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Sign Rules and Properties of Integers

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Rules of Addition and Subtraction of Integers

source: www.slideshare.net Fig: Addition and Subtraction of Integers
source: www.slideshare.net
Fig: Addition and Subtraction of Integers
  1. The positive integers are always added holding the positive (+) sign in resulting value. For example,
    (+5) + (+6) = 11 or (+11)
  2. The negative integers are always added holding the negative (-) sign in the resulting value. For example,
    (-5) + (-6) = -11
  3. The positive and negative integers are always added holding the negative (-) sign in the resulting value. For example,
    (+6) + (-5) = 1 or (+1)
    (-6) + (+5) = -1

Properties of addition of Integers

source: www.slideshare.net Fig: Properties of Additional of Integers
source: www.slideshare.net
Fig: Properties of Additional of Integers
  1. Closure property
    Closure property states that the sum of any two integers is also integers. For example,
    (+2) + (+3) = +5, which is an integer
    (+3) + (-2) = +1, which is an integer
    (-3) + (+2) = -1, which is an integer
    Thus, if x and y be any two integers and z is the set of integers then x + y∈ z.
  2. Commutative property
    Commutative property states that thesum of any two integers remains unchanged if their places are interchanged. If x and y are two integers, then x + y = y + z
    For example,
    (+2) + (+3) = (+3) + (+2) = +5
    (-3) + (+2) = (+2) + (-3) = -1
  3. Associative property
    Associative property states that the sum of any three integers remains unchanged if the order in which they are grouped is altered. If x, y and z are three integers, then (x + y) + z = x + (y + z)
    For example,
    (+3) + (+4) + (+5) = (+3) + [(+4) + (+5)] = (+3) + (+9) = +12
    (+3) + (-4) + (+5) = (+3) + [(-4) + (+5)] = (+3) + (+1) = +4
  4. Additive property of zero (0)
    If zero (0) is added +0 any integers, the sum is equal to the integer itself. So, zero (0) is known as the identity element of addition. If a is any integer, then a + 0 = a
    For example,
    (+2) + 0 = (+2) or 2
    (-3) + 0 = (-3)
  5. Additive inverse
    Each integer is said to the additive inverse of the other if the sum of any two integer is zero (0). If a is any integer, then (+a) + (-a) = 0, where (+a) is the additive inverse of (-a) and (-a) is te additive inverse of (+a).



  • The positive integers are always added holding the positive (+) sign in resulting value.
  • Commutative property states that the sum of any two integers remains unchanged if their places are interchanged.
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Questions and Answers

Click on the questions below to reveal the answers

The sign rules for the addition and subtraction of integers are:

  • The positive integers are always added.
  • The negative integers are always added.
  • The positive and negative integers are always subtracted.

Solution:

Here, (+2) + (+5)

 = +7 or 7 ans.

Solution

Here, (+4) + (-1)

 = +3 or 3

Similarly, (+4) + (-7)

 = -7 (The difference holds the sign of the bigger integer.)

0%
  • Simplify :
    2 × 5 -7 + 12

    14
    15
    12
    13
  • What will be the answer of 5 times the sum of 6 and 2. 

    40
    42
    44
    46
  • What will be the answer of 10 is subtracted from 3 times the sum of 8 and 12.

    20
    24
    26
    22
  • If (+2) × x = (-6), find the value of x.

    -3
    -2
    -4
    -6
  • What will be the answer of 6 times the difference of 12 and 4 is divided by the product of 8 and 3.

    4
    8
    2
    6
  • The total cost 5 pens at Rs 12 each and 3 boxes at Rs 18 each, find the correct answer.

    Rs 112
    Rs 108
    Rs 114
    Rs 110
  • What will be the answer of 3 times the sum of 7 and 8 is divided by 9.

    7
    6
    5
    4
  • Simplify:
    20 ÷ 2 (18 - 32 ÷ 4)

    5
    1
    3
    7
  • Make the mathematical expression and simplify, 4 times the difference of 9 and 3 is divided by 8. 

    6
    4
    3
    5
  • Simplify:

    18 - {23 - 3 (3 - 5)}

    -14
    -11
    -12
    -13
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use associative to workout 9 6


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