There are many ways to represent numbers. One way to represent numbers is with a number line. The number line also shows the order of numbers; 2 is to the left of 3, so 2 is smaller than three.
A negative
number is a number less than zero. To include negative numbers on a number
line, extend the line to the left of zero and mark off equal distances.
Negative whole numbers are members of the set of integers. So, integers can also be
represented on a number line.
Sets of numbers can also be represented by Venn diagrams.
natural numbers 1, 2, 3, 4, . . .
whole numbers 0, 1,
2, 3, . . .
integers .
. . –3, –2, –1,
0, 1, 2, 3, . . .
The Venn diagram shows that every natural number is also a
whole number. Natural numbers are a subset of whole numbers. Similarly,
whole numbers are a subset of integers.
To graph
a set of integers, locate the points named by those numbers on a number
line and place a dot on the number line. The number that corresponds to a point
is called the coordinate
of that point.
Example
1. Name the coordinates of A, B, and C
Alternative Solutions :
The
coordinate of A is –4, B is 2, and C is –1.
2. Graph
points X, Y, and Z on a number line if X
has coordinate 4, Y has coordinate 0,
and Z has coordinate 3.
Alternative Solutions :
Find
each number on a number line. Place a dot on the mark above the number. Then write
the letter above the dot.
The numbers on a number line increase as you move to the
right and decrease as you move to the left. When graphing two integers on a number
line, the number to the right is always greater.
Words : 3 is greater than –2. Words : –2 is less than 3.
Symbols : 3 > –2 Symbols :
–2 < 3
Example
Replace each ○ with < or > to make a true sentence.
3. 4
○ –1
Alternative Solutions :
4 is to the
right of –1 on the number line. So, 4 > –1.
4. –5
○ 3
Alternative Solutions :
–5 is to
the left of –3 on the number line. So, –5 < –3.
Integers are used to compare numbers in many everyday
applications.
Example
Meteorology Link
5. The
table shows the average high temperatures for January in selected cities. Order
the temperatures from least to greatest.
Alternative Solutions :
Graph
each integer on a number line.
Use
the first letter of each city name to label the points.
Write
the integers as they appear on the number line from left to right.
–3°, –2°,
–1°, 2°, 3°, 4° are in order from least to greatest.
Looking at the graphs of 4 and 4 on a number line, you can
see that they are the same number of units from 0. We say that they have the
same absolute value.
Sumber
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