Subtraction by Regrouping: Definitions, Facts, Examples

Subtraction by regrouping is one of the basic topics that contribute towards building the base for Mathematics in students. In Mathematics, addition and subtraction are the two most basic arithmetic operators that will help students answer the problem sums appropriately. The two other basic operators that are commonly used are multiplication and division. These basic arithmetic operators are majorly used in our day-to-day life. This article will focus on the topic of subtraction by regrouping and will help students to understand the correct approach to be followed to answer problem sums independently.

It is however important to understand the process of subtraction to be able to follow the regrouping method correctly. Subtraction means to reduce a number from the other number. We borrow something whenever we do not have enough. The other name for borrowing is regrouping. Let us explore more about subtraction and the method of subtraction by regrouping.

What is Subtraction?

The method of subtraction remains the same whether the numbers to be subtracted are small or large.

Subtraction is one of the basic arithmetic operators representing the operation of removing objects from a collection. Subtraction is the operation of finding the difference between two numbers. When we apply subtraction to a group, the number of things in the group reduces or becomes less.

Subtraction is denoted by the symbol “-“. Subtraction is a minus in most situations, but we still have a vast terminology used for subtraction based on the conditions. The synonym of subtraction is, take away, subtract, minus, decrease, leave, how many leftovers, how much less, etc.

For example, while withdrawing money from the bank, you subtract the withdrawn money from the sum you have in the bank. Like, if you have \({\rm{₹ 25,000}}\) in your account and you need to withdraw \({\rm{₹ 15,000}}\), so the amount left in your account will be \({\rm{₹ 25,000 – ₹ 15,000 = ₹ 10,000}}\).

Let us look at the various parts of subtraction.

Subtraction by Regrouping: Definition

Many times, we use the word borrow in school. For instance, we borrow notes from our classmates, and we borrow money from our friends when we are short of cash, we borrow pen or pencil when we forget to carry our pencil box while going to school, etc.,

Thus, we borrow something whenever we do not have enough. The other name for borrowing is regrouping. We use regrouping in subtraction when the minuend is smaller than the subtrahend.

Let us recall the steps involved in subtraction by regrouping.

Step 1: Write the numbers in the place value chart one below the other. The greater number will come above the smaller number.

Step 2: Subtraction is done column-wise, from right to left. So, always start subtracting from the lowest (ones) place and move to the higher places.

Step 3: Regroup (borrow) if the digit is minuend of a place is smaller than the subtrahend digit.

Let us consider the real-life scenario.

You went to the market with a \({\rm{₹ 100}}\) note in your hand. You bought some toffees, a couple of chocolates and one packet of gems—the total amount added up to \({\rm{₹ 37}}\). Then, you handed the \({\rm{₹ 100}}\) note to the shopkeeper.

When you started calculating how much money the shopkeeper will give you, you realized that the ones and tens digit minuend are smaller than the ones and tens digit of the subtrahend. Then how to do the subtraction???

Here comes the role of subtraction by regrouping or borrowing.

Let us understand it step by step.

Thus, the shopkeeper will return \({\rm{₹ 63}}\).

Let us try subtraction by regrouping on a \(4\)- digit number.

Subtract \(3528\) from \(7495\).

Subtract \({\rm{94,13,205}}\) from \({\rm{1,78,40,926}}\).

Thus, the difference is \({\rm{ = 84,27,721}}\).

Checking Subtraction

After carrying out the subtraction operation, always check for the correctness of the answer obtained.

To do that, add the difference obtained to the subtrahend (the smaller number). If you get the same answer as the minuend (the greater number), then the answer is correct; otherwise, the answer is incorrect, and you need to do the subtraction again. 

Define Subtraction Without Regrouping

This method is the most convenient method to subtract, as in this method, and we do not have to borrow from adjacent left digits because the value of minuend is always greater than the value of the subtrahend.

Take care of the rules given below, and the problems based on without regrouping can be done in no time.
1. Place the subtrahend below the minuend so that the one’s place numbers fall in the same column.
2. Now subtract each column separately and in order, starting with the one’s place column.
3. And lastly, place the answer of the subtractions below each one of the columns, but in order.

Let us understand the subtraction without regrouping with the help of a couple of examples.

Now, let’s take the example of a \(4\)- digit number.

What are Subtraction Rules?

The rules for subtraction are given below.

Subtraction of Two Positive Numbers

While subtracting two positive numbers, take the difference of absolute values of both numbers and assign the sign of the greater number before the answer. For example,

\({\rm{20 – 15 = 5}}\)

\({\rm{5 – 12 = – 7}}\)

Subtraction of a Positive Number and a Negative Number

While subtracting a positive number and a negative number, take the sum of the absolute values of both the numbers and assign the sign of minuend with the answer. For example,

\({\rm{5 – ( – 20) = 25}}\)

\({\rm{( – 12) – 7 = – 19}}\)

Subtraction of Two Negative Numbers

While subtracting two negative numbers, the sign of subtrahend must be changed. Then, take the difference of the numbers’ absolute values and assign the sign of the greater number. For example,

\({\rm{( – 5) – ( – 7) = – 5 + 7 = 2}}\)

\({\rm{( – 16) – (14) = – 16 – 14 = – 30}}\)

Properties of Subtraction

1. We cannot change the order of the numbers in subtraction.

2. When \(0\) is subtracted from a number, the difference is the number itself. For example, \({\rm{32,50,622 – 0 = 32,50,622}}\).

