Properties of Subtracting Integers

The properties of subtracting integers are explained here along with the examples.

1. The difference (subtraction) of any two integers is always an integer.

Examples:

(a) (+7) – (+4) = 7 - 4 = 3, which is an integer.

(b) (-8) – (+3) = -8 – 3 = -11, which is an integer.

2. For any two different integers ‘a’ and ‘b’, a - b ≠ b - a

3. For any three integers ‘a’, ‘b’ and ‘c’, a - (b - c) ≠ (a - b) - c

4. For any integer ‘a’, a - 0 ≠ 0 - a

To evaluate an expression containing various integers with plus and minus sign:

1. Evaluate:

(i) (+15) + (-11) - (+5) - (-7)

= 15 - 11 - 5 + 7

= 22 – 16, [Adding all integers with plus (+) sign together and with minus (-) sign respectively together]

= +6 or simply 6.

(ii) (-72) + (-93) - (-85) + (+78)

= -72 -93 + 85 + 78

= -165 + 163, [Adding all integers with plus (+) sign together and with minus (-) sign respectively together]

= - 2


2. Evaluate the expression (-45) + (-32) – (-69) + (87)

Solution:

(-45) + (-32) – (-69) + (87)

= -45 – 32 + 69 +87

Add all the positive terms and add all the negative terms

= -(45 + 32) + (69 + 87)

= -77 + 156

= +79

= 79


3. Simplify: 32 – 13 + 35 + 18 - 60

Solution:

32 – 13 + 35 + 18 – 60

Add all the positive terms and add all the negative terms

= (32 + 35 + 18) – (13 + 60)

= 85 – 73

= +12 or simply 12


4. The sum of two integers is -17. If one of them is -7, find the other.

Solution:

Other integer = Sum of two integers - the given integer

= (-17) – (-7)

= -17 + 7

= -10

Therefore the other number is -10.








Numbers Page

6th Grade Page

From Properties of Subtracting Integers to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



Share this page: What’s this?

Recent Articles

  1. Method of L.C.M. | Finding L.C.M. | Smallest Common Multiple | Common

    Apr 15, 24 01:29 AM

    LCM of 24 and 30
    We will discuss here about the method of l.c.m. (least common multiple). Let us consider the numbers 8, 12 and 16. Multiples of 8 are → 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, ......

    Read More

  2. Common Multiples | How to Find Common Multiples of Two Numbers?

    Apr 15, 24 01:13 AM

    Common multiples of two or more given numbers are the numbers which can exactly be divided by each of the given numbers. Consider the following. (i) Multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24…

    Read More

  3. Least Common Multiple |Lowest Common Multiple|Smallest Common Multiple

    Apr 14, 24 03:06 PM

    Lowest Common Multiple
    The least common multiple (L.C.M.) of two or more numbers is the smallest number which can be exactly divided by each of the given number. The lowest common multiple or LCM of two or more numbers is t…

    Read More

  4. Worksheet on H.C.F. | Word Problems on H.C.F. | H.C.F. Worksheet | Ans

    Apr 14, 24 02:23 PM

    HCF Using Venn Diagram
    Practice the questions given in the worksheet on hcf (highest common factor) by factorization method, prime factorization method and division method. Find the common factors of the following numbers…

    Read More

  5. Common Factors | Find the Common Factor | Worksheet | Answer

    Apr 14, 24 02:01 PM

    Common Factors of 24 and 36
    Common factors of two or more numbers are a number which divides each of the given numbers exactly. For examples 1. Find the common factor of 6 and 8. Factor of 6 = 1, 2, 3 and 6. Factor

    Read More