No one wondered if math could be so easy to use by grouping the numbers to make the calculations go easier. The methodology becomes easier when the numbers are grouped in multiples of 10s or 100s. Subtraction with regrouping is one of those easiest methods that will help to quicken your numerical calculations and enhance reasoning and problem-solving skills!
Subtraction with regrouping is a technique for determining the difference between two supplied integers by progressively rearranging two or more big numbers. Regrouping is the procedure of producing sets of tens when two-digit integers are added or removed (or more). It is also known as carrying and borrowing. Borrowing is more prevalent in regrouping subtraction, where we subtract one integer from the matching place value. Subtraction is performed when the bottom index is greater than the top integer.
Subtraction with regrouping is incredibly useful in everyday life, including when handling money, such as purchasing, measuring time, determining the correct time from a foreign standard time, and measuring distance. Whenever we subtract two integers, we employ the following terms from the subtraction expression:
Minuend: The integer which is subtracted from another number.
Subtrahend: The amount to be removed from the minuend.
Difference: The outcome of deducting the subtrahend from the minuend.
Minuend – Subtrahend = difference is the subtraction formula.
For example: Let us evaluate the difference between 8 and 6.
Subtraction With Regrouping Steps
Subtraction with regrouping is often referred to as borrowing with subtraction. We apply the regrouping approach when the minuend is less than the subtrahend. We borrow one integer from the following column while regrouping to get the minuend greater than the subtrahend. The methods for subtracting numbers using regrouping are as follows:
Step 1: Place the numerals vertically as per their place value.
Step 2: Begin deducting numbers from one’s spot. If the value at the bottom is larger than the integer at the top, we will take 1 from the tens column and add it to the integer at the one’s position.
Step 3: Following put 1 in the one’s position, the integer in the ten’s position will decrease by one. Deduct the integers starting with a one.
Step 4: Then repeat step 2 with the remaining 2 digits and higher digits. When we lend, we deduct the integers at the same time.
Step 5: To obtain the overall difference, deduct the last number.
2-Digit Subtraction With Regrouping
Using the procedures outlined above, you can execute 2-digit subtraction using regrouping. Ones and tens are the place values for two-digit numerals. For a greater grasp, let’s consider the example and solve it together with the steps. Subtraction of 37 from 92.
Step 1: Organize the numbers in ascending order of place value, with the larger number on top. So 2 and 7 are in position one, and 9 and 3 are in position ten.
Step 2: Let’s start with number one. Because 7 is greater than 2, we borrow 1 from the tens position, i.e. 9, to make 8.
Step 3: The borrowed 1 adds up to 2 as 12. As a result, 12 – 7 = 5.
Step 4: After we’ve deducted the one’s place, we’ll go to the ten’s place. 3 is smaller than 8.
Step 5: now 8 – 3 = 5.
As a result, the gap between 92 – 37 = 55
Regrouping 3-Digit Subtraction
3 digit subtraction with regrouping is performed the same way as one-digit and two-digit integers. Three-digit numerals have place values of hundreds, tens, and ones. For a greater grasp, consider the following example. Subtraction of 156 from 951.
Step 1: Organize the integers in ascending order of place value, with the larger amount on top. So, 1 and 6 are at the one position, 5 and 5 are at the ten positions, and 9 and 1 are at the hundred positions.
Step 2: Let’s start with number one. Because 1 is less than 6, we borrow 1 from the tens place, resulting in 5, which decreases to 4.
Step 3: The borrowed 1 adds up to 1 as 11. As a result, 11 – 6 = 5.
Step 4: Repeat step 2 for the tens and hundreds of places, taking 1 of each of the integers that creates it; 9 at the hundred’s place will drop to 8, and 4 at the ten’s place will make it 14. To calculate the difference, subtract all of the numbers.
As a result, the difference between 951 and 156 is 795
4-Digit Subtraction with Regrouping
4-digit subtraction with regrouping is done the same way as one-digit, two-digit, and three-digit integers. Because this is a four-digit number, the place values are thousands, hundreds, tens, and ones. Consider the following example: subtract 4598 from 9165.
Step 1: Put the integers in ascending order of place value. Begin subtracting the numerals at one. As we’ve seen, 8 is bigger than 5. So, we’ll take 1 from the tens column and increase it by 1 to get 15. Now, 15 – 8 equals 7.
Step 2: After assigning 1 to the column of one in the previous stage, 6 becomes 5. Then remove the numbers at the tens position. Because 5 is less than 9, we will take 1 from the hundreds column. It brings the total to 15. As a result, 15 – 9 = 6.
Step 3: Because we assigned a 1 to the tens column in step 2, we now have a 0 at the hundreds spot. To subtract the digits on the hundreds, i.e., (0 – 5), we shall use 1 from the thousands column. That brings the total to ten. As a result, 10 -5 = 5.
Step 4: Now subtract the digits in the thousands place. We have 8 after adding 1 to the hundreds column. As a result, 8 – 4 = 4.
As a result, the difference between the two integers is 9165 – 4598 = 4567.
Subtraction of Decimals with Regrouping
