23. are also used to describe situations
involving , ,
, , and
.
In all of these examples, integers are used to
count and units.
24. Example 1:
a. 27°C above 0°C
b. 13°C below 0°C
c. 400°C below 0°C
d. 1735°C above 0°C
e. 97°C above zero
a. 27
b. −13
c. −400
d. 1735
e. 97
25. Example 2:
a. A loss of P1
b. A profit of P300
c. A gain of 450m.
d. A gain of P1,503
e. A loss of 300km.
a. −1
b. 300
c. 450
d. 1503
e. −300
26. Example 3:
a. P211 deposit in a bank
b. P2,300 withdraw in a bank
c. P150 deposit in a bank
d. P7,889 withdraw in a bank
e. P1,202 deposit in a bank
a. 211
b. −2300
c. 150
d. -7889
e. 1202
39. The of an integer is equal to its
distance from 0.
It’s concept is so important in mathematics that
it has its own symbol.
The absolute value of x is written as | x |.
40. Example 1:
Find each absolute value.
a. | 5 |
Answer:
Since 5 is 5 units from zero, the absolute value of
5 is 5.
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
41. Example 2:
Find each absolute value.
a. | −5 |
Answer:
Since −5 is 5 units from zero, the absolute value
of −5 is 5.
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
42. Example 3:
Find each absolute value.
a. | 3 |
Answer:
Since 3 is 3 units from zero, the absolute value of
3 is 3.
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
43. Example 4:
Find each absolute value.
a. | −3 |
Answer:
Since −3 is 3 units from zero, the absolute value
of −3 is 3.
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
44. Example 5:
Find each absolute value.
a. | 0 |
Answer:
The Absolute value of 0 is 0.
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
62. An is used when comparing,
translating different mathematical sentences
including integers.
If integers are graphed on a
, the to the of
is the .
63. Example 1:
Replace each with <, >, 𝑜𝑟 =.
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
5 4
• An is used when comparing, translating
different mathematical sentences including integers.
• If integers are graphed on a ,
the to the of is the
.
64. -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
5 4>
“five is four”
Example 1:
Replace each with <, >, 𝑜𝑟 =.
• An is used when comparing, translating
different mathematical sentences including integers.
• If integers are graphed on a ,
the to the of is the
.
65. Example 2:
Replace each with <, >, 𝑜𝑟 =.
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
−6 −7
• An is used when comparing, translating
different mathematical sentences including integers.
• If integers are graphed on a ,
the to the of is the
.
66. -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
>
“negative six is negative seven”
Example 2:
Replace each with <, >, 𝑜𝑟 =.
−6 −7
• An is used when comparing, translating
different mathematical sentences including integers.
• If integers are graphed on a ,
the to the of is the
.
67. Example 3:
Replace each with <, >, 𝑜𝑟 =.
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
−8 4
• An is used when comparing, translating
different mathematical sentences including integers.
• If integers are graphed on a ,
the to the of is the
.
68. -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
<
“negative eight is four”
Example 3:
Replace each with <, >, 𝑜𝑟 =.
−8 4
• An is used when comparing, translating
different mathematical sentences including integers.
• If integers are graphed on a ,
the to the of is the
.
69. Example 4:
Replace each with <, >, 𝑜𝑟 =.
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
−4 4
• An is used when comparing, translating
different mathematical sentences including integers.
• If integers are graphed on a ,
the to the of is the
.
70. -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
<
“negative four is four”
Example 4:
Replace each with <, >, 𝑜𝑟 =.
−4 4
• An is used when comparing, translating
different mathematical sentences including integers.
• If integers are graphed on a ,
the to the of is the
.
71. Example 5:
Replace each with <, >, 𝑜𝑟 =.
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
2
10
2
• An is used when comparing, translating
different mathematical sentences including integers.
• If integers are graphed on a ,
the to the of is the
.
72. -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
>
“10 over 2 is four”
Example 5:
Replace each with <, >, 𝑜𝑟 =.
10
2
2
• An is used when comparing, translating
different mathematical sentences including integers.
• If integers are graphed on a ,
the to the of is the
.
73. Example 6:
Replace each with <, >, 𝑜𝑟 =.
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
8
24
3
• An is used when comparing, translating
different mathematical sentences including integers.
• If integers are graphed on a ,
the to the of is the
.
74. -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
=
“24 over 3 is to eight”
Example 6:
Replace each with <, >, 𝑜𝑟 =.
24
3
8
• An is used when comparing, translating
different mathematical sentences including integers.
• If integers are graphed on a ,
the to the of is the
.
76. Two important terms are common in inequality
problems.
1. The phrase “ ” means ≤ (
).
2. The phrase “ ” means ≥ (
).
77. Example 1:
a. The team (t) must have 8
members.
Translation: t 8≥
Two important terms are common in inequality problems.
1. The phrase “ ” means ≤ ( ).
2. The phrase “ ” means ≥ ( ).
78. Example 2:
a. The height (h) must be 6’3”.
Translation: t 8≤
Two important terms are common in inequality problems.
1. The phrase “ ” means ≤ ( ).
2. The phrase “ ” means ≥ ( ).