We have learned to add, subtract, multiply and divide numbers in our previous class. We also learnt the calculations, with and without carryover of numbers 1 to 100.
In this chapter, let us learn more about these four fundamental operations – Addition, subtraction, multiplication and division.
Addition of Numbers
Addition of two or more numbers
Adding 145 and 232, we get 377
|
145 |
|
+ 232 |
|
= 377 |
Addition with carryover
The carried over from ones to be added in tens, carried over from tens to be added in the hundred, and so on use the carry forward process.
For example:
There are 462184 apples and 462526 mangoes in a fruit bowl. How many fruits are there?
Let us add the numbers by carryover.
Solution:
|
1 |
1 |
1 |
Carryover |
|||
|
L |
TTh |
Th |
H |
T |
O |
|
|
4 |
6 |
2 |
1 |
8 |
4 |
Apples |
|
4 |
6 |
2 |
5 |
2 |
6 |
Mangoes |
|
9 |
2 |
4 |
7 |
1 |
0 |
Hence, total fruits in a fruit bowl are – 9,24,710.
Properties of Subtraction
- While subtracting, the smaller number is subtracted from the larger number.
- The calculation starts from the right and goes to the left in subtraction.
- Borrowing is from the digits placed on the left of the digit for which borrowing is done.
Subtract the following numbers
- 45963 – 24542
- 8,54,445 – 32,123
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TTh |
Th |
H |
T |
O |
|
4 |
5 |
9 |
6 |
3 |
|
2 |
4 |
5 |
4 |
2 |
|
2 |
1 |
4 |
2 |
1 |
|
L |
TTh |
Th |
H |
T |
O |
|
8 |
5 |
4 |
4 |
4 |
5 |
|
3 |
2 |
1 |
2 |
3 |
|
|
8 |
2 |
2 |
3 |
2 |
2 |
Subtraction by borrowing
The number of boys in a school is 48974. If the total strength of the school is 89543, find the number of girls in the school.
Solution:
To find the total number of girls in the school, we have to subtract the number of boys from the total strength of the school.
The total strength of the school = 89543
The number of boys in a school = 48974
The number of girls in a school = 89543 – 48974 =?
|
8 |
14 |
13 |
13 |
Borrowing |
|
|
TTh |
Th |
H |
T |
O |
|
|
8 |
9 |
5 |
4 |
3 |
Strength of the school |
|
4 |
8 |
9 |
7 |
4 |
Number of boys |
|
4 |
0 |
5 |
6 |
9 |
Number of boys |
Hence the number of girls in a school = 40,569.
Properties of Multiplication
- Multiplicand * Multiplier = Product
- Multiplying a number by 1 does not change the value of the number.
- Changing the order of two numbers while multiplying will not change the product.
- For finding the product of a three-digit number by another three-digit number, we add the products of ones, tens and hundreds with the given number.
- Multiplying a number by 1000, 2000, 3000, ….. 9000, we multiply the number by 1, 2, 3, and 9 and write as many zeros on the right side with the multiplier. For example – 40×1000 = 40,000.
Examples:
Multiply 583 by 43
Solution:
|
TTh |
Th |
H |
T |
O |
|
|
5 |
8 |
3 |
|||
|
* |
4 |
3 |
|||
|
1 |
7 |
4 |
9 |
Multiplication by 3 |
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|
2 |
3 |
3 |
2 |
– |
Multiplication by 4 |
|
2 |
5 |
0 |
6 |
9 |
Multiply 326 by 310
Solution:
|
L |
TTh |
Th |
H |
T |
O |
|
|
3 |
2 |
6 |
||||
|
* |
3 |
1 |
0 |
|||
|
0 |
0 |
0 |
Multiplication by 0 |
|||
|
3 |
2 |
6 |
– |
Multiplication by 1 |
||
|
9 |
7 |
8 |
– |
– |
Multiplication by 3 |
|
|
1 |
0 |
1 |
0 |
6 |
0 |
Properties of Division
- The division process is to start from the left.
- Dividend = Quotient × Divisor + Remainder.
- Dividing ‘0’ by any number except the ‘0’ quotient is ‘0’.
- Dividing any number by 1 will give the result as the number.
- Dividing any number by 10, the one’s place of that number is the remainder, and the remaining digit will be the quotient.
Examples:
Divide 456 by 6 and write the dividend, divisor, quotient and remainder.
Solution:
6 ) 456 ( 76
42↓
_________
36
36
_________
00
_________
The dividend is 456, the divisor is 6, the quotient is 76, and the remainder is 0.
Divide 2255 by 5 and write the dividend, divisor, quotient and remainder.
Solution:
5 ) 2255 ( 451
20 ↓↓
_________
025↓
25↓
_________
005
_________
005
005
_________
0
_________
The dividend is 2255, the divisor is 5, the quotient is 451, and the remainder is 0.
Stay tuned to BYJU’S for more information on NIOS, syllabus, notes, along with its important questions and solutions.
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