Informative line

# Identification of an Integer

• Integers are a group of numbers that consists of a set of negative and positive numbers.

$$(...\;-5,\;-4,\;-3,\;-2,\;-1,\;0,\;1,\;2,\;3,\;4,\;5\,...)$$

• They do not include any fractional or decimal part.
• They are whole numbers and their opposites.
• The opposite of an integer can be written by changing its sign.
• For example: Opposite of the integer $$5$$ is $$-5$$ which is obtained by changing its sign (positive changes to negative).

• A group of numbers that consists of a set of whole numbers except zero are called positive integers.

Example: $$(1,\;2,\;3,\;4,\;5\,...)$$

Positive integers are either represented by '+' sign or without any sign.

Example: $$(+1,\;+2,\;+3\,...)\;\text{or}\;(1,\;2,\;3\,...)$$

• A group of numbers that consists of a set of opposite of whole numbers except zero are called negative integers.

Example: $$(-1,\;-2,\;-3,\;-4\,...)$$

Negative integers are represented by '–' sign.

Example: $$(-1,\;-2,\;-3,\;-4,\;-5\,...)$$

• Zero is an integer but it is neither positive nor negative.

#### Which one of the following numbers is an integer?

A $$-10$$

B $$\dfrac{5}{2}$$

C $$-10.5$$

D $$2.5$$

×

An integer is a whole number that can be positive, negative or zero.

It does not include any fractional or decimal part.

Hence, option (A) is correct.

### Which one of the following numbers is an integer?

A

$$-10$$

.

B

$$\dfrac{5}{2}$$

C

$$-10.5$$

D

$$2.5$$

Option A is Correct

# Representation of Integers on the Number Line

• We can plot negative and positive integers on the number line.
• Negative integers are to the left side of zero and positive integers are to the right side of zero.  For example: If we wish to represent $$2$$ and its opposite $$(-2)$$ on the number line then

for $$2,$$ start from $$0$$ and move $$2$$ points forward (right side of zero).  • Since, we have moved $$2$$ points forward to show $$2,$$ so for the opposite of $$2,$$ we move $$2$$ points backward from $$0$$ (left side of zero).  #### Which number represents the location of point $$Q$$ on the number line?

A $$-3$$

B $$3$$

C $$2$$

D $$7$$

×

To find the location of point $$Q$$ on the number line, we start from zero and move one point forward. Now, keep on making such moves till we reach the point $$Q.$$ We made $$3$$ moves to the right side of zero. So, point $$Q$$ represents the number $$3$$ on the number line.

Hence, option (B) is correct.

### Which number represents the location of point $$Q$$ on the number line? A

$$-3$$

.

B

$$3$$

C

$$2$$

D

$$7$$

Option B is Correct

# Absolute Value

• The absolute value of an integer is the distance of that integer from zero.
• Suppose, we want to find the absolute value of $$-2$$.

Absolute value of $$-2$$ is the distance of $$-2$$ from zero.

• Since the distance of $$-2$$ from zero is $$2$$ units, so the absolute value of $$-2$$ is $$2.$$  • Distance can never be negative. It is always positive. Thus, the absolute value of any integer is always positive.
• The absolute value is shown by enclosing the number between two vertical bars $$(||)$$, such as:

$$|10|=10$$

The absolute value of $$|10|$$ is $$10$$.

$$|-10|$$ is equivalent to $$10$$.

Note: The absolute values of an integer and its opposite are always same.

#### Find the absolute value of $$-5$$.

A $$5$$

B $$0$$

C $$-5$$

D $$151$$

×

The absolute value of $$-5$$, i.e. $$|-5|$$, is the distance of $$-5$$ from $$0$$. The distance of $$-5$$ from zero is $$5$$ units.

So, the absolute value of $$-5$$ is $$5.$$

Hence, option (A) is correct.

### Find the absolute value of $$-5$$.

A

$$5$$

.

B

$$0$$

C

$$-5$$

D

$$151$$

Option A is Correct

# Elevation as Integers

• Integers can be used to represent the elevation.
• The sea level represents the $$0$$ (zero) integer and is taken as the point of reference.
• Any location above the sea level represents a positive integer.
• Any location below the sea level represents a negative integer.

