This section is a brief overview of math division. It covers the concept of sharing in equal amounts, the basic division operation and long division. The sections most relevant to you will depend on your child’s level. Use the information and resources to help review and practice what your child’s teacher will have covered in the classroom.
Introducing division
When you start teaching division to your child you should introduce division as being a sharing operation where objects are shared (or divided) into a number of groups of equal number. Below is a video that shows examples of the types of exercise you can try with your child as you introduce division to them.
Once you have build an understanding of the concept of division you can try using these division worksheets.When teaching early division you should also discuss that division has an opposite. Discuss how division is about separating sets, while the opposite type of math, called multiplication is about combining sets. Explore this relationship with your child as it will be important when recalling basic facts to solve division problems. Introduce fact families (e.g. 5 x 3 =15, 3 x 5 = 15, 15 ÷ 3 = 5, 15 ÷ 5 = 3).
Dividing numbers
After your child grasps the concept of dividing and the relationship with multiplication you can start working with numbers. Be sure your child is familiar with the format and signs for division
With the concept grasped, teaching division will become more about guided practice to help your child to become familiar with the division operation (although it’s really going to be a different type of multiplication practice.) Start by practicing division by 1, 2 and 3 and then gradually move up to 9. Use the worksheets to help.Division with remainders
Your child will most likely come across or ask about situations where division “doesn’t work.” These can be explained with the introduction of the remainder. It is an important idea to understand as the division of larger numbers will require the “carrying” of this remainder.
Teaching division with larger numbers
There are a number of methods for dividing larger numbers. One of these is shown below:
These printable worksheets will provide practice with similar types of division problems.
Long Division
There are different methods for dividing multi-digit numbers (long division). One way is a combination of estimation/ trial and error and multiplication. Another method
is well explained and illustrated on mathisfun.com.
87 subtracted from 98 gives 11.
We descend the next (last) digit of the dividend, 3 to the right of 11 to make it 113. We know 3 x 29 = 87.
Let us find 4 x 29:
after 3 and 87 below 113. 87 subtracted from 113 gives 26 which is the remainder.
is well explained and illustrated on mathisfun.com.There, we studied problems on long division by a single digit number. Here, we extend that study by solving Long Division of a Five digit number by a single digit number. We also introduce long division by two digit numbers.
Example 1
Divide 79865 by 8.
Solution:
Step 1:
Here first digit of dividend is 7 which is less than the divisor 8. So we see the first two digits of the dividend which is 79. We find how many times 8 divides 79. We know 9 x 8 = 72. We put 9 in the right bracket and 72 below 79 of the dividend. 72 subtracted from 79 gives 7.
Dividend
Divisor 8 ) 79865 ( 9
72
-----
7
Step2: Learning Long Division
72 subtracted from 78 gives 6. We descend the next digit of the dividend, 8 to the right of 7 to make it 78. We know 8 divides 78,
nine times. 9 x 8 = 72. We write 9 in the right bracket after 9 and 72 below 78.
nine times. 9 x 8 = 72. We write 9 in the right bracket after 9 and 72 below 78.
Dividend
Divisor 8 ) 79865 ( 99
72
-----
78
72
-----
6
Step 3: Learning Long Division
We descend the next digit of the dividend, 6 to the right of 6 to make it 66. We know 8 divides 66,
eight times. 8 x 8 = 64. (Note that 9 x 8 = 72 exceeds 66.)
We write 8 in the right bracket after 99 and 64 below 66. 64 subtracted from 66 gives 2.
eight times. 8 x 8 = 64. (Note that 9 x 8 = 72 exceeds 66.)
We write 8 in the right bracket after 99 and 64 below 66. 64 subtracted from 66 gives 2.
Dividend
Divisor 8 ) 79865 ( 998
72
-----
78
72
-----
66
64
-----
2
Step 4: Learning Long Division
We descend the next (last) digit of the dividend, 5 to the right of 2 to make it 25. We know 8 divides 25, three times. 3 x 8 = 24. (Note that 4 x 8 = 32 exceeds 25.)
We write 3 in the right bracket after 998 and 24 below 25. 24 subtracted from 25 gives 1 which is the remainder.
We write 3 in the right bracket after 998 and 24 below 25. 24 subtracted from 25 gives 1 which is the remainder.
DividendThus 79865 ÷ 8 gives quotient = 9983 and remainder = 1. Ans.
