Real Numbers & Number Lines (Geometry 2_1)
rfant
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Jul 30, 2007
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About This Presentation
Students consider real numbers and number lines, decimals, and rational numbers.
Slide Content
Real Numbers and Number LinesReal Numbers and Number Lines
You will learn to find the distance between two points on a
number line.
1) Whole Numbers
2) Natural Numbers
3) Integers
4) Rational Numbers
5) Terminating Decimals
6) Nonterminating Decimals
7) Irrational Numbers
8) Real Numbers
9) Coordinate
10 Origin
11) Measure
12) Absolute Value
You will learn to find the distance between two points on a
number line.
1) Whole Numbers
2) Natural Numbers
3) Integers
4) Rational Numbers
5) Terminating Decimals
6) Nonterminating Decimals
7) Irrational Numbers
8) Real Numbers
9) Coordinate
10 Origin
11) Measure
12) Absolute Value
Real Numbers and Number LinesReal Numbers and Number Lines
Numbers that share common properties can be classified or grouped into sets.
Different sets of numbers can be shown on numbers lines.
0 21 43 65 7 98 10
This figure shows the set of _____________ .
Numbers that share common properties can be classified or grouped into sets.
Different sets of numbers can be shown on numbers lines.
0 21 43 65 7 98 10
This figure shows the set of _____________ .
Real Numbers and Number LinesReal Numbers and Number Lines
Numbers that share common properties can be classified or grouped into sets.
Different sets of numbers can be shown on numbers lines.
0 21 43 65 7 98 10
This figure shows the set of _____________ . whole numbers
Numbers that share common properties can be classified or grouped into sets.
Different sets of numbers can be shown on numbers lines.
0 21 43 65 7 98 10
This figure shows the set of _____________ . whole numbers
Real Numbers and Number LinesReal Numbers and Number Lines
Numbers that share common properties can be classified or grouped into sets.
Different sets of numbers can be shown on numbers lines.
0 21 43 65 7 98 10
This figure shows the set of _____________ . whole numbers
The whole numbers include 0 and the natural, or counting numbers.
Numbers that share common properties can be classified or grouped into sets.
Different sets of numbers can be shown on numbers lines.
0 21 43 65 7 98 10
This figure shows the set of _____________ . whole numbers
The whole numbers include 0 and the natural, or counting numbers.
Real Numbers and Number LinesReal Numbers and Number Lines
Numbers that share common properties can be classified or grouped into sets.
Different sets of numbers can be shown on numbers lines.
0 21 43 65 7 98 10
This figure shows the set of _____________ . whole numbers
The whole numbers include 0 and the natural, or counting numbers.
The arrow to the right indicate that the whole numbers continue _________.
Numbers that share common properties can be classified or grouped into sets.
Different sets of numbers can be shown on numbers lines.
0 21 43 65 7 98 10
This figure shows the set of _____________ . whole numbers
The whole numbers include 0 and the natural, or counting numbers.
The arrow to the right indicate that the whole numbers continue _________.
Real Numbers and Number LinesReal Numbers and Number Lines
Numbers that share common properties can be classified or grouped into sets.
Different sets of numbers can be shown on numbers lines.
0 21 43 65 7 98 10
This figure shows the set of _____________ . whole numbers
The whole numbers include 0 and the natural, or counting numbers.
The arrow to the right indicate that the whole numbers continue _________.indefinitely
Numbers that share common properties can be classified or grouped into sets.
Different sets of numbers can be shown on numbers lines.
0 21 43 65 7 98 10
This figure shows the set of _____________ . whole numbers
The whole numbers include 0 and the natural, or counting numbers.
The arrow to the right indicate that the whole numbers continue _________.indefinitely
Real Numbers and Number LinesReal Numbers and Number Lines
0 21 43-5 5-4 -2-3 -1
This figure shows the set of _______ .
0 21 43-5 5-4 -2-3 -1
This figure shows the set of _______ .
