Repeated Subtraction: Definition, Diagram, Properties, Examples
Repeated Subtraction: The term Repeated subtraction subtracts an equal number of items from the larger group, also known as division. Suppose the exact number is repeatedly subtracted from the other more significant digit until you get the remainder as zero or a number smaller than the number being removed. In that case, you can write that in the form of division.
What is Subtraction?
Definition: The term subtraction means to reduce the value of one number from another to get the required deal (difference), and the symbol representing subtraction is ().
Example: \(5\) subtracted from \(10\) we get \(5\) as the answer.
\(105=5\)
If we imagine \(10\) peaches in a basket and take out \(5\) peaches from the basket, how many peaches are left?
The answer is \(5\) peaches.
\(105=1+1+1+1+1+1+1+1+1+111111=5\)
Division: The division is the opposite operation of multiplication. It is how one tries to determine how many times a number is contained into another.
The division is also known as the repeated subtraction.
We know that dividing \(20\) by \(5\) means finding the number that multiplied with \(5\) gives us \(20\). Such a number is \(4\).
Therefore, we write \(20 \div 5 = 4\) or, \(\frac{{20}}{5} = 4\) or \(20 – 5 = 15,15 – 5 = 10,10 – 5 = 5,5 – 5 = 0\)
Example: The repeated subtraction sentence is \(366=30, 306=24, 246=18, 186=12, 126=6, 66=0\), now we have subtracted the number \(6\) for \(6\) times division sentence will be \(36÷6=6\).
The repeated subtraction sentence is \(56 – 7 = 49,49 – 7 = 42,42 – 7 = 35,\) \(35 – 7 = 28,28 – 7 = 21,21 – 7 = 14,14 – 7 = 7,7 – 7 = 0\)
now we have subtracted the number \(7\) for \(8\) times, so the division sentence will be \(56÷7=8\).
Division as Repeated Subtraction
Definition: Repeated subtraction of the number is known as division. The mathematical sign denotes the term division consists of a short horizontal line with a dot each above and below the line
Example: The subtraction sentence is \(42=2, 22=0\), and we have subtracted the number \(2\) for two times, so the division sentence will be \(4÷2\).
The subtraction sentence will be \(155=10, 105=5, 55=0\); we have subtracted the number \(5\) for three times so that the division sentence will be \(15÷3\).
Define Repeated Subtraction
Definition: Subtracting the equal number of items from a more extensive group is known as repeated subtraction, or you can also call it division.
When the exact number is repeatedly subtracted from the other number until you get the remainder as zero or the number smaller than the number removed, you can write that in the form of division.
Example: There are \(25\) balls with a group of \(5\) balls in each group.
In the above image, you can see that the number \(5\) has been repeatedly subtracted \(5\) times. Therefore, you can also write as \(5\) has been deducted \(5\) times from the number \(25\), and you write this subtraction as \(25÷5=5\).
In the same way, to solve any division problem using repeated subtraction, you have to repeatedly subtract the same number again and again until you get the answer. In the given below diagram, you can see there are \(32\) stars. By using the repeated subtraction, you can make small groups of \(4\) stars in each group. You can continuously subtract four stars until you get the answer as zero or more negligible than the number four.
The repeated subtraction will be \(324=28, 284=24, 244=20,\)
\(204=16, 164=12, 124=8, 84=4, 44=0\),
so you have subtracted the number \(4\) for \(8\) times, so the division will be \(932÷4=8\).
Facts of Repeated Subtraction
The repeated subtraction can also be helpful for us to learn the division facts like:
1. Repeated subtraction is somewhat like jumping backwards from the more significant number until you get the required answer.
2. You can see the above diagram repeated subtraction on the number line, \(186=12→126=6→66=0\) or \(18÷6=3\).
3. You can even subtract the large numbers in the same way like \(72\), you will write \(72 – 9 = 63,{\rm{ }}63 – 9 = 54,{\rm{ }}54 – 9 = 45,{\rm{ }}45 – 9 = 36,\) \(36 – 9 = 27,{\rm{ }}27 – 9 = 18,{\rm{ }}18 – 9 = 9,{\rm{ }}9 – 9 = 0\) now you have subtracted the number \(9\) for eight times, so the division sentence will be \(72÷9=8\).
Solved Examples – Repeated Subtraction (Practice Problems)
Q.1. Divide the numbers \(27÷3\) using repeated subtraction.
Ans: We are given to divide the numbers \(27÷3\) using repeated subtraction.
So, the repeated subtraction sentence will be \(273=24, 243=21, 213=18,\)
\(183=15, 153=12, 123=9, 93=6, 63=3, 33=0\)
Now, the number \(3\) is subtracted for ninetime, so the division sentence is \(27÷3=9\).
Here, you can see the remainder is zero, and the quotient is \(9\).
Q.2. Divide the numbers \(81÷9\) using repeated subtraction.