3. When a number is subtracted from itself, the difference is always \(0\). For example, \({\rm{26,34,789 – 26,34,789 = 0}}\).

Solved Examples – Subtraction by Regrouping

Q.1 Subtract \({\rm{638120}}\) from \({\rm{1442721}}\).
Ans:

Q.2. A computer manufacturing company earned \({\rm{₹ 1017609}}\) by selling computers in the first six months of \(2021\). It earned \({\rm{₹ 433000}}\) in January and February, \({\rm{₹ 323656}}\) in March and April and rest in May and June. How much did it earn in May and June?
Ans: Earning in January and February \({\rm{ =₹  433000}}\)

Earning in March and April \({\rm{ =₹  323656}}\)

Therefore, total earning from January to April;

Total earning in the six months \({\rm{ =₹  1017609}}\)

Earning from January to April \({\rm{ =₹  753656}}\)

Therefore, earnings in May and June

Hence, the company earned \({\rm{₹ 263953}}\) in May and June.

Q.3. Subtract \({\rm{1416300}}\) from \({\rm{62342750}}\) and write the steps to verify the answer.
Ans:

Verifying subtraction result:

After carrying out the subtraction operation, always check for the correctness of the answer obtained.

To do that, add the difference obtained to the subtrahend. If you get the same answer as the minuend, the answer is correct; otherwise, the answer is incorrect, and you need to do the subtraction again. 

Lets us understand the concept with the example taken above.

Here, after adding, we get \({\rm{6,23,42,750}}\) which is the same as minuend.

Q.4. ABC airlines require a pilot to have \({\rm{506500}}\) hours of flying experience before promotion. If Kunal has completed \({\rm{346320}}\) hours, how many more hours of experience does he need to qualify for the promotion?
Ans: ABC airlines require total hours of flying experience before promotion \({\rm{ = 506500}}\) hours.

Kunal completed \({\rm{ = 346320}}\)

Thus, the number of hours required more can be found out by subtracting.

Hence, Kunal requires \({\rm{160180}}\) more hours to qualify for the promotion.

Q.5. Subtract \({\rm{5465932}}\) from \({\rm{9695503}}\).
Ans:

Summary

In this article, we learned about the need to subtract numbers with regrouping and then learned the technique to subtract the numbers with the help of borrowing or regrouping. We also learned the way to subtract the numbers without regrouping. In addition to this, we also learned the properties of subtraction.

Frequently Asked Questions (FAQs) – Subtraction by Regrouping

Frequently asked questions related to subtraction by regrouping is listed as follows:

Q.1. How do you subtract without regrouping?
Ans: Place the subtrahend below the minuend so that the one’s place numbers fall in the same column. Now subtract each column separately and in order, starting with the one’s place column. And lastly, place the answer of the subtractions below each of the columns, but in order.

Q.2. What are the basic properties of subtraction?
Ans: The basic properties of subtraction are

1. We cannot change the order of the numbers in subtraction.
2. When \(0\) is subtracted from a number, the difference is the number itself.
3. When a number is subtracted from itself, the difference is always \(0\).

Q.3. Explain subtraction by regrouping with example?
Ans: We use regrouping in subtraction when the minuend is smaller than the subtrahend.

1. Write the numbers in the place value chart one below the other. The greater number will come above the smaller number.
2. Subtraction is done column-wise, from right to left. So, always start subtracting from the lowest (ones) place and move to the higher places.
3. Regroup (borrow) if the digit of minuend of a place is smaller than the subtrahend digit. Let us consider the real-life scenario.

Q.4. How do you explain regrouping?
Ans: Many times, we use the word borrow in school. For instance, we borrow notes from our classmates, and we borrow money from our friends when we are short of cash, we borrow pen or pencil when we forget to carry our pencil box while going to school, etc., Thus, we borrow something whenever we do not have enough. The other name for borrowing is regrouping. We use regrouping in subtraction when the minuend is smaller than the subtrahend.

Q.5. Do we always need to regroup when we subtract?
Ans: No, it’s not always necessary to subtract with regrouping. If the value of minuend is greater than the value of subtrahend, then we subtract without regrouping or without borrowing; otherwise, we have to subtract by regrouping or with the help of borrowing.

We hope this detailed article on subtraction by regrouping helped you in your studies. If you have any doubts or queries regarding the topic, feel to ask us in the comment section.