Repeated Subtraction: Definition, Diagram, Properties, Examples

Repeated subtraction is called subtraction of 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.

In this article, let’s learn more about repeated subtraction with some solved examples.

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.

\(10-5=5\) 

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.

\(10-5=1+1+1+1+1+1+1+1+1+1-1-1-1-1-1=5\)

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 \(36-6=30, 30-6=24, 24-6=18, 18-6=12, 12-6=6, 6-6=0\), 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 \(56÷7=8\).

Repeated Subtraction Definition

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.

The above image shows 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. 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 \(32-4=28, 28-4=24, 24-4=20,\)
\(20-4=16, 16-4=12, 12-4=8, 8-4=4, 4-4=0\),
so you have subtracted the number \(4\) for \(8\) times, so the division will be \(932÷4=8\).

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 \(4-2=2, 2-2=0\), and we have subtracted the number \(2\) for two times, so the division sentence will be \(4÷2\).

The subtraction sentence will be \(15-5=10, 10-5=5, 5-5=0\); we have subtracted the number \(5\) for three times so that the division sentence will be \(15÷3\).

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, \(18-6=12→12-6=6→6-6=0\) 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

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 \(27-3=24, 24-3=21, 21-3=18,\)
\(18-3=15, 15-3=12, 12-3=9, 9-3=6, 6-3=3, 3-3=0\)
Now, the number \(3\) is subtracted for nine-time, 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 nine-time, 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 \(28-7=21, 21-7=14, 14-7=7, 7-7=0\)
Now, the number \(7\) is subtracted four-time, 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 \(175-35=140, 140-35=105, 105-35=70, 70-35=35, 35-35=0\)
Now, the number \(35\) is subtracted for five-time, 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 \(342-171=171, 171-171=0\)
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 \(784-261=522, 522-261=261, 261-261=0\)
Now, the number \(261\) is subtracted for three-time, 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 \(9000-3000=6000, 6000-3000=3000, 3000-3000=0\)
Now, the number \(3000\) is subtracted for three-time, 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 \(20000-5000=15000, 15000-5000=10000, 10000-5000=5000, 5000-5000=0\)
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 talked about the term subtraction and an example. Then we have discussed what repeated subtraction is and have provided a 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.

FAQs

Q.1. 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, \(42-6=36, 36-6=30, 30-6=24, 24-6=18, 18-6=12, 12-6=6, 6-6=0\), 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.2. 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.3. 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.4. 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 \(45-9=36, 36-9=27, 27-9=18, 18-9=9, 9-9=0\), 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 \(72÷9=8\).

Q.5. 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.

We hope you find this detailed article on repeated subtraction helpful. If you have any doubts or queries regarding this topic, feel to ask us in the comment section and we will assist you at the earliest.