Division is like sharing or splitting things into equal parts. For example, if you have 12 candies and you want to share them with 3 friends, you divide 12 by 3. Each friend gets 4 candies because 12 divided by 3 equals 4. Division helps us figure out how many equal parts we can make from a total amount.
Division means equal sharing or equal grouping.
When we do division, there are different terms to know:
1. Verifying Division
To check a division result, multiply the quotient by the divisor and add the remainder to this product. The result should be equal to the dividend. Thus,
From the above division fact, we have,
So, our answer is correct.
2. Some Important Points Related to Division
We always start division from the place of highest value. In case of 2digit dividends, we start from tens place and in case of 3digit dividend, we always start from hundreds place. The remainder is always smaller than the divisor.
3. Properties of Division
(i) When any number is divided by 1, the quotient is the number itself.
Examples: 62 ÷ 1 = 62, 125 ÷ 1 = 125
(ii) When any number is divided by itself (except 0), the quotient is 1.
Examples: 64 ÷ 64 = 1, 586 ÷ 586 = 1.
(iii) When 0 is divided by any number (except 0), the quotient is always 0.
Examples: 0 ÷ 58 = 0, 0 ÷ 6423 = 0.
(iv) Division by zero is not allowed.
Let's Learn with some example
Example 1: Divide 649 by 7.
We divide, as shown alongside.
Thus, 649 ÷ 7 gives Q = 92 and R = 5.
Check:
Divisor × Quotient + Remainder
= 7 × 92 + 5 = 644 + 5 = 649
Example 2: Divide 4589 by 6.
Solution:
Check: To check answer, we use the relationship,
Dividend = Divisor × Quotient + Remainder
Example 3: Divide 7982 by 7.
Solution:
Thus, 7982 ÷ 7 gives Q = 1140 and R = 2.
Example 4: Divide 67316 by 7.
Solution:
Thus, 67316 ÷ 7 gives Q = 9616 and R = 4.
EduRev Tip: 7 does not go into 2 so, we put a 0 in the quotient and bring down 2.
Let's Learn with some example
Example 5: Divide 5975 by 14.
Solution:
Example 6: Divide 92682 by 21 and check your answer.
Solution:
Thus, 92682 ÷ 21 gives Q = 4413 and R = 9.
Check:
Here, divisor = 21, quotient = 4413, remainder = 9 and dividend = 92682.
We have,
Dividend = Divisor × Quotient + Remainder
= 21 × 4413 + 9
= 92673 + 9 = 92682
So, the answer is correct.
When you divide a number by 10, 100, or 1000, you move the decimal point to the left by 1, 2, or 3 places, respectively. This makes the number 10, 100, or 1000 times smaller. For example, 2500 ÷ 100 = 25.
Example 7: Divide each of the following numbers by 10.
(a) 58
(b) 723
(c) 8165
Solution:
(a)
Thus, 58 ÷ 10 gives Q = 5 and R = 8.
(b)
Thus, 723 ÷ 10 gives Q = 72 and R = 3.
(c)
Thus, 8165 ÷ 10 gives Q = 816 and R = 5.
From the above examples, we get the following rule:
Rule: On dividing a number by 10, we remove the digit at the ones place leaving the rest of the digits to form the quotient and the digit we remove from the ones place is the remainder.
Thus,
Example 8: Divide each of the following numbers by 100.
(a) 563
(b) 7289
(c) 17019
Solution:
(a)
Thus, 563 ÷ 100 gives Q = 5 and R = 63.
(b)
Thus, 7289 ÷ 100 gives Q = 72 and R = 89.
(c)
Thus, 17019 ÷ 100 gives Q = 170 and R = 19.
From the above examples, we get the following rule:
Rule: On dividing a number by 100, we remove the digits at the ones and tens places leaving the rest of the digits to form the quotient and the digits we remove from the ones and tens places form the remainder.
Thus,
Example 9: Divide each of the following numbers by 1000.
(a) 5637
(b) 15863
(c) 743895
Solution:
(a)
Thus, 5637 ÷ 1000 gives Q = 5 and R = 637.
(b)
Thus, 15863 ÷ 1000 gives Q = 15 and R = 863.
(c)
Thus, 743895 ÷ 1000 gives Q = 743 and R = 895.
From the above examples, we get the following rule:
Rule: On dividing a number by 1000, we remove the digits at the ones, tens and hundreds places to get the remainder and the rest of the digits form the quotient.
Thus,
42÷8;Q=5,R=2
A)
B)
C)
D)
Example 10: Divide 6832 by 50.
Solution:
Thus, 6832 ÷ 50 gives Q = 136 and R = 32.
Example 11: Divide 52891 by 600.
Solution:
Thus, 52891 ÷ 600 gives Q = 88 and R = 91.
When you do a division problem, sometimes the remainder forms the part of your answer and sometimes it doesn’t.
Example 12: 996 students of a school went on a picnic. They boarded buses each of which could hold only 24 students. How many buses were required?
Solution:
Thus, 42 buses were needed to take the students for the picnic.
Example 13: The sports teacher is cutting ribbons for the sports medals. How many ribbons of 30 cm length can the teacher get from a roll of ribbon that is 1520 cm long?
Solution:
At first, we divide 1520 by 30.
Thus, the teacher will get 50 pieces each of 30 cm length.
Example 14: Five friends together purchased a cricket kit for ₹ 7925. Find the money contributed by each child.
Solution:
Thus, the money contributed by each child is ₹ 1585.
Example 15: The product of two numbers is 22120. If one of the numbers is 35, find the other number.
Solution:
Thus, the other number is 632.
28 videos110 docs30 tests

1. What is the meaning of division in mathematics? 
2. How is division related to multiplication? 
3. How do you divide a number by a 1digit number? 
4. What is the significance of division by multiples of 10 and 100? 
5. Can you give an example of a reallife situation where division is used? 

Explore Courses for Class 4 exam
