Sat math Essentials

N u m b e r L i n e s a n d S i g n e d N u m b e r s
On a number line,
less than 0
is to the 
left
of 0 and 
greater than 0
is to the 
right
of 0.
Negative numbers are the opposites of positive numbers.
–7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7
greater than 0
le
ss
 than 0
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N U M B E R S A N D O P E R AT I O N S R E V I E W
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5 1

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Examples
5 is five to the 
right
of zero.
5 is five to the 
left
of zero.
If a number is 
less than
another number, it is farther to the left on the number line.
Example
4 is to the left of
2, so 
4 < 
2.
If a number is 
greater than
another number, it is farther to the right on the number line.
Example
3 is to the right of
1, so 3 >
1.
A positive number is always greater than a negative number. A negative number is always less than a posi-
tive number.
Examples
2 is greater than 
3,675.
25,812 is less than 3.
As a shortcut to avoiding confusion when comparing two negative numbers, remember the following rules:
When 
a
and 
b
are positive, if
a
> 
b
, then 
a
< 
b
.
When 
a
and 
b
are positive, if
a
< 
b
, then 
a
> 
b
.
Examples
If 8 > 6, then 
6 > 
8. (8 is to the right of 6 on the number line. Therefore,
8 is to the left of
6 on the num-
ber line.)
If 132 < 267, then 
132 > 
267. (132 is to the left of 267 on the number line. Therefore,
132 is to the right
of
267 on the number line.)
Practice Question
Which of the following statements is true?
a.
25 > 
24
b.
48 > 16
c.
14 > 17
d.
22 > 19
e.
37 > 
62
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N U M B E R S A N D O P E R AT I O N S R E V I E W
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5 2

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Answer
e.
37 > 
62 because 
37 is to the right of
62 on the number line.
A b s o l u t e Va l u e
The 
absolute value
of a number is the distance the number is from zero on a number line. Absolute value is rep-
resented by the symbol ||. Absolute values are 
always
positive or zero.
Examples
|
1| 
1
The absolute value of
1 is 1. The distance of
1 from zero on a number line is 1.
|1| 
1
The absolute value of 1 is 1. The distance of 1 from zero on a number line is 1.
|
23| 
23
The absolute value of
23 is 23. The distance of
23 from zero on a number line is 23.
|23| 
23
The absolute value of 23 is 23. The distance of 23 from zero on a number line is 23.
The 
absolute value
of an expression is the distance the value of the expression is from zero on a number line.
Absolute values of expressions are 
always
positive or zero.
Examples
|3 
5| 
|
2| 
2 The absolute value of 3 
5 is 2. The distance of 3 
5 from zero on a number line is 2.
|5 
3| 
|2| 
2
The absolute value of 5 
3 is 2. The distance of 5 
3 from zero on a number line is 2.
Practice Question
|
x
y
| 
5
Which values of
x
and 
y
make the above equation NOT true?