We can test whether all the properties of integers that are true for addition still hold for subtraction or not.

**Properties
of Subtraction**

We can test whether all the properties of
integers that are true for addition still hold for subtraction or not.

Recall that subtraction of two whole numbers
did not always result in a whole number. However, this extended form of
integers is enough to make sure that the difference of two integers is also an
integer. For example, (−7) − (−2) is an integer, ( −5) +14
is an integer and 0 − ( −8) is an integer. From these examples we observe
that the collection of integers is “closed”,
that is, the difference of two integers is always an integer.

Therefore, for any two integers *a*, *b* ; *a*–*b* is also an integer.

What about the other properties? Can you see
that ( −2) − (−5) = 3 but ( −5) − ( −2) = −3 Also, 10 − ( −5) = 15 but ( −5) −10 = −15 . Therefore, changing the order of integers
in subtraction will not give the same value. Hence, the commutative property
does not hold for subtraction of integers.

Therefore, for any two integers *a*, *b* ; *a*–*b* ≠ *b*–*a*.

** **

**Try these **

**1. Fill in the blanks.**

(i) ( −7) − ( −15) = __±8__

(ii) 12 − ** (–7)** = 19

(iii) ** –4** − ( −5) = 1

**2. Find the values and compare the answers.**

**(i) 15 – 12 and 12 –15**

15 – 12 = 3

12 – 15 = –3

+3 > –3

15 –12 > 12 –15

**(ii) –21 –32 and –32 –(–21)**

–21 – 32 = –53

–32 – (–21) = –32 + 21 = –11

–53 < –11

–21 – 32 < –32 – (–21)

**Think****
**

Is assosiative property true for
subtraction of integers?

Take any three examples and
check.

Tags : Number System | Term 1 Chapter 1 | 7th Maths , 7th Maths : Term 1 Unit 1 : Number System

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7th Maths : Term 1 Unit 1 : Number System : Properties of Subtraction | Number System | Term 1 Chapter 1 | 7th Maths

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