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CBSE / NCERT

Class 7 Maths

L – 1 Integers !!

Points to Remember !! With Mock Test !!!

Integers on Number Line

On the number line, for positive integers we move to the right from zero and for negative integers move to the left of zero.

Facts about how to Add and Subtract Integers on the Number Line

1. If we add a positive integer, we go to the right.

2. If we add a negative integer, we go to the left.

3. If we subtract a positive integer, we go to the left.

4. If we subtract a negative integer, we go to the right.

This shows that the number which we add to a number to get zero is the additive inverse of that number.

As you can see that the addition of two integers will always be an integer, hence integers are closed under addition.

If we have two integers p and q, p + q is an integer.

As you can see that the subtraction of two integers will always be an integer, hence integers are closed under subtraction.

For any two integers p and q, p – q is an integer.

3. Commutative Property

a. If we change the order of the integers while adding then also the result is the same then it is said that addition is commutative for integers.

For any two integers p and q

p + q = q + p

There is no difference in answer after changing the order of the numbers.

b. If we change the order of the integers while subtracting then the result is not the same so subtraction is not commutative for integers.

For any two integers p and q

p – q ≠ q – p will not always equal.

4. Associative Property

If we change the grouping of the integers while adding in case of more than two integers and the result is same then we will call it that addition is associative for integers.

For any three integers, p, q and r

p + (q + r) = (p + q) + r

5. Additive Identity

If we add zero to an integer, we get the same integer as the answer. So zero is an additive identity for integers.

For any integer p,

p + 0 = 0 + p =p

1. Multiplication of a Positive Integer and a Negative Integer

To multiply a positive integer with a negative integer, we can multiply them as a whole number and then put the negative sign before their product.

So the product of a negative and a positive integer will always be a negative integer.

For two integers p and q,

p × (-q) = (-p) × q = – (p × q) = – pq

The Mock test Link :

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