Chapter3. OPERATIONS WITH
SIGNED NUMBERS
3.1.1 Introduction: We can use the number line to explain the addition of
signed numbers.
3.2 Arithmetic
Operations
3.2.1 Addition
3.2.1.1 Addition
of integer with like signs: Find the
sum of the absolute values and write the answer along with the common number
sign.
Take two positive integers like 2 and 4 are to be added.
(+2) + (+4) = (+6)
The “+“sign inside the
parentheses shows the number sign and the one outside the parenthesis is sign
of addition.
Draw the number line
6
2 +4
<
-6
-5-4 -3-2 -1 0 1
2 3 4
5 6
Find 2 on the number line, and go four
units more in the positive direction. The number you get is (+6)
To add two negative integers, such as -2 and -4, find -2 on the number
line and then go four units more in the negative direction. The number you get
is -6
3.2.1.2 Addition
of integer with unlike signs: To add
a positive and a negative integer find the difference between their absolute
value and place sign of the greatest of the two number
Take two numbers -3 and
+2. The difference between their absolute value is 1, and on comparing the
absolute numbers we find that 3 > 2 therefore (-) sign will be taken along
with the result
And can be showed as
(-3) + (+2) = (-1)
-3 + 2
= -1
Draw the number line
Place -3 and +2 in a
number line. Start from -3, move 2 units towards positive direction.
The number we get is -1
>
+2
-3-2 -1 0
1 2 3
4 5 6
7 8 9
3.2.1 Subtraction
3.2.1.1 Subtraction
of integer with like signs: Find the
difference of the absolute values and write the answer along with the common
number sign.
Take two positive integers
like +2and+ 4 are to be subtracted and can be showed as
(+4) - (+2) = (+2)
Draw the number line
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2
-5 -4 -3 -2 -1 0
1 2 3
4 5 6 7
Find +4 on the number
line, and go two units in the negative direction. The number you get is +2
To subtract two negative integers, such as -2 and
-4, Negative integers like (-2) and (-4)
are to be subtracted and can be showed as
(-2)
- (-4) = (-6)
find -2 on the number line and then go
four units more in the negative direction. The number you get is (-6)
3.2.1.2 Subtraction
of integer with unlike signs: To
subtract a positive and a negative integer find the sum of their absolute value
and place sign of the greater of the two numbers
Take a positive integer and a
negative integer like +3 and - 4 respectively, to be subtracted. The sum of
their absolute values is 7 and since 4> 3 answer will be -7
(+3)
- (-4) = (-7)
Draw the number line
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3
-7 -6
-5 -4 -3 -2
-1 0 1
2 3 4
Find -4 on the number
line, and go three units in the negative direction. The number is -7
3.2.3 Multiplication
3.2.3.1 Multiplication
of integers with like signs:
Multiplication of two integers with like signs (either negative or positive)
gives a positive product
(+) x (+) =
(+)
(-) x (-) =
(+)
Example: (+4) x (+5) =
+20
(-4) x (-5) = +20
3.2.3.2 Multiplication
of integers with unlike signs:
Multiplication of two integers with unlike signs (one negative and other
positive) gives a negative product.
(+) x (-) =
(-)
Example: (+7)
x (-5) = -35
3.2.4 Division
3.2.4.1 Division of
integers with like signs: Division of
two integers with like signs (either negative or positive) gives a positive quotient
(+) / (+) =
(+)
(-) x (-) =
(+)
Example: (+10) / (+5) = +2
(-10) / (-5) = +2
3.2.4.2 Division of
integers with unlike signs: Division
of two integers with unlike signs (one negative and other positive) gives a negative quotient.
(+) / (-) =
(-)
Example: (+42)
/ (-7) = -6