Real Numbers and Number LinesReal Numbers and Number Lines
0 21 43-5 5-4 -2-3 -1
This figure shows the set of _______ . integers
positive integers
0 21 43-5 5-4 -2-3 -1
This figure shows the set of _______ . integers
positive integers
Real Numbers and Number LinesReal Numbers and Number Lines
0 21 43-5 5-4 -2-3 -1
This figure shows the set of _______ . integers
positive integersnegative integers
0 21 43-5 5-4 -2-3 -1
This figure shows the set of _______ . integers
positive integersnegative integers
Real Numbers and Number LinesReal Numbers and Number Lines
0 21 43-5 5-4 -2-3 -1
This figure shows the set of _______ . integers
positive integersnegative integers
The integers include zero, the positive integers, and the negative integers.
The arrows indicate that the numbers go on forever in both directions.
0 21 43-5 5-4 -2-3 -1
This figure shows the set of _______ . integers
positive integersnegative integers
The integers include zero, the positive integers, and the negative integers.
The arrows indicate that the numbers go on forever in both directions.
Real Numbers and Number LinesReal Numbers and Number Lines
A number line can also show ______________.
0 21-1-2 4
3
3
8
2
3
13
8
1
5
-
5
3
-
11
8
-
A number line can also show ______________.
0 21-1-2 4
3
3
8
2
3
13
8
1
5
-
5
3
-
11
8
-
Real Numbers and Number LinesReal Numbers and Number Lines
A number line can also show ______________. rational numbers
0 21-1-2 4
3
3
8
2
3
13
8
1
5
-
5
3
-
11
8
-
A number line can also show ______________. rational numbers
0 21-1-2 4
3
3
8
2
3
13
8
1
5
-
5
3
-
11
8
-
Real Numbers and Number LinesReal Numbers and Number Lines
A number line can also show ______________. rational numbers
0 21-1-2 4
3
3
8
2
3
13
8
1
5
-
5
3
-
11
8
-
A rational number is any number that can be written as a _______,
where a and b are integers and b cannot equal ____.
a
b
A number line can also show ______________. rational numbers
0 21-1-2 4
3
3
8
2
3
13
8
1
5
-
5
3
-
11
8
-
A rational number is any number that can be written as a _______,
where a and b are integers and b cannot equal ____.
a
b
Real Numbers and Number LinesReal Numbers and Number Lines
A number line can also show ______________. rational numbers
0 21-1-2 4
3
3
8
2
3
13
8
1
5
-
5
3
-
11
8
-
A rational number is any number that can be written as a _______,
where a and b are integers and b cannot equal ____.
a
b
fraction
A number line can also show ______________. rational numbers
0 21-1-2 4
3
3
8
2
3
13
8
1
5
-
5
3
-
11
8
-
A rational number is any number that can be written as a _______,
where a and b are integers and b cannot equal ____.
a
b
fraction
Real Numbers and Number LinesReal Numbers and Number Lines
A number line can also show ______________. rational numbers
0 21-1-2 4
3
3
8
2
3
13
8
1
5
-
5
3
-
11
8
-
A rational number is any number that can be written as a _______,
where a and b are integers and b cannot equal ____.
a
b
fraction
zero
A number line can also show ______________. rational numbers
0 21-1-2 4
3
3
8
2
3
13
8
1
5
-
5
3
-
11
8
-
A rational number is any number that can be written as a _______,
where a and b are integers and b cannot equal ____.
a
b
fraction
zero
Real Numbers and Number LinesReal Numbers and Number Lines
A number line can also show ______________. rational numbers
0 21-1-2 4
3
3
8
2
3
13
8
1
5
-
5
3
-
11
8
-
A rational number is any number that can be written as a _______,
where a and b are integers and b cannot equal ____.
a
b
fraction
zero
The number line above shows some of the rational numbers between -2 and 2.
In fact, there are _______ many rational numbers between any two integers.
A number line can also show ______________. rational numbers
0 21-1-2 4
3
3
8
2
3
13
8
1
5
-
5
3
-
11
8
-
A rational number is any number that can be written as a _______,
where a and b are integers and b cannot equal ____.
a
b
fraction
zero
The number line above shows some of the rational numbers between -2 and 2.