Ans: We are given to divide the numbers \(81÷9\) using repeated subtraction.
So, the repeated subtraction sentence will be \(81 – 9 = 72,{\rm{ }}72 – 9 = 63,{\rm{ }}63 – 9 = 54,{\rm{ }}54 – 9 = 45,\)
\(45 – 9 = 36,{\rm{ }}36 – 9 = 27,{\rm{ }}27 – 9 = 18,{\rm{ }}18 – 9 = 9,\;{\rm{ }}9 – 9 = 0\)
Now, the number \(9\) is subtracted for ninetime, so the division sentence is \(81÷9=9\).
Here, you can see the remainder is zero, and the quotient is \(9\).
Q.3. Divide the numbers \(28÷7\) using repeated subtraction.
Ans: We are given to divide the numbers \(28÷7\) using repeated subtraction.
So, the repeated subtraction sentence will be \(287=21, 217=14, 147=7, 77=0\)
Now, the number \(7\) is subtracted fourtime, so the division sentence is \(28÷7=4\).
Here, you can see the remainder is zero, and the quotient is \(4\).
Q.4. Divide the numbers \(175÷35\) using repeated subtraction.
Ans: We are given to divide the numbers \(175÷35\) using repeated subtraction.
So, the repeated subtraction sentence will be \(17535=140, 14035=105, 10535=70, 7035=35, 3535=0\)
Now, the number \(35\) is subtracted for fivetime, so the division sentence is \(175÷35=5\).
Here, you can see the remainder is zero, and the quotient is \(5\).
Q.5. Divide the numbers \(342÷171\) using repeated subtraction.
Ans:We are given to divide the numbers \(342÷171\) using repeated subtraction.
So, the repeated subtraction sentence will be \(342171=171, 171171=0\)
Now, the number \(171\) is subtracted two times, so the division sentence is \(342÷171=2\).
Here, you can see the remainder is zero, and the quotient is \(2\).
Q.6. Divide the numbers \(783÷261\) using repeated subtraction.
Ans:We are given to divide the numbers \(784÷261\) using repeated subtraction.
So, the repeated subtraction sentence will be \(784261=522, 522261=261, 261261=0\)
Now, the number \(261\) is subtracted for threetime, so the division sentence is \(784÷261=3\).
Here, you can see the remainder is zero, and the quotient is \(3\).
Q.7. Divide the numbers \(9000÷3000\) using repeated subtraction.
Ans: We are given to divide the numbers \(9000÷3000\) using repeated subtraction.
So, the repeated subtraction sentence will be \(90003000=6000, 60003000=3000, 30003000=0\)
Now, the number \(3000\) is subtracted for threetime, so the division sentence is \(9000÷3000=3\).
Here, you can see the remainder is zero, and the quotient is \(3\).
Q.8. Divide the numbers \(20000÷5000\) using repeated subtraction.
Ans: We are given to divide the numbers \(20000÷5000\) using repeated subtraction.
So, the repeated subtraction sentence will be \(200005000=15000, 150005000=10000, 100005000=5000, 50005000=0\)
Now, the number \(5000\) is subtracted four times, so the division sentence is \(20000÷5000=4\).
Here, you can see the remainder is zero, and the quotient is \(4\).
Summary
In this given article, we have talked about the term subtraction along with an example. Then we have discussed what the repeated subtraction is and have provided few examples for better understanding. You can also see the definition and the examples of division as repeated subtraction. We had glanced at the facts of repeated subtraction and then provided a few of the solved examples along with a few FAQs.
Frequently Asked Questions (FAQ) – Repeated Subtraction
Q.1. Explain repeated subtraction with an example.
Ans: Subtracting the equal number of items from a more extensive group is known as repeated subtraction, or you can also call it division.
When the exact number is repeated subtracted from the other number until you get the remainder as zero or the number smaller than the number removed, you can write that in the form of division.
Example: The repeated subtraction will be \(32 – 4 = 28,{\rm{ }}28 – 4 = 24,{\rm{ }}24 – 4 = 20,\) \(20 – 4 = 16,{\rm{ }}16 – 4 = 12,{\rm{ }}12 – 4 = 8,{\rm{ }}8 – 4 = 4,{\rm{ }}4 – 4 = 0,\) so you have subtracted the number \(4\) for \(8\) times so that the division will be \(32÷4=8\).
Q.2. How can arrays help with repeated subtraction?
Ans: Array has a fixed number of objects, and all the things are of the same type. It helps to understand the repeated subtraction in a better way without any confusion.
In the above image, you can see that the number \(5\) has been repeatedly subtracted \(5\) times. Therefore, you can also write as \(5\) has been deducted \(5\) times from the number \(25\), and you write this subtraction as \(25÷5=5\).
Q.3. How do you find the quotient by repeated subtraction?
Ans: When you solve any problem using repeated subtraction, you learn to find out the quotient and the remainder.
For example, \(426=36, 366=30, 306=24, 246=18, 186=12, 126=6, 66=0\), now you subtracted the number \(6\) for seven times division sentence will be \(42÷6=7\), where zero is the remainder, and the number \(7\) is the quotient.
