Integers

​do you know how to represent numbers on a number line? if not, then let's check it out!

​<-----l----------l-----------l-------------l-----------l----------l-----------l------>

-3​ -2 -1 0 1 2 3 now you see!

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​Q.1)True or False

a)when two positive integers are added,we get a positive integer​.

​b)when two negative integers are multiplied, we get a negative integer.

c) -8 + (6 x 5) = 18

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In next slide, answers of true or false​!

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​Now you want to know the first three numbers of ascending and descending order of that representation?

here it is!

​ascending: -3,-2,-1

​descending:3,2,1

a)true

b)false

c)​false

Now​ let's learn the properties of addition and subtraction. Shall we?

closure under addition.​

We have learned that a sum of two whole numbers is again a whole number

Ex.66 + 24 = 90 which is again a whole number.this property is known as the closure property for the addition of the whole numbers.​

closure under subtraction

can we say integers are closed under subtraction? yes, we can see that integers are closed under subtraction.

ex.​ (-29) - 13 = -42 which is an integer.

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First question showing up!​

​COMMUTATIVE PROPERTY

We know that 27 + 33 = 33 + 27. the whole numbers can be added in any order. in other words, addition is commutative for whole numbers.

can we say the same for integers too?

​take ex. of 5+ (-6) = -1 and (-6) +5 = -1

5+ (-6) = (-6) +5

so, addition is commutative for integers.​

​We know that subtraction is not commutative for whole numbers.

can we also say that subtraction is commutative for ​integers? we shall see forward.​

Refer to the tip in the Up-Right corner.​ if it isn't commutative for whole numbers then it's also not commutative for integers. smart tip, am I right?

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​tip: if it isn't commutative for whole numbers, it is also not commutative for integers

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