In fact, there are _______ many rational numbers between any two integers.
Real Numbers and Number LinesReal Numbers and Number Lines
A number line can also show ______________. rational numbers
0 21-1-2 4
3
3
8
2
3
13
8
1
5
-
5
3
-
11
8
-
A rational number is any number that can be written as a _______,
where a and b are integers and b cannot equal ____.
a
b
fraction
zero
The number line above shows some of the rational numbers between -2 and 2.
In fact, there are _______ many rational numbers between any two integers.infinitely
A number line can also show ______________. rational numbers
0 21-1-2 4
3
3
8
2
3
13
8
1
5
-
5
3
-
11
8
-
A rational number is any number that can be written as a _______,
where a and b are integers and b cannot equal ____.
a
b
fraction
zero
The number line above shows some of the rational numbers between -2 and 2.
In fact, there are _______ many rational numbers between any two integers.infinitely
Real Numbers and Number LinesReal Numbers and Number Lines
Rational numbers can also be represented by ________.
Rational numbers can also be represented by ________.
Real Numbers and Number LinesReal Numbers and Number Lines
Rational numbers can also be represented by ________.decimals
3
0.375
8
=
2
0.666 . . .
3
=
0
0
7
=
Rational numbers can also be represented by ________.decimals
3
0.375
8
=
2
0.666 . . .
3
=
0
0
7
=
Real Numbers and Number LinesReal Numbers and Number Lines
Rational numbers can also be represented by ________.decimals
3
0.375
8
=
2
0.666 . . .
3
=
0
0
7
=
Decimals may be __________ or _____________.
Rational numbers can also be represented by ________.decimals
3
0.375
8
=
2
0.666 . . .
3
=
0
0
7
=
Decimals may be __________ or _____________.
Real Numbers and Number LinesReal Numbers and Number Lines
Rational numbers can also be represented by ________.decimals
3
0.375
8
=
2
0.666 . . .
3
=
0
0
7
=
Decimals may be __________ or _____________.terminating
0.375
0.49
terminating decimals.
Rational numbers can also be represented by ________.decimals
3
0.375
8
=
2
0.666 . . .
3
=
0
0
7
=
Decimals may be __________ or _____________.terminating
0.375
0.49
terminating decimals.
Real Numbers and Number LinesReal Numbers and Number Lines
Rational numbers can also be represented by ________.decimals
3
0.375
8
=
2
0.666 . . .
3
=
0
0
7
=
Decimals may be __________ or _____________.terminating nonterminating
0.375
0.49
terminating decimals.
0.666 . . .
-0.12345 . . .
nonterminating decimals.
Rational numbers can also be represented by ________.decimals
3
0.375
8
=
2
0.666 . . .
3
=
0
0
7
=
Decimals may be __________ or _____________.terminating nonterminating
0.375
0.49
terminating decimals.
0.666 . . .
-0.12345 . . .
nonterminating decimals.
Real Numbers and Number LinesReal Numbers and Number Lines
Rational numbers can also be represented by ________.decimals
3
0.375
8
=
2
0.666 . . .
3
=
0
0
7
=
Decimals may be __________ or _____________.terminating nonterminating
0.375
0.49
terminating decimals.
0.666 . . .
-0.12345 . . .
nonterminating decimals.
The three periods following the digits in the nonterminating decimals indicate
that there are infinitely many digits in the decimal.
Rational numbers can also be represented by ________.decimals
3
0.375
8
=
2
0.666 . . .
3
=
0
0
7
=
Decimals may be __________ or _____________.terminating nonterminating
0.375
0.49
terminating decimals.
0.666 . . .
-0.12345 . . .
nonterminating decimals.
The three periods following the digits in the nonterminating decimals indicate
that there are infinitely many digits in the decimal.
Real Numbers and Number LinesReal Numbers and Number Lines
Some nonterminating decimals have a repeating pattern.
0.17171717 . . . repeats the digits 1 and 7 to the right of the decimal point.