Divisor 8 ) 79865 ( 9983 Quotient
72
-----
78
72
-----
66
64
-----
25
24
-----
1 Remainder
-----
Check:
Verify whether
Dividend = Divisor x Quotient + Remainder
is satisfied or not.
Verify whether
Dividend = Divisor x Quotient + Remainder
is satisfied or not.
R.H.S. = Divisor x Quotient + Remainder
= 8 x 9983 + 1 = 9983 x 8 + 1
= 8 x 9983 + 1 = 9983 x 8 + 1
To Find 9983 x 8 :
9983R.H.S. = Divisor x Quotient + Remainder = 8 x 9983 + 1 = 79864 + 1 = 79865 = Dividend = L.H.S. (Verified. )
8
------267
79864
------
Example 2 of Learning Long Division
Divide 983 by 29.
Solution:
Step 1: Learning Long Division
Here the divisor is a two digit number, 29. So we see the first two digits of the dividend which is 98. We have to find how many times 29 divides 98. Unlike in the previous sums where the knowlegde of Multiplication Tables was sufficient to decide how many times the divisor divides the number, here we have to calculate to decide.
We don't remember (not supposed to remember) 29 table.29 is near 30. We know 3 x 30 = 90 which is near 98. (To find 3 x 30, we simply find 3 x 3 and then put a 0 to the right of the result.) So we try 3 x 29.
Here, we use the knowledge of Multiplication.
2987 is less than 98 by 11 only. So 4 times 29 is not required. We have 3 x 29 = 87. We put 3 in the right bracket and 87 below 98 of the dividend.
3
---2
87
---
87 subtracted from 98 gives 11.
DividendStep 2: Learning Long Division
Divisor 29 ) 983 ( 3
87
-----
11
We descend the next (last) digit of the dividend, 3 to the right of 11 to make it 113. We know 3 x 29 = 87.
Let us find 4 x 29:
294 x 29 = 116 exceeds 113. So 29 divides 113, three times and 3 x 29 = 87. We write 3 in the right bracket
4
---3
116
---
after 3 and 87 below 113. 87 subtracted from 113 gives 26 which is the remainder.
DividendThus 983 ÷ 29 gives quotient = 33 and remainder = 26. Ans.
Divisor 29 ) 983 ( 33 Quotient
87
-----
113
87
-----
26 Remainder
-----
Check:
Verify whether
Dividend = Divisor x Quotient + Remainder
is satisfied or not.
Verify whether
Dividend = Divisor x Quotient + Remainder
is satisfied or not.
R.H.S. = Divisor x Quotient + Remainder
= 29 x 33 + 26
= 29 x 33 + 26
To Find 29 x 33 :
29R.H.S. = Divisor x Quotient + Remainder = 29 x 33 + 26 = 957 + 26 = 983 = Dividend = L.H.S. (Verified.)
33
----2
87
87
----
957
----
Example 3
Divide 5892 by 37.
Solution:
Step 1:
Here the divisor is a two digit number, 37. So we see the first two digits of the dividend which is 58. We have to find how many times 37 divides 58. 1 x 37 = 37; 2 x 37 is more than 2 x 30 i.e. 60 > 58.
So 37 divided 58 one time.We have 1 x 37 = 37. We put 1 in the right bracket and 37 below 58 of the dividend.
So 37 divided 58 one time.We have 1 x 37 = 37. We put 1 in the right bracket and 37 below 58 of the dividend.
37 subtracted from 58 gives 21.
DividendStep 2:
Divisor 37 ) 5892 ( 1
37
-----
21
We descend the next digit of the dividend, 9 to the right of 21 to make it 219. 37 is near 40 and we know 5 x 40 = 200 which is near 219.
Let us find 5 x 37 and 6 x 37.
37
5
---3
185
---
376 x 37 = 222 exceeds 219. So 37 divides 219, five times and 5 x 37 = 185. We write 5 in the right bracket
6
---4
222
---
after 1 and 185 below 219.
185 subtracted from 219 gives 34.
DividendStep 3 : Teaching Long Division
Divisor 37 ) 5892 ( 15
37
-----
219
185
-----
34
We descend the next (last) digit of the dividend, 2 to the right of 34 to make it 342. 37 is near 40 and we know 8 x 40 = 320 which is near 342.
Let us find 8 x 37 and 9 x 37.
37
8
---5
296
---
379 x 37 = 333 is less than 342. So 37 divides 342, nine times and 9 x 37 = 333. We write 9 in the right bracket after 15 and 333 below 342. 333 subtracted from 342 gives 9 which is the remainder.
