Division of whole numbers is discussed here step by step.
1. Division is repeated subtraction.
(a) 25 ÷ 5 = 5
(Repeated Subtraction)
(i) 25 - 5 = 20
(ii) 20 - 5 = 15
(iii) 15 - 5 =10
(iv) 10 - 5 = 5
(v) 5 - 5 = 0
(b) 10 ÷ 2 = 5
(Repeated Subtraction)
(i) 10 - 2 = 8
(ii) 8 - 2 = 6
(iii) 6 - 2 = 4
(iv) 4 - 2 = 2
(v) 2 - 2 = 0
(c) 50 ÷ 10 = 5
(Repeated Subtraction)
(i) 50 - 10 = 40.
(ii) 40 - 10 = 30
(iii) 30 - 10 = 20
(iv) 20 - 10 = 10
(v) 10 - 10 = 0
2. Division is the inverse of multiplication.
(a) (i) 12 × 10 = 120
(ii) 120 ÷ 10= 12
(iii) 120 ÷ 12 = 10
(b) (i) 25 × 5 = 125
(ii) 125 ÷ 5 = 25
(iii) 125 ÷ 25 = 5
3. Relation between Dividend, Divisor, Quotient and Remainder is.
Dividend = Divisor × Quotient + Remainder
To understand the relation between dividend, divisor, quotient
and remainder let us follow the following examples:
(a) Divide 537809 by 35 and find the quotient and remainder.
We need to divide the dividend i.e. 537809 by the divisor i.e. 35 to get the quotient and remainder.
5 cannot be divided by 35 as 5 < 35. So, we will move to the next digit of the dividend i.e. 3 and now we have 53 which can be divided by 35 as 53 > 35. We first divide 53 by 35. 35 into 53 is 1 leaving 18.
Then we bring down the next digit of the dividend i.e. 7 and we have 187. Now we divide 187 by 35 so, 35 into 187 is 5 leaving 12.
Again we bring down the next digit of the dividend i.e. 8 and we have 128. Now we divide 128 by 35 so, 35 into 128 is 3 leaving 23.
Similarly, again we bring down the next digit of the dividend i.e. 0 and we have 230. Now we divide 230 by 35 so, 35 into 230 is 6 leaving 20.
And at last we bring down the last digit of the dividend i.e. 9 and we have 209. So, we divide 209 by 35 then, 35 into 209 is 5 leaving 34.
Check the answer of the division:
Dividend = Divisor × Quotient + Remainder
537809 = 35 × 15365 + 34
537809 = 537775 + 34
537809 = 537809
(b) Divide 86228364 by 2768 and check the answer.
We need to divide the dividend i.e. 86228364 by the divisor i.e. 2768 to get the quotient and remainder.
8 cannot be divided by 2768 as 8 < 2768. So, we will move to the second digit of the dividend i.e. 6 and now we have 86 which cannot be divided by 2768 as 86 < 2768. So, we will move to the third digit of the dividend i.e. 2 and now we have 862 which also cannot be divided by 2768 as 862 < 2768. So, we will move to the fourth digit of the dividend i.e. 2 and now we have 8622 which can be divided by 2768 as 8622 > 2768. We first divide 8622 by 2768. 2768 into 8622 is 3 leaving 318.
Then we bring down the fifth digit of the dividend i.e. 8 and we have 3188. Now we divide 3188 by 2768 so, 2768 into 3188 is 1 leaving 420.
Again we bring down the sixth digit of the dividend i.e. 3 and we have 4203. Now we divide 4203 by 2768 so, 2768 into 4203 is 1 leaving 1435.
Similarly, again we bring down the seventh digit of the dividend i.e. 6 and we have 14356. Now we divide 14356 by 2768 so, 2768 into 14356 is 5 leaving 516.
And at last we bring down the last digit of the dividend i.e. 4 and we have 5164. So, we divide 5164 by 2768 then, 2768 into 5164 is 1 leaving 2396.
Now to check the answer of the division:
Dividend = Divisor × Quotient + Remainder
86228364 = 2768 × 31151 + 2396
86228364 = 86225968 + 2396
86228364 = 86228364
4. Divide 682592 by 32 and verify the answer.
Solution:
Hence, 682592 ÷ 32 =21331
Now to check the answer of the division:
Divisor × Quotient + Remainder = Dividend
32 × 21331 + 0 = 682592
Division by numerals ending with zeroes:
We know that division is the inverse operation of multiplication. When we divide a number by 10, 100 or 1000, we take away as many zeroes from dividend as in the divisor.
For example:
60 ÷ 10 = 6 600 ÷ 10 = 60 6000 ÷ 10 = 600 60000 ÷ 10 = 6000 |
600 ÷ 100 = 6 6000 ÷ 100 = 60 60000 ÷ 100 = 600 600000 ÷ 100 = 6000 |
6000 ÷ 1000 = 6 60000 ÷ 1000 = 60 600000 ÷ 1000 = 600 6000000 ÷ 1000 = 6000 |
Questions and Answers on Division of Whole Numbers:
I. Find the quotient and check the answers in each of the following:
(i) 22786 ÷ 3
(ii) 389458 ÷ 7
(iii) 6872419 ÷ 24
(iv) 7714592 ÷ 32
(v) 9600729 ÷ 84
(vi) 11682000 ÷ 125
(vii) 66921036 ÷ 170
(viii) 6017635 ÷ 580
(ix) 7654981 ÷ 53
Answers:
(i) Quotient = 7595; Remainder = 1.
(ii) Quotient = 55636; Remainder = 6.
(iii) Quotient = 286350; Remainder = 19.
(iv) Quotient = 241081; Remainder = 0.
(v) Quotient = 114294; Remainder = 33.
(vi) Quotient = 93456; Remainder = 0.
(vii) Quotient = 393653; Remainder = 26.
(viii) Quotient = 10375; Remainder = 135.
(ix) Quotient = 144433; Remainder = 32.
2. Find the quotient and remainder for the given.
(i) 8703364 ÷ 10
(ii) 6933453 ÷ 10000
(iii) 459827 ÷ 100
(iv) 7768232 ÷ 100000
(v) 5672861 ÷ 1000
(vi) 97367140 ÷ 10000
Answers:
(i) Quotient = 870336; Remainder = 4.
(ii) Quotient = 693; Remainder = 3453.
(iii) Quotient = 4598; Remainder = 27.
(iv) Quotient = 77; Remainder = 68232.
(v) Quotient = 5672; Remainder = 861.
(vi) Quotient = 9736; Remainder = 7140.
3. Fill In the blanks.
(i) 4928831 ÷ 1 = ________
(ii) 6582110 × ________ = 6582110
(iii) 5082240 ÷ 10 = ________
(iv) ________ × 0 = 0
(v) 7433925 ÷ 7433925 = ________
(vi) 8953022 + ________ = 8953023
(vii) 3800452 × (0 × 883245) = ________
Answers:
(i) 4928831
(ii) 1
(iii) 508224
(iv) Any number
(v) 1
(vi) 1
(vii) 0
Word Problems on Division of Whole Numbers:
4. 125896 tiles are to be loaded in 8 vehicles equally. How many tiles are loaded in each vehicle?
Answer: 15737 tiles
5. 3792780 voters are to be equally distributed in 18 blocks. How many voters will there be in each block?
Answer: 210710 voters
5th Grade Math Problems
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