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Signed Numbers

Numbers are said to be the main source of mathematics. The numbers preceded by a "+ " sign indicates a positive number and a number preceded by a - sign indicates a negative number. Addition of two numbers is represented by plus sign and the subtraction of two numbers are represented by "-" sign. Depends upon the sign in the number the operation varies. Let us see about signed numbers definition in this article.

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Signed Numbers Definition

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Numbers are main source of math. Signed numbers that defined for a term to perform specific operations (addition, subtraction, multiplication and division) with the integers. We have perform operations between numbers having same signs and numbers having opposite signs.Operations with signed numbers:
  • Addition of number having same sign.
  • Addition of numbers having opposite signs.
  • Subtraction between numbers having same sign.
  • Subtraction between numbers having opposite signs.
  • Multiplication between numbers having same sign.
  • Multiplication between opposite signed numbers
  • Dividing same signed numbers
  • Dividing opposite signed numbers

Addition

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Adding signed numbers are nothing but the arithmetic operations. The addition in which undergoes both in addition and negative numbers. These positive integers are represented as by the sign (+) in front of the each n integer. The negative numbers are the collection of individuals. The numbers which have the negative sign (-) in front of the standard numerals are named as negative numbers.

Solved Examples

Question 1: What is +6 + (+2)?
Solution:
From above: + (+) becomes a positive sign.
+6+ (+2) = +6 + 2
Start at +6 on the number line, move forward 2, and you end up at 8

Correct answer is 8
Question 2: What is -6 + (+3)?
Solution:
From above: + (+) becomes a positive sign.
-6 + (+3) = -6 + 3
Start at -6 on the number line, move forward 3, and you end up at -3

Correct answer is -3

Subtraction

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Subtraction is defined as one of the arithmetic operations in the mathematics. Subtraction using signed means, we have to subtract the given functions by using the positive and the negative sign for the numbers.

Solved Examples

Question 1: What is the value for the given expression (-2) - (-7).
Solution:
Since both the numbers are negative, we are converting this to addition problem (By using rule 3). So the problem becomes,
 (-2) + (+7)
 = - 2 + 7
 = 5
 This is the required solution by subtracting signed numbers.

Correct answer is 5
Question 2: What is the value for the given expression (+2) - (-7)?
Solution:
Since the first number is positive and second number is negative, we are converting this to addition problem (By using rule 3). So the problem becomes,
 (+2) + (+7)
 = 2 + 7
 = 9
 This is the required solution by subtracting signed numbers.

Correct answer is 9

Multiplication

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In multiplication there are three terms such as multiplicand and multiplier. The result of multiplying multiplicand and multiplier is called as product.

Solved Examples

Question 1: Multiplying 9 × (-2)
Solution:
The number -9 is the opposite of 9 and -2 is the opposite of 2.
The number 9 sets of the opposite of 2 is the opposite of 18.
9 × (-2) = 9 × -2 = -18.

Correct answer is - 18
Question 2: Multiplying -5 × 8
Solution:
The number -5 is the opposite of 5 and -8 is the opposite of 8.
The number 8 sets of the opposite of 5 is the opposite of 40.
-5 × 8 = -40

Correct answer is - 40

Division

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In division there are four terms such as dividend and divisor. The result of dividing dividend and divisor is called as quotient. The remaining number after left over division is known as remainder.

Solved Examples

Question 1: Dividing 12 by -4
Solution:
Here, the dividend is 12 and divisor is -4. The result of dividing 12 ÷ -4 is said to be quotient.
Check whether the number 4 go into 1 or not. The number 4 cannot go into 1. So, that take the dividend as two digits as 12 as given. The number 4 should go into 12 for 3 times.

4)12(3
     0
--------------
    12
    12
--------------
     0
--------------

Put the negative sign before the quotient and the remainder is 0.

Therefore, the solution for dividing 12 by -4 is -3.


Correct answer is - 3
Question 2: Dividing -108 by 27.
Solution:
Here, the dividend is -108 and divisor is 27. The result of dividing -108 ÷ 27 is said to be quotient.

Check whether the number 27 go into 1 or not. If it is possible divide by 27 otherwise, go for taking two digits as 10 and 27 cannot go into 10. So that takes the dividend as three digits 108 as given in the problem. The number 27 should go into 108 for 4 times.

27)108(4
          0
-------------
      10
-------------
     108
     108
-------------
      0
-------------

Put the negative sign before the quotient and the remainder is 0.

The solution for dividing -108 by 27 is -4.


Correct answer is - 4

Solved Examples

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Below are the examples on signed numbers -

Addition of Same Signed Numbers

Example 1:

13 + 14

Solution:

Step 1:

Add 13 + 14

Step 2:

Place the sign of positive while adding two positive numbers.

Step 3:

Add the two positive numbers, we get,

13 + 14 = 27

Hence, solution for adding same signed numbers of 13 + 14 is 27.

Example 2 :

(-3) + (-7)

Solution:

Step 1:

Add (-3) + (-7)

Step 2:

Place the sign of negative while adding two negative numbers.

Step 3:

Add the two negative numbers, we get,

(-3) + (-7) = - (3 + 7) = - 10

Hence, the solution for adding same signed numbers of (-3) + (-7) is -10.

Addition of Different Signed Numbers

Example 3 :

7 + (-9)

Solution:

Step 1:

Add 7 + (-9)

Step 2:

Place the sign of greater number while adding one negative and positive number.

Step 3:

Subtract the numbers while one is negative numbers, we get,

7 - 9 = 2

Step 4:

The greatest number is - 9. So, place the negative sign before the result.

Hence, the solution for adding different signed numbers of 7 + (-9) is -2.

Subtraction of Same Signed Numbers

Example 4:

18 - 8

Solution:

Step 1:

Subtract 18 - 8

Step 2:

Subtract the given numbers, we get,

18 - 8 = 10

Hence, the solution for subtracting same signed numbers of 18 - 8 are 10.

Example 5 :

(-13) - (-5)

Solution:

Step 1:

Subtract (-13) - (-5)

Step 2:

Subtract the given numbers and then place the sign of larger number before the result.

Step 3:

Add the numbers, while subtracting two negative numbers, we get,

(-13) - (-5) = -13 + 5 = -8

Hence, the solution for subtracting same signed numbers of (-13) - (-5) is -8.

Subtraction of Different Signed Numbers

Example 6 :

18 - (-7)

Solution:

Step 1:

Subtract 18 - (-7)

Step 2:

Subtract the given numbers and then place the sign of larger number before the result.

Step 3:

Add the given numbers, while subtracting negative number from the positive number, we get,

18 - (-7) = 18 + 7 = 25

Hence, the solution for subtracting different signed numbers of 18 - (-7) is 25.

Practice Problems

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Below you could see signed numbers practice

Practice Problems

Question 1: Adding 23 and 21
Question 2: Adding (-8) + (-19)
Question 3: Adding 9 + (-17)
Question 4: Subtracting 34 from 52
Question 5: Subtracting (-9) from (-12)
Question 6: Subtracting -27 from 58
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