9
---6
333
---
DividendThus 5892 ÷ 37 gives quotient
Divisor 37 ) 5892 ( 159 Quotient
37
-----
219
185
-----
342
333
-----
9 Remainder
-----
= 159 and remainder = 9. Ans.
Check :
Verify whether
Dividend = Divisor x Quotient + Remainder
is satisfied or not.
Verify whether
Dividend = Divisor x Quotient + Remainder
is satisfied or not.
R.H.S. = Divisor x Quotient + Remainder
= 37 x 159 + 9 = 159 x 37 + 9
= 37 x 159 + 9 = 159 x 37 + 9
To Find 159 x 37 :
159R.H.S. = Divisor x Quotient + Remainder = 37 x 159 + 9 = 5883 + 9 = 5892 = Dividend = L.H.S. (Verified.)
37
----64
111321
477
----
5883
----
As the number of digits of the dividend increases, the number of steps in the process increases. Except for that
the procedure is same.Teaching Long Division is done by the above three steps. Let us see another example in
which a six digit number is divided by a three digit number. the procedure is same.Teaching Long Division is done by the above three steps. Let us see another example in
Example 4 of Teaching Long Division
Divide 609182 by 463.
Solution:
Step 1: Teaching Long Division
Here the divisor is a three digit number 463. So we see the first three digits of the dividend which is 609. We have to find how many times 463 divides 609. 1 x 463 = 463; 2 x 463 is more than 800 > 609. So 463 divides 609 one time.We have 1 x 463 = 463. We put 1 in the right bracket and 463 below 609 of the dividend. 463 subtracted from 609 gives 146.
DividendStep 2: Teaching Long Division
Divisor 463 ) 609182 ( 1
463
---
146
We descend the next digit of the dividend, 1 to the right of 146 to make it 1461. 463 is near 500 and we know 3 x 500 = 1500 which is near 1461.
Let us find 3 x 463.
4634 x 463 is more than 1600 which exceeds 1461. So 463 divides 1461, three times and 3 x 463 = 1389.
3
----1
1389
----
We write 3 in the right bracket after 1 and 1389 below 1461. 1389 subtracted from 1461 gives 72.
DividendStep 3: Teaching Long Division
Divisor 463 ) 609182 ( 13
463
---
1461
1389
----
72
We descend the next digit of the dividend, 8 to the right of 72 to make it 728. 1 x 463 = 463; 2 x 463 is more than 800 > 728. So 463 divides 728 one time.
We have 1 x 463 = 463.
We put 1 in the right bracket
after 13 and 463 below 728.
463 subtracted from 728 gives 265.
We put 1 in the right bracket
after 13 and 463 below 728.
463 subtracted from 728 gives 265.
DividendStep 4: Teaching Long Division
Divisor 463 ) 609182 ( 131
463
---
1461
1389
----
728
463
-----
265
We descend the next (last) digit of the dividend, 2 to the right of 265 to make it 2652. 463 is near 500 and we know 5 x 500 = 2500 which is near 2652.
Let us find 5 x 463 and 6 x 463.
463
5
----13
2315
----
4636 x 463 = 2778 exceeds 2652. So 463 divides 2652, five times and 5 x 463 = 2315. We write 5 in the right bracket after 131 and 2315 below 2652. 2315 subtracted from 2652 gives 337 which is the remainder.
6
----13
2778
----
DividendThus 609182 ÷ 463 gives quotient
Divisor 463 ) 609182 ( 1315 Quotient
463
---
1461
1389
----
728
463
-----
2652
2315
-----
337 Remainder
-----
= 1315 and remainder = 337. Ans.
Check:
Verify whether
Dividend = Divisor x Quotient + Remainder is satisfied or not. R.H.S. = Divisor x Quotient + Remainder
= 463 x 1315 + 337 = 1315 x 463 + 337
Verify whether
Dividend = Divisor x Quotient + Remainder is satisfied or not. R.H.S. = Divisor x Quotient + Remainder
= 463 x 1315 + 337 = 1315 x 463 + 337
To Find 1315 x 463 :
1315R.H.S. = Divisor x Quotient + Remainder = 463 x 1315 + 337 = 608845 + 337 = 609182 = Dividend = L.H.S. (Verified.). Thus, with any Dividend and any Divisor, we can carry out the division by following the same procedure.
463
------1
394531
789021
5260
------
608845
------
Labels:
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