Q.4. Is division similar to subtraction?
Ans: The term division is related to multiplication in the same way subtraction is related to addition. Removal is related to but not precisely like addition; the repeated subtraction can calculate division in such a way that is related to the way multiplication can be calculated by repeated addition.
Q.5. What is a repeated subtraction example?
Ans: Subtracting the equal number of items from a more extensive group is known as repeated subtraction, or you can also call it division.
Example: You will write the repeated subtraction sentence as \(459=36, 369=27, 279=18, 189=9, 99=0\), now you have subtracted the number \(9\) for five times, so the division sentence will be \(45÷9=5\). You can even subtract the large numbers in the same way as \(72\). You will write \(72 – 9 = 63,{\rm{ }}63 – 9 = 54,{\rm{ }}54 – 9 = 45,{\rm{ }}45 – 9 = 36,\) \(36 – 9 = 27,{\rm{ }}27 – 9 = 18,{\rm{ }}18 – 9 = 9,{\rm{ }}9 – 9 = 0,\) now you have subtracted the number \(9\) for eight times, so the division sentence will be \(72÷9=8\).
We hope you find this detailed article on repeated subtraction helpful. If you have any doubts or queries regarding this topic, feel free to ask us in the comment section and we will assist you at the earliest.
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How to divide by repeated subtraction?
We will learn how to find the quotient and remainder by the method of repeated subtraction a division problem may be solved.
Solved examples on divide by repeated subtraction:
1. Solve 16 ÷ 8
Solution:
8 is subtracted repeatedly from 16 as shown:
When 8 is subtracted from 16, 2 times, then we get the remainder zero.
Hence, 16 ÷ 8 = 2, 2 is the quotient.
2. Divide 20 ÷ 5
5 is subtracted repeatedly from 20 as shown:
When 5 is subtracted from 20, four times, then we get the remainder zero.
Hence, 20 ÷ 5 = 4, 4 is the quotient.
3. Solve 12 by 3
Solution:
3 is subtracted repeatedly from 12 as shown:
When 3 is subtracted from 12, four times, then we get the remainder zero.
Hence, 12 ÷ 3 = 4, 4 is the quotient.
4. Divide 28 ÷ 7
7 is subtracted repeatedly from 28 as shown:
When 7 is subtracted from 28, four times, then we get the remainder zero.
Hence, 28 ÷ 7 = 4, 4 is the quotient.
5. Divide 32 ÷ 4
4 is subtracted repeatedly from 32 as shown:
When 4 is subtracted from 32, eight times, then we get the remainder zero.
Hence, 32 ÷ 4 = 8, 8 is the quotient.
6. Solve 18 by 6.
6 is subtracted repeatedly from 18 as shown:
When 6 is subtracted from 18, three times, then we get the remainder zero.
Hence, 18 ÷ 6 = 3, 3 is the quotient.
7. Divide 18 ice creams among 6 children by repeated subtraction.
The above examples will help us to solve various division problems on 2digit number by a single digit number using the method of repeated subtraction.
2nd Grade Math Practice
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Repeated Subtraction  Definition with Examples
What is Repeated Subtraction?
Repeated subtraction is a method of subtracting the equal number of items from a larger group. It is also known as division.
If the same number is repeatedly subtracted from another larger number until the remainder is zero or a number smaller than the number being subtracted, we can write that in the form of division.
For example:
If there are 25 balls and we form a group of 5 balls each.
Here, the number 5 has been repeatedly subtracted 5 times. We can say that the number 5 has been subtracted 5 times from 25. So, we can write this subtraction as 25 ÷ 5 = 5.
Similarly, to solve a division problem through repeated subtraction, we repetitively group and subtract the same number again and again to find the answer.
Here are a few examples of repeated subtraction.
There are 34 stars. How many groups of 4 stars in each can be formed?
In the given image we can see 34 stars. Now, using repeated subtraction, we can group them in smaller groups of 4 stars in each group. We can start to subtract 4 stars repeatedly until we are left with 0 or a number less than 4.
34  4 = 30 30  4 = 26 26  4 = 22 22  4 = 18 18  4 = 14 14  4 = 10 10  4 = 6 6  4 = 2
We get 8 groups of 4 and with 2 stars remaining.
This example can be mathematically written as 34 ÷ 4. Where 34 is the dividend. The divisor is the number of stars in each group, that is, 4. The number of times 4 is subtracted is the quotient. So, 8 is the quotient and the leftover stars are the remainder. So, 2 is the remainder.
Since repeated subtraction is division, it can be written in 2 ways.
Example: Let’s say there are 18 items. These can be written in 2 ways as shown.
18 ÷ 6  18 ÷ 3 
When the divisor is 6, we make groups of 6. We get, 3 groups of 6. So, 18 ÷ 6 = 3  When the divisor is 3, we make groups of 3. We get, 6 groups of 3. So, 18 ÷ 3 = 6 
Fun fact:

18 – 6 = 12 → 12 – 6 = 6 → 6 – 6 = 0
or
18 ÷ 6 = 3
Is multiplication repeated subtraction?
Ans: Yes, Multiplication is repeated subtraction.
What is successive subtraction?
The square root of a number, is that number which when multiplied by itself gives the number itself. Finding the square root of a number by repeatedly subtracting successive odd numbers from the given square number, till you get zero is known as repeated subtraction method.
What is repeated division method?
Repeated Division Method The decimal number is repeatedly divided by 2, with the remainder recorded on the right side. This continues until you cannot divide further by 2. The answer is obtained by recording the remainders, from the bottom to the top. The remainder is placed to the right.
What is repeated subtraction example?
Repeated subtraction is a method of subtracting the equal number of items from a larger group. So, we can write this subtraction as 25 ÷ 5 = 5. Similarly, to solve a division problem through repeated subtraction, we repetitively group and subtract the same number again and again to find the answer.
What is the result of repeated division called?
The result of division is to separate a group of objects into several equal smaller groups. The starting group is called the dividend. The number of groups that are separated out is called the divisor. The number of objects in each smaller group is called the quotient.
What is the result of a subtraction problem called?
Formally, the number being subtracted is known as the subtrahend, while the number it is subtracted from is the minuend. The result is the difference.
When a number is divided by 7 its remainder is always?
Description Divisibility Rules – 7 A number is divisible by 7 if it has a remainder of zero when divided by 7. Examples of numbers which are divisible by 7 are 28, 42, 56, 63, and 98.
How do you find the quotient and remainder?
Quotient and Remainder are parts of division along with dividend and divisor. The number which we divide is known as the dividend. The number which divides the dividend is known as the divisor. The result obtained after the division is known as the quotient and the number left over is the remainder.
What is the quotient of 8 and 4?
1 Expert Answer Since negative one is on the top and the bottom, we can cancel them out, leaving 8/4 which is 2.
What is the quotient of two polynomials called?
A quotient of two polynomials, such as , is called a rational expression.
What is the quotient of 7 divided by 3?
7 divided by 3 is 2 with a remainder of 1.
What is the quotient of 42 and 7?
14
How many 7s is 40?
There are 5 times 7 in 40.
How many 7s is 28?
There are 4 times 7 in 28.
How do you solve 49 divided by 7?
Before you continue, note that in the problem 49 divided by 7, the numbers are defined as follows:
 49 = dividend.
 7 = divisor.
 Start by setting it up with the divisor 7 on the left side and the dividend 49 on the right side like this:
 The divisor (7) goes into the first digit of the dividend (4), 0 time(s).
What is the quotient of 35 and 7?
Here, when 35 ÷ 7, the quotient would be 5, while 35 would be called the dividend, and 7, the divisor.
How do you solve 8 divided by 3?
The number 8 divided by 3 is 2 with a remainder of 2 (8 / 3 = 2 R. 2).
How many times can 3 go into 24?
There are 8 times 3 in 24.
Is repeated subtraction what
Division as Repeated Subtraction
This is a complete lesson with teaching and exercises, showing how division can be seen as repeated subtraction. It is meant for third grade.
Students solve divisions by "subtracting" or crossing out equalsize groups from the total in the visual model, until there is nothing left. Examples show how divisions can be solved by repeatedly subtracting the same number (the divisor). Often, it is actually easier to add intead of subtract, and figure out how many times you will add the number (divisor) until you reach the dividend.
The lesson also shows how numberline jumps tie in with this concept: we jump backwards from the dividend, making jumps of same size (the size being the divisor), until we reach zero. The lesson also has several word problems to solve.
You drew _____ groups of four. 5 × 4 = 4 + 4 + 4 + 4 + 4 = 20. 
20 − 4 − 4 − 4 − 4 − 4 = 0 This is repeated subtraction. You subtract 4 repeatedly till you reach zero. 
1. Make groups, but in your mind 'move them away' or subtract. Write a subtraction sentence.
DIVISION can be solved by repeated subtraction:  
20 ÷ 4 = ??
20 − 4 − 4 − 4 − 4 − 4 = 0.  75 ÷ 25 = ??
I subtracted 25 three times,  84 ÷ 21 = ??
I subtracted 21 four times, 
Often, it is handier to actually add instead of subtract:
Since 13 + 13 = 26,  Since 25 + 25 + 25 = 75,  Since 21 + 21 + 21 + 21 = 84, 
2. Write a multiplication sentence AND a division sentence that fits the addition/subtraction facts.
a. 15 − 5 − 5 − 5 = 0 ___ × ___ = ______ _____ ÷ ___ = ____  b. ____ − 20 − 20 − 20 − 20 − 20 = 0 ___ × ___ = ______ ___ ÷ ___ = ___ 
c. _____ − 23 − 23 − 23 = 0 ___ × ___ = ______ ___ ÷ ___ = ___  d. ____ − 14 − 14 − 14 − 14 − 14 = 0 ___ × ___ = ______ ___ ÷ ___ = ___ 
3. Write a subtraction sentence for each division sentence.
a. 45 ÷ 15 = _______ 45 −  b. 32 ÷ 8 = _______ 32 − 
c. 100 ÷ 20 = _______ 100 −  d. 50 ÷ 10 = _______ 50 − 
e. 50 ÷ 25= _______ 50 −  f. 78 ÷ 26 = _______ 78 − 
Multiplication is like jumps on the number line.
5 × 4 = 20. Five jumps of 4 gets you to 20. 
Division is like making jumps of four backwards from 20 till you get to 0:
20 ÷ 4 = 5. 20 − 4 − 4 − 4 − 4 − 4 = 0 Five jumps of 4 gets you from 20 till 0. 
What division is illustrated here? 
4. Draw jumps backwards to illustrate the division sentences.
a. 
b. 
c. 
d.