Some nonterminating decimals have a repeating pattern.
0.17171717 . . . repeats the digits 1 and 7 to the right of the decimal point.
Real Numbers and Number LinesReal Numbers and Number Lines
Some nonterminating decimals have a repeating pattern.
0.17171717 . . . repeats the digits 1 and 7 to the right of the decimal point.
A bar over the repeating digits is used to indicate a repeating decimal.
0.171717 . . . 0.17=
Some nonterminating decimals have a repeating pattern.
0.17171717 . . . repeats the digits 1 and 7 to the right of the decimal point.
A bar over the repeating digits is used to indicate a repeating decimal.
0.171717 . . . 0.17=
Real Numbers and Number LinesReal Numbers and Number Lines
Some nonterminating decimals have a repeating pattern.
0.17171717 . . . repeats the digits 1 and 7 to the right of the decimal point.
A bar over the repeating digits is used to indicate a repeating decimal.
0.171717 . . . 0.17=
Each rational number can be expressed as a terminating decimal or a
nonterminating decimal with a repeating pattern.
Some nonterminating decimals have a repeating pattern.
0.17171717 . . . repeats the digits 1 and 7 to the right of the decimal point.
A bar over the repeating digits is used to indicate a repeating decimal.
0.171717 . . . 0.17=
Each rational number can be expressed as a terminating decimal or a
nonterminating decimal with a repeating pattern.
Real Numbers and Number LinesReal Numbers and Number Lines
Decimals that are nonterminating and do not repeat
are called _______________.
Decimals that are nonterminating and do not repeat
are called _______________.
Real Numbers and Number LinesReal Numbers and Number Lines
Decimals that are nonterminating and do not repeat
are called _______________.irrational numbers
Decimals that are nonterminating and do not repeat
are called _______________.irrational numbers
Real Numbers and Number LinesReal Numbers and Number Lines
Decimals that are nonterminating and do not repeat
are called _______________.irrational numbers
6.028716 . . .
and
0.101001000 . . .
appear to be irrational numbers
Decimals that are nonterminating and do not repeat
are called _______________.irrational numbers
6.028716 . . .
and
0.101001000 . . .
appear to be irrational numbers
Real Numbers and Number LinesReal Numbers and Number Lines
____________ include both rational and irrational numbers.
0 21-1-2 3
8
1.8603 . . .- 0.8- 0.6 1.762 . . .
0.25-
____________ include both rational and irrational numbers.
0 21-1-2 3
8
1.8603 . . .- 0.8- 0.6 1.762 . . .
0.25-
Real Numbers and Number LinesReal Numbers and Number Lines
____________ include both rational and irrational numbers.Real numbers
0 21-1-2 3
8
1.8603 . . .- 0.8- 0.6 1.762 . . .
0.25-
____________ include both rational and irrational numbers.Real numbers
0 21-1-2 3
8
1.8603 . . .- 0.8- 0.6 1.762 . . .
0.25-
Real Numbers and Number LinesReal Numbers and Number Lines
The number line above shows some real numbers between -2 and 2.
____________ include both rational and irrational numbers.Real numbers
0 21-1-2 3
8
1.8603 . . .- 0.8- 0.6 1.762 . . .
0.25-
The number line above shows some real numbers between -2 and 2.
____________ include both rational and irrational numbers.Real numbers
0 21-1-2 3
8
1.8603 . . .- 0.8- 0.6 1.762 . . .
0.25-
Real Numbers and Number LinesReal Numbers and Number Lines
The number line above shows some real numbers between -2 and 2.
____________ include both rational and irrational numbers.Real numbers
Each real number corresponds to exactly one point on a number
line.
Each point on a number line corresponds to exactly one real
number
Postulate 2-1
Number Line
Postulate
0 21-1-2 3
8
1.8603 . . .- 0.8- 0.6 1.762 . . .
0.25-
The number line above shows some real numbers between -2 and 2.
____________ include both rational and irrational numbers.Real numbers
Each real number corresponds to exactly one point on a number
line.
