Transcript 3-2

Page ?? #?-?? ANSWERS
Student Learning Goal Chart
Lesson Reflections
Pre-Algebra Learning Goal
Student will
understand rational
and real numbers.
Students will understand rational and real
numbers by being able to do the following:
• Learn to write rational numbers in equivalent forms (3.1)
• Learn to add and subtract decimals and rational numbers
with like denominators (3.2)
Adding and Subtracting
3-2 Rational Numbers
Today’s Learning Goal Assignment
Learn to add and
subtract decimals and
rational numbers with
like denominators.
Pre-Algebra
Adding and Subtracting
3-2 Rational Numbers
ADDING AND SUBTRACTING WITH
LIKE DENOMINATORS
Words
To add or subtract
rational numbers
with the same
denominator, add
or subtract the
numerators and
keep the
denominator.
Pre-Algebra
Numbers
2+(–4)
4
2
+–
=
7
7
7
2
–2
=
, or –
7
7
Adding and Subtracting
3-2 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.
Pre-Algebra
b =– a+b
a
+
d
d
d
Adding and Subtracting
3-2 Rational Numbers
Pre-Algebra
Adding and Subtracting
3-2 Rational Numbers
Lesson Quiz: Part 1
Simplify.
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
Pre-Algebra
–64.9
Adding and Subtracting
3-2 Rational Numbers
Lesson Quiz: Part 2
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?
0.13m
Pre-Algebra
Adding and Subtracting
3-2 Rational Numbers
Are you ready for the FAST Track?
If YES, prepare for Ch. 3 Section 5
YES, Ch. 3 Section FIVE!
If NO, continue with the Ch. 3 Section 2
lesson!

Pre-Algebra
Adding and Subtracting
3-2 Rational Numbers
Pre-Algebra HW
(3-1, 3-2)
Page 119
#1-21 all
Pre-Algebra
Adding
and
Subtracting
Adding
and
Subtracting
3-2
3-2 Rational
Numbers
Rational
Numbers
Warm Up
Problem of the Day
Lesson Presentation
Pre-Algebra
Pre-Algebra
Adding and Subtracting
3-2 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
Pre-Algebra
Adding and Subtracting
3-2 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
Adding and Subtracting
3-2 Rational Numbers
Today’s Learning Goal Assignment
Learn to add and
subtract decimals and
rational numbers with
like denominators.
Pre-Algebra
Adding and Subtracting
3-2 Rational Numbers
The 100-meter dash is measured in
hundredths 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
Adding and Subtracting
3-2 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
–23.35
0.73
Align the decimals.
She ran 0.73 second faster in June.
Pre-Algebra
Adding and Subtracting
3-2 Rational Numbers
Try This: 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 2 zeros so the
decimals align.
Tom ran the 100-meter dash in 10.932 seconds
this year.
Pre-Algebra
Adding and Subtracting
3-2 Rational Numbers
Additional Example 2A: 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
–1.4 –1.0
–0.4
0
0.4
You finish at –0.9, so 0.3 + (–1.2) = –0.9.
Pre-Algebra
Adding and Subtracting
3-2 Rational Numbers
Additional Example 2B: Using a Number Line to Add
Rational Decimals
Use a number line to find the sum.
B.
2
1
+
5
5
1
Move right
units.
5
1
From , move right 2 units.
5
2
5
1
5
0
Pre-Algebra
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
3-2 Rational Numbers
Try This: Example 2A
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
–0.4
0
0.4 0.8 1.4 1.6
You finish at –0.3, so 1.5 + (–1.8) = –0.3.
Pre-Algebra
Adding and Subtracting
3-2 Rational Numbers
Try This: Example 2B
Use a number line to find the sum.
1
3
+
B.
8
8
3
Move right
units.
8
From 3 , move right 1 units.
8
8
3
8
0
Pre-Algebra
1
8
You finish at 4 ,
1
8
1
4
3
8
8
which simplifies to 1 .
2
1
2
5
8
Adding and Subtracting
3-2 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.
Pre-Algebra
2+(–4)
4
2
+–
=
7
7
7
2
= –2 , or –
7
7
Adding and Subtracting
3-2 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.
Pre-Algebra
b =– a+b
a
+
d
d
d
Adding and Subtracting
3-2 Rational Numbers
Additional Example 3: Adding and Subtracting
Fractions with Like Denominators
Add or subtract.
2
A. –
9
2
–
9
B.
Pre-Algebra
–
–
5
9
5
9
6
7
3
+ –
7
6
7
–3
+
7
Subtract numerators.
Keep the denominator.
–2 – 5
7
=
= –
9
9
3
–3
–
can be written as 7 .
7
=
6 + (–3)
3
=
7
7
Adding and Subtracting
3-2 Rational Numbers
Try This: Example 3
Add or subtract.
1
–
A.
5
1
–
5
B.
Pre-Algebra
–
3
5
–
3
5
Subtract numerators.
Keep the denominator.
=
5
9
+ –
5
9
–4
=
+
9
4
9
–1 – 3
5
4
=–
5
4
–4
–
can be written as 9 .
9
5 + (–4)
1
=
9
9
Adding and Subtracting
3-2 Rational Numbers
Additional Example 4A: Evaluating Expressions with
Rational Numbers
Evaluate the expression for the given value of
the variable.
A. 12.1 – x for x = –0.1
Pre-Algebra
12.1 – (–0.1)
Substitute –0.1 for x.
12.2
Think: 12.1 – (–0.1) =
12.1 + 0.1
Adding and Subtracting
3-2 Rational Numbers
Additional Example 4B: Evaluating Expressions with
Rational Numbers
Evaluate the expression for the given value of
the variable.
1
7
B. 10 + m for m = 3 10
7
1
1
Substitute
3
for m.
+ 3
10
10
10
7
31
3(10) + 1
31
1
+
3
=
=
10
10
10
10
10
7 + 31 = 38
Add numerators,
10
10
keep the denominator.
4
=3
Simplify.
5
Pre-Algebra
Adding and Subtracting
3-2 Rational Numbers
Try This: Example 4A
Evaluate the expression for the given value of
the variable.
A. 52.3 – y for y = –7.8
Pre-Algebra
52.3 – (–7.8)
Substitute –7.8 for y.
60.1
Think: 52.3 – (–7.8) =
52.3 + 7.8
Adding and Subtracting
3-2 Rational Numbers
Try This: Example 4B
Evaluate the expression for the given value of
the variable.
B.
7
5
+ m for m = 5
8
8
5
7
7
Substitute
5
for m.
+ 5
8
8
8
5(8) + 7
31
5
47
7
+
5
=
=
8
8
8
8
8
52
5 + 47
=
8
8
1
=6
2
Pre-Algebra
Add numerators,
keep the denominator.
Simplify.
Adding and Subtracting
3-2 Rational Numbers
Lesson Quiz: Part 1
Simplify.
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
Pre-Algebra
–64.9
Adding and Subtracting
3-2 Rational Numbers
Lesson Quiz: Part 2
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?
0.13m
Pre-Algebra