Example: $$50$$ feet below the sea level.

The sea level represents zero and any location which is below the sea level, is represented by a negative integer.

So, $$50$$ feet below the sea level represents $$-50$$ feet.

#### Which one of the following represents $$'\text{11 feet below the sea level}'$$?

A 11

B -11

C 0

D 12

×

Any location which is below the sea level is represented by a negative integer.

Here, $$11$$ feet below the sea level is represented by the integer $$-11$$

Hence, option (B) is correct.

### Which one of the following represents $$'\text{11 feet below the sea level}'$$?

A

11

.

B

-11

C

0

D

12

Option B is Correct

# Opposite of an Integer

• Integers are wholes and their opposites.

Example: Opposite of $$a$$ is $$–a$$.

• If two integers are placed at the same distance from zero on both sides of the number line, then they are opposite of each other.
• Thus, the opposite of $$-3$$ is $$3.$$  • Opposite of a whole number $$(a)$$ is a negative integer $$(-a)$$.

Opposite of $$(1)$$ is $$(-1)$$.

• Opposite of a negative integer $$(-1)$$ is a positive integer $$(1)$$ or $$-(-1)$$.

Example: (1) Opposite of $$5$$ is $$-5$$.

(2) Opposite of $$-6$$ is $$-(-6)$$ or $$6$$.

(3) Opposite of $$10$$ is $$-10$$.

(4) Opposite of $$-(-2)$$ is $$-2$$.

(5) Opposite of $$-8$$ is $$-(-8)$$ or $$8$$.

Note: Opposite of the opposite of a number is the number itself.

#### Which one of the following number lines represents the locations of $$-6$$ and its opposite?

A B C D ×

Integers are wholes and their opposites.

So, the opposite of $$-6$$ is $$6.$$

On a number line, the opposite of an integer has the same distance from zero on the other side. Hence, option (C) is correct.

### Which one of the following number lines represents the locations of $$-6$$ and its opposite?

A B C D Option C is Correct

# Temperature as Integers

• Integers can be used to represent temperatures.
• Zero is used as a reference point.

(1) Any temperature above zero is represented as a positive integer.

$$15°F$$ above zero $$=15°F$$

(2) Any temperature below zero is represented as a negative integer.

$$15°F$$  below zero $$=-15°F$$

• Smaller the integer, colder the temperature is and greater the integer, warmer the temperature is.

$$-15°F$$  is colder than $$-13°F$$.

$$15°F$$  is warmer than $$13°F$$.

Examples:

$$10°F$$  above zero $$=10°F$$

$$5°F$$  below zero $$=-5°F$$

#### Which one of the following temperatures represents $$11°F$$ below zero?

A $$11°F$$

B $$-11°F$$

C $$0°F$$

D $$12°F$$

×

Any temperature below zero is represented by a negative integer.

Thus, $$11°$$ below zero $$=-11°F$$

Hence, option (B) is correct.

### Which one of the following temperatures represents $$11°F$$ below zero?

A

$$11°F$$

.

B

$$-11°F$$

C

$$0°F$$

D

$$12°F$$

Option B is Correct

# Money as Integers

• Integers can be used to represent loss and gain of money.
• Loss of money would be a negative integer.
• Gain (profit) of money would be a positive integer.
• An account (bank) is credited when money is deposited in it, which means gain of money, so this would be a positive integer.
• An account is debited when money is taken out of it, which means loss of money, so this would be a negative integer.

Example: Ms. Wendy deposits $200. When money is deposited into an account, it means gain of money, so this would be a positive integer. Thus, it represents the integer$200.

#### Which one of these represents $$'Sam \;earns\; 20'$$?

A 2

B -20

C 20

D 0

×

Gain of money would be a positive integer.

Here, Sam earns $$20$$ means he gains money.

So, the integer is $$20$$.

Hence, option (C) is correct.

### Which one of these represents $$'Sam \;earns\; 20'$$?

A

2

.

B

-20

C

20

D

0

Option C is Correct