 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?
24.08
Write the numbers so
–23.35
that the decimals line up.
0.73
She ran 0.73 second faster in June.
Adding and Subtracting
2-3 Rational Numbers
Check It Out: Example 1
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.
11.500
–0.568
10.932
Add two zeros so
the decimals align.
Tom ran the 100-meter dash in 10.932 seconds
this year.
Adding and Subtracting
2-3 Rational Numbers
Additional Example 2A: Using a Number Line to Add
Rational Decimals
Use a number line to find the sum.
0.3 + (–1.2)
Move right 0.3 units.
From 0.3, move left 1.2 units.
–1.2
0.3
–1.4 –1.0
–0.4
0
0.4
You finish at –0.9, so 0.3 + (–1.2) = –0.9.
Adding and Subtracting
2-3 Rational Numbers
Additional Example 2B: Using a Number Line to Add
Rational Decimals
Use a number line to find the sum.
2
1
+
5
5
1
Move right
units.
5
1
From , move right 2 units.
5
2
5
1
5
0
5
1
5
2
5
You finish at 3 , so
3
5
4
5
1
5
3
2
1
+
=
.
5
5
5
Adding and Subtracting
2-3 Rational Numbers
Check It Out: Example 2A
Use a number line to find the sum.
1.5 + (–1.8)
Move right 1.5 units.
From 1.5, move left 1.8 units.
–1.8
1.5
–0.4
0
0.4 0.8 1.4 1.6
You finish at –0.3, so 1.5 + (–1.8) = –0.3.
Adding and Subtracting
2-3 Rational Numbers
Check It Out: Example 2B
Use a number line to find the sum.
1
3
+
8
8
3
Move right
units.
8
From 3 , move right 1 units.
8
8
4,
You
finish
at
3
1
8
0
1
8
8
which simplifies to 1 .
8
1
4
3
8
2
1
2
5
8
Adding and Subtracting
2-3 Rational Numbers
Adding and Subtracting
2-3 Rational Numbers
Remember!
Subtracting a number is the
same as adding its opposite.
Adding and Subtracting
2-3 Rational Numbers
Additional Example 3: Adding and Subtracting
Fractions with Like Denominators
Add or subtract. Write each answer in
simplest form
2
A. –
9
2
–
9
B.
6
7
6
7
–
–
+ –
–
Subtract numerators.
Keep the denominator.
–2 – 5
7
=
= –
9
9
5
9
5
9
3
7
3
7
3
To add –
subtract the
7 3
opposite
.
7
=
6–3
7
3
=
7
Adding and Subtracting
2-3 Rational Numbers
Check It Out: Example 3
Add or subtract. Write each answer in
simplest form
A. – 1
5
1
–
5
B.
5
9
5
9
–
3
5
–
3
5
+ –
–
Subtract numerators.
Keep the denominator.
=
4
9
–1 – 3
5
4
=–
5
4
To add –
subtract the
9 4
opposite
.
4
=
9
9
5–4
9
1
=
9
Adding and Subtracting
2-3 Rational Numbers
Additional Example 4A: Evaluating Expressions with
Rational Numbers
Evaluate the expression for the given value of
the variable.
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
Adding and Subtracting
2-3 Rational Numbers
Additional Example 4B: Evaluating Expressions with
Rational Numbers
Evaluate the expression for the given value of
the variable.
1
7
+ m for m = 3
10
10
7
1
+ 3
10
10
7
31
+
10
10
7 + 31 = 38
10
10
4
=3
5
1
Substitute 3 10
for m.
3(10) + 1
31
1
3
=
=
10
10
10
Add numerators,
keep the denominator.
Simplify.
Adding and Subtracting
2-3 Rational Numbers
Check It Out: Example 4A
Evaluate the expression for the given value of
the variable.
52.3 – y for y = –7.8
52.3 – (–7.8)
Substitute –7.8 for y.
60.1
Think: 52.3 – (–7.8) =
52.3 + 7.8
Adding and Subtracting
2-3 Rational Numbers
Check It Out: Example 4B
Evaluate the expression for the given value of
the variable.
7
5
+ m for m = 5
8
8
5
7
7
Substitute
5
for m.
+ 5
8
8
8
5(8) + 7
47
5
47
7
+
5
=
=
8
8
8
8
8
52
5 + 47
=
8
8
1
=6
2
Add numerators,
keep the denominator.
Simplify.
Adding and Subtracting
2-3 Rational Numbers
Lesson Quizzes
Standard Lesson Quiz
Lesson Quiz for Student Response Systems
Adding and Subtracting
2-3 Rational Numbers
Lesson Quiz: Part I
Add or subtract.
1. –1.2 + 8.4
7.2
2. 2.5 + (–2.8)
–0.3
3.
3
5
+–
4
4
–
1
2
Evaluate.
4. 62.1 + x for x = –127.0
–64.9
Adding and Subtracting
2-3 Rational Numbers
Lesson Quiz: Part II
5. 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?
0.13 m
Adding and Subtracting
2-3 Rational Numbers
Lesson Quiz for Student Response Systems
1. Add or subtract.
–4.9 + 14.2
A. 4.9
B. 9.3
C. 14.2
D. 19.1
Adding and Subtracting
2-3 Rational Numbers
Lesson Quiz for Student Response Systems
2. Add or subtract.
3.6 + (–3.8)
A. –0.2
B. –0.1
C. 0.1
D. 0.2
Adding and Subtracting
2-3 Rational Numbers
Lesson Quiz for Student Response Systems
3. Add or subtract.
4+ –3
5
5
2
5
A. 4
5
C.
B. 3
5
D. 1
5
Adding and Subtracting
2-3 Rational Numbers
Lesson Quiz for Student Response Systems
4. Evaluate 76.3 + a for a = –143.9.
A. –67.6
B. –43.2
C. –22.3
D. –17.6
Adding and Subtracting
2-3 Rational Numbers
Lesson Quiz for Student Response Systems
5. William threw a discus a distance of 48.6 m
and Robert threw a distance of 49.3 m.
How much farther did Robert throw the
discus than William?
A. 0.5 m
B. 0.6 m
C. 0.7 m
D. 0.8 m