Each point on a number line corresponds to exactly one real
number
Postulate 2-1
Number Line
Postulate
0 21-1-2 3
8
1.8603 . . .- 0.8- 0.6 1.762 . . .
0.25-
Real Numbers and Number LinesReal Numbers and Number Lines
The number that corresponds to a point on a number line is called the
_________ of the point.
The number that corresponds to a point on a number line is called the
_________ of the point.
Real Numbers and Number LinesReal Numbers and Number Lines
The number that corresponds to a point on a number line is called the
_________ of the point.coordinate
The number that corresponds to a point on a number line is called the
_________ of the point.coordinate
Real Numbers and Number LinesReal Numbers and Number Lines
The number that corresponds to a point on a number line is called the
_________ of the point.coordinate
On the number line below, __ is the coordinate of point A.
x
11-5 -3 -1 1 3 5 7 9-6 -4 0 4 8-6 2 106-2
AB C
The number that corresponds to a point on a number line is called the
_________ of the point.coordinate
On the number line below, __ is the coordinate of point A.
x
11-5 -3 -1 1 3 5 7 9-6 -4 0 4 8-6 2 106-2
AB C
Real Numbers and Number LinesReal Numbers and Number Lines
The number that corresponds to a point on a number line is called the
_________ of the point.coordinate
On the number line below, __ is the coordinate of point A.10
x
11-5 -3 -1 1 3 5 7 9-6 -4 0 4 8-6 2 106-2
AB C
The number that corresponds to a point on a number line is called the
_________ of the point.coordinate
On the number line below, __ is the coordinate of point A.10
x
11-5 -3 -1 1 3 5 7 9-6 -4 0 4 8-6 2 106-2
AB C
Real Numbers and Number LinesReal Numbers and Number Lines
The number that corresponds to a point on a number line is called the
_________ of the point.coordinate
On the number line below, __ is the coordinate of point A.
The coordinate of point B is __
10
x
11-5 -3 -1 1 3 5 7 9-6 -4 0 4 8-6 2 106-2
AB C
The number that corresponds to a point on a number line is called the
_________ of the point.coordinate
On the number line below, __ is the coordinate of point A.
The coordinate of point B is __
10
x
11-5 -3 -1 1 3 5 7 9-6 -4 0 4 8-6 2 106-2
AB C
Real Numbers and Number LinesReal Numbers and Number Lines
The number that corresponds to a point on a number line is called the
_________ of the point.coordinate
On the number line below, __ is the coordinate of point A.
The coordinate of point B is __-4
10
x
11-5 -3 -1 1 3 5 7 9-6 -4 0 4 8-6 2 106-2
AB C
The number that corresponds to a point on a number line is called the
_________ of the point.coordinate
On the number line below, __ is the coordinate of point A.
The coordinate of point B is __-4
10
x
11-5 -3 -1 1 3 5 7 9-6 -4 0 4 8-6 2 106-2
AB C
Real Numbers and Number LinesReal Numbers and Number Lines
The number that corresponds to a point on a number line is called the
_________ of the point.coordinate
On the number line below, __ is the coordinate of point A.
The coordinate of point B is __
Point C has coordinate 0 and is called the _____.
-4
10
x
11-5 -3 -1 1 3 5 7 9-6 -4 0 4 8-6 2 106-2
AB C
The number that corresponds to a point on a number line is called the
_________ of the point.coordinate
On the number line below, __ is the coordinate of point A.
The coordinate of point B is __
Point C has coordinate 0 and is called the _____.
-4
10
x
11-5 -3 -1 1 3 5 7 9-6 -4 0 4 8-6 2 106-2
AB C
Real Numbers and Number LinesReal Numbers and Number Lines
The number that corresponds to a point on a number line is called the
_________ of the point.coordinate
On the number line below, __ is the coordinate of point A.
The coordinate of point B is __
Point C has coordinate 0 and is called the _____.
