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Numbers and Operations

Whole numbers is the set of all positive numbers including zero. All positive numbers, negative numbers and zero make up the set of integers. The fractions are known as rational numbers. There are four basic mathematical operations, that is, addition, subtraction, multiplication and division, and these operations can be performed on all real numbers. Adding two numbers will get the sum and subtracting two numbers will get their difference. Multiplication is a short form of addition and division is a short form of subtraction. These operations can be performed whole numbers, integers, rational numbers, irrational numbers and even on imaginary numbers. In imaginary numbers reals parts and imaginary parts are taken separately.

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Operations on Numbers in Math

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The non negative integers has series like 0, 1, 2, 3 and so on.
The positive integer series has 1, 2, 3 and so on.
The another name of whole number is counting numbers.

The basic operations of numbers are as follows:

  • Addition
  • Subtraction
  • Multiplication
  • Division

The whole numbers are added to one another. This is similar to counting because it gives the total value of numbers. The whole number addition operation is represented as ‘ + ’.

Solved Examples

Question 1: Add the given two numbers 12 and 13.
Solution:
 
The given two numbers are 12 and 13.
   1 2
+ 1 3
_ 2 5

Therefore, the value of addition for 12 and 13 is 25.
 

Correct answer is 25
Question 2: Find the sum of 26 and 43.
Solution:
 
The given two numbers are 26 and 43.
   26
+ 43
    69

Therefore, the sum of 26 and 43 is 69.
 

Correct answer is 69
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Difference of any two whole numbers is calculated by subtraction operation. As per the rule, small whole number is subtracted from large number. The symbol ‘ - ‘ is represent the subtraction operation.

Solved Examples

Question 1: Find the difference between 56 and 14
Solution:
 
We have to subtract 56 from 14
  5 6
- 1 4
_4 2

So the difference is 42
 

Correct answer is 42
Question 2: Subtract the given numbers 37 and 16
Solution:
We have to subtract 37 from 16
   37
-  16
   21

So the value after subtraction is 21.


Correct answer is 21
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Multiplication of two whole numbers is represented by ‘ x ’ symbol. We can also make use of the multiplication table to cross check the product.

Solved Examples

Question 1: Multiply the given two numbers 14 and 4.
Solution:
The given two numbers are 14 and 4.
1 4
x 4
5 6

Therefore, the value of multiplication is 56.

Correct answer is 56
Question 2: What will be the product of 24 and 5?
Solution:
The given two numbers are 24 and 5.
   24
   x 5 
  120

Therefore, the product is 120.

Correct answer is 120
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Dividing Numbers

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The last basic operations in math is division and is represented by ‘ ÷ ’ symbol.
This operation may also give the remainder value on division.

Solved Examples

Question 1: Divide the given number 12 by 2.
Solution:
The given numbers are 12 and 2
   __6_____
2 |  12
  (-)12____
        0
Number after division is = 6

Correct answer is 6
Question 2: Divide the given number 28 by 7.
Solution:
The given numbers are 28 and 7.

    __4_____
7 |  28
  (-)28____
        0
Number after division is = 4

Correct answer is 4

Addition and Subtraction Word Problems

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Below you could see addition and subtraction word problems

Solved Examples

Question 1: Mr. Rohit drove 40 miles in his car on Thursday and 35 miles on Monday. How many miles did he drive in these two days?
Solution:
Step 1: We know that Mr. Rohit drive 40 miles in his car on Thursday and 35 miles on Monday.
Step 2: We need to find how many miles did he drive.
Step 3: So, we need to add this given miles.
Step 4: Therefore the answer is 75 miles.

Correct answer is 75 miles
Question 2: Mukund has to repair 120 buses. He has repaired 3. How many more does he have to repair?
Solution:
Step 1: We know that Tania already repairs 3 buses.
Step 2: We need to find the remaining buses he have to repair.
Step 3: Here we need to perform subtraction.
Step 4: Therefore the answer is 117 buses.

Correct answer is 117 buses

Multiplication and Division Word Problems

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Below you could see multiplication and division word problems

Solved Examples

Question 1: In each of 12 vases at a flower shop, there are 8 flowers. How many total flowers are there in the vases?
Solution:
Step 1: We know that each vase has 8 flowers. And totally we have 12 vases.
Step 2: Here we need to multiply 12 and 8 .
Step 3: Therefore, totally we have 96 vases.

Correct answer is 96 vases
Question 2: A board game has 44 total coins. There are equal numbers of coins of 4 different colors. How many coins are there of each color
Solution:
Step 1: We know that we have 44 coins and it has 4 different colors.
Step 2: Here we need to divide 44 and 4
Step 3: Therefore, the result is 11 coins in each colors.

Correct answer is 11 coins

Numbers and Operations Practice Problems

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Practice problems are provided below for you to get a better understanding of math operations.

Solved Examples

Question 1: The whole numbers are 54 and 50. Subtract these whole numbers.
Options :
  • 6
  • 7
  • 4
  • 12
Correct answer is 4
Question 2: Divide the whole number 100 by 5.
Options :
  • 20
  • 85
  • 25
  • 40
Correct answer is 20
More topics in Numbers and Operations
Adding Numbers Subtracting Numbers
Multiplying Numbers Dividing Integers
Fact Families Order of Operations
Multiplication and Division Tables Number Sentences
NCERT Solutions
NCERT Solutions NCERT Solutions CLASS 6 NCERT Solutions CLASS 7 NCERT Solutions CLASS 8 NCERT Solutions CLASS 9 NCERT Solutions CLASS 10 NCERT Solutions CLASS 11 NCERT Solutions CLASS 12
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