This page contains main concepts and results for Class 7, Chapter-1 INTEGERS. This chapter is mainly about representation of integers on the number line and their addition and subtraction.
We use numbers to count anything. So, what are various types of numbers?
Natural numbers are counting numbers but these set of numbers do not include zero. This is because you cannot count zero. So numbers,
1,2,3,4,5,6……etc are all natural numbers
All natural numbers along with zero are called whole numbers. For example
0, 1, 2, 3, 4, 5, 6………etc are all whole numbers.
NOTE:- Thes types of numbers do not include fractions.
From the definition of natural numbers we can conclude that every natural or counting number is a whole number.
Integers include all natural numbers, zero and negative numbers for example,
-4, -3, -2, -1, 0, 1, 2, 3, ………. etc are all integers.
So now we have,
Note:- Integers like whole numbers do not include fractions for example 3.5 , ½ etc.
Number line for integers is
Now from this number line you can see that numbers to the left of zero are all negative. Again from this number line you can observe that numbers to the right of zero are all positive.
Important note:- If the number has no sign attached to it as prefix then it means that it is a positive number.
For example number 3 is really number +3
Important Points
On the number line when we
For any two integers a and b.
for any three integers a, b and c.
a + 0 = 0 + a = a
for any integer a.
a × 1 = 1 × a = a
for any integer a.
a × (b + c) = a × b + a × c
for any three integers a, b and c.
a × (–b) = – ab
where a and b are positive integers.
(–a) × (–b) = ab
where a and b are positive integers.
\[a\div \left( b \right)=\left( a \right)\div b\text{ =}\frac{a}{b}\]
where a and b are positive integers and $-\frac{a}{b}$is an integer
\[\left( a \right)\div \left( b \right)=\frac{a}{b}\] , where a and b are positive integers and \[\frac{a}{b}\] is also an integer.
\[a\div 1=a~\]
and
a ÷ 0 is not defined.
Now let us consider solving a problem and apply the above mentioned problem solving strategy. For this purpose we will solve a NCERT book problem.
Question:
Mohan deposits Rs 2,000 in his bank account and withdraws Rs 1,642 from it, the next day. If withdrawal of amount from the account is represented by a negative integer, then how will you represent the amount deposited? Find the balance in Mohan's account after the withdrawal.
Solution:
Step 1:- Understand the problem
For this step first read your problem carefully. So,
Here find ‘what is the amount Mohan deposited in his bank account and how much he withdraws’.
Balance in Mohan’s bank account after the withdrawal.
Amount deposited = Rs 2000
Amount withdrawn = Rs 1642
Step 2:- Plan your strategy
Here we have to find the amount he removed from his account. So,
Balance in Mohan's account = Money deposited - Money withdrawn
Step 3:- Solve the problem
Now that you have all the known and unknown quantities and you also have a strategy to solve your problem, you can now carefully carry out your calculations.
Balance in Mohan's account = 2000 + (-1642) = 2000 - 1642 = 358
Therefore, balance in Mohan's account after withdrawal is Rs 358.
Step 4:- Revise
Now in this step check your answer.
Resources for further reading
These are most of the resources that you can use to learn more about this chapter Integers