-4
10
origin
x
11-5 -3 -1 1 3 5 7 9-6 -4 0 4 8-6 2 106-2
AB C
The number that corresponds to a point on a number line is called the
_________ of the point.coordinate
On the number line below, __ is the coordinate of point A.
The coordinate of point B is __
Point C has coordinate 0 and is called the _____.
-4
10
origin
x
11-5 -3 -1 1 3 5 7 9-6 -4 0 4 8-6 2 106-2
AB C
Real Numbers and Number LinesReal Numbers and Number Lines
The distance between two points A and B on a number line is found by
using the Distance and Ruler Postulates.
For any two points on a line and a given unit of measure, there is a
unique positive real number called the measure of the distance
between the points.
Postulate 2-2
Distance
Postulate
The distance between two points A and B on a number line is found by
using the Distance and Ruler Postulates.
For any two points on a line and a given unit of measure, there is a
unique positive real number called the measure of the distance
between the points.
Postulate 2-2
Distance
Postulate
Real Numbers and Number LinesReal Numbers and Number Lines
The distance between two points A and B on a number line is found by
using the Distance and Ruler Postulates.
For any two points on a line and a given unit of measure, there is a
unique positive real number called the measure of the distance
between the points.
Postulate 2-2
Distance
Postulate
AB
measure
The distance between two points A and B on a number line is found by
using the Distance and Ruler Postulates.
For any two points on a line and a given unit of measure, there is a
unique positive real number called the measure of the distance
between the points.
Postulate 2-2
Distance
Postulate
AB
measure
Real Numbers and Number LinesReal Numbers and Number Lines
The distance between two points A and B on a number line is found by
using the Distance and Ruler Postulates.
For any two points on a line and a given unit of measure, there is a
unique positive real number called the measure of the distance
between the points.
Postulate 2-2
Distance
Postulate
AB
measure
Points on a line are paired with real numbers, and the measure of
the distance between two points is the positive difference of the
corresponding numbers.
Postulate 2-3
Ruler
Postulate
The distance between two points A and B on a number line is found by
using the Distance and Ruler Postulates.
For any two points on a line and a given unit of measure, there is a
unique positive real number called the measure of the distance
between the points.
Postulate 2-2
Distance
Postulate
AB
measure
Points on a line are paired with real numbers, and the measure of
the distance between two points is the positive difference of the
corresponding numbers.
Postulate 2-3
Ruler
Postulate
Real Numbers and Number LinesReal Numbers and Number Lines
The distance between two points A and B on a number line is found by
using the Distance and Ruler Postulates.
For any two points on a line and a given unit of measure, there is a
unique positive real number called the measure of the distance
between the points.
Postulate 2-2
Distance
Postulate
AB
measure
Points on a line are paired with real numbers, and the measure of
the distance between two points is the positive difference of the
corresponding numbers.
Postulate 2-3
Ruler
Postulate
measure = a – b
B A
ab
The distance between two points A and B on a number line is found by
using the Distance and Ruler Postulates.
For any two points on a line and a given unit of measure, there is a
unique positive real number called the measure of the distance
between the points.
Postulate 2-2
Distance
Postulate
AB
measure
Points on a line are paired with real numbers, and the measure of
the distance between two points is the positive difference of the
corresponding numbers.
Postulate 2-3
Ruler
Postulate
measure = a – b
B A
ab
Real Numbers and Number LinesReal Numbers and Number Lines
x
11-5 -3 -1 1 3 5 7 9-6 -4 0 4 82 106-2
AB
The measure of the distance between B and A is the positive difference
10 – 2, or 8.
Another way to calculate the measure of the distance is by using
____________.
x
11-5 -3 -1 1 3 5 7 9-6 -4 0 4 82 106-2
AB
The measure of the distance between B and A is the positive difference
10 – 2, or 8.
Another way to calculate the measure of the distance is by using
____________.
Real Numbers and Number LinesReal Numbers and Number Lines
x
11-5 -3 -1 1 3 5 7 9-6 -4 0 4 82 106-2
AB
The measure of the distance between B and A is the positive difference
10 – 2, or 8.