e.

f.

g.

h.

i.

5. Solve using repeated subtraction OR adding up to the number being divided.
a. 90 ÷ 30 = ______ 30 ÷ 15 = ______  b. 34 ÷ 17 = ______ 69 ÷ 23 = ______  c. 32 ÷ 16 = ______ 72 ÷ 18 = ______  d. 90 ÷ 15 = ______ 90 ÷ 18 = ______ 
6. If 12 × 2 = 24, then 13 × 2 is _____ . How about division? Use the previous
problem to help you solve the next one.
a. 26 ÷ 2 = ______ 28 ÷ 2 = ______ 30 ÷ 2 = ______  b. 36 ÷ 2 = ______ 38 ÷ 2 = ______ 42 ÷ 2 = ______  c. 50 ÷ 2 = ______ 52 ÷ 2 = ______ 58 ÷ 2 = ______  d. 66 ÷ 2 = ______ 70 ÷ 2 = ______ 78 ÷ 2 = ______ 
7. Try the same kind of thing when dividing by 3.
a. 36 ÷ 3 = ______ 39 ÷ 3 = ______  b. 45 ÷ 3 = ______ 51 ÷ 3 = ______  c. 69 ÷ 3 = ______ 72 ÷ 3 = ______  d. 90 ÷ 3 = ______ 99 ÷ 3 = ______ 
8. Solve the problems.
a. Complete the tables for Alice's reading schedules, if
If her book has 235 pages and she wants to read it in two weeks, which reading schedule should she choose?
 
b. Jerry reads 25 pages a day. How many pages does he read in  
c. Jerry's book has 325 pages. How many days does it take him to read it? Use the previous exercise to help.
 
d. In a bookstore there are many copies of the same book on the shelf. One book is 2 cm thick. Fill in the table:
How many books can you fit on a shelf 66 cm long?

This lesson is taken from Maria Miller's book Math Mammoth Division 1, and posted at www.HomeschoolMath.net with permission from the author. Copyright © Maria Miller.
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