Another way to calculate the measure of the distance is by using
____________.absolute value
102AB=-
8=
8=
210BA=-
8=-
8=
12 43 5 76 891011
x
11-5 -3 -1 1 3 5 7 9-6 -4 0 4 82 106-2
AB
The measure of the distance between B and A is the positive difference
10 – 2, or 8.
Another way to calculate the measure of the distance is by using
____________.absolute value
102AB=-
8=
8=
210BA=-
8=-
8=
12 43 5 76 891011
Real Numbers and Number LinesReal Numbers and Number Lines
x
-2 0 2-1-3 1
Use the number line below to find the following measures.
A B C F
BA= CF=
x
-2 0 2-1-3 1
Use the number line below to find the following measures.
A B C F
BA= CF=
Real Numbers and Number LinesReal Numbers and Number Lines
x
-2 0 2-1-3 1
Use the number line below to find the following measures.
A B C F
BA=
5 8
3 3
￦
---
￨
3
3
=
1=
CF=
x
-2 0 2-1-3 1
Use the number line below to find the following measures.
A B C F
BA=
5 8
3 3
￦
---
￨
3
3
=
1=
CF=
Real Numbers and Number LinesReal Numbers and Number Lines
x
-2 0 2-1-3 1
Use the number line below to find the following measures.
A B C F
BA=
5 8
3 3
￦
---
￨
3
3
=
1=
CF=(1)2--
3=-
3=
x
-2 0 2-1-3 1
Use the number line below to find the following measures.
A B C F
BA=
5 8
3 3
￦
---
￨
3
3
=
1=
CF=(1)2--
3=-
3=
Real Numbers and Number LinesReal Numbers and Number Lines
x
-2 0 2-1-3 1
Use the number line below to find the following measures.
A D E F
DA= EF=
x
-2 0 2-1-3 1
Use the number line below to find the following measures.
A D E F
DA= EF=
Real Numbers and Number LinesReal Numbers and Number Lines
x
-2 0 2-1-3 1
Use the number line below to find the following measures.
A D E F
DA=
1 8
3 3
￦
---
￨
7
3
=
7
3
=
EF=
x
-2 0 2-1-3 1
Use the number line below to find the following measures.
A D E F
DA=
1 8
3 3
￦
---
￨
7
3
=
7
3
=
EF=
Real Numbers and Number LinesReal Numbers and Number Lines
x
-2 0 2-1-3 1
Use the number line below to find the following measures.
A D E F
DA=
1 8
3 3
￦
---
￨
7
3
=
7
3
=
EF=
1
2
3
-
5
3
=-
5
3
=
x
-2 0 2-1-3 1
Use the number line below to find the following measures.
A D E F
DA=
1 8
3 3
￦
---
￨
7
3
=
7
3
=
EF=
1
2
3
-
5
3
=-
5
3
=
Real Numbers and Number LinesReal Numbers and Number Lines
Traveling on I-70, the Manhattan exit is at mile marker 313.
The Hays exit is mile marker 154.
What is the distance between these two towns?
MH=
Traveling on I-70, the Manhattan exit is at mile marker 313.
The Hays exit is mile marker 154.
What is the distance between these two towns?
MH=
Real Numbers and Number LinesReal Numbers and Number Lines
Traveling on I-70, the Manhattan exit is at mile marker 313.
The Hays exit is mile marker 154.
What is the distance between these two towns?
MH=
Traveling on I-70, the Manhattan exit is at mile marker 313.
The Hays exit is mile marker 154.
What is the distance between these two towns?
MH=
Real Numbers and Number LinesReal Numbers and Number Lines
Traveling on I-70, the Manhattan exit is at mile marker 313.
The Hays exit is mile marker 154.
What is the distance between these two towns?
313154-
159=
159 miles=
MH=
Traveling on I-70, the Manhattan exit is at mile marker 313.
The Hays exit is mile marker 154.
What is the distance between these two towns?
313154-
159=
159 miles=
MH=
Real Numbers and Number LinesReal Numbers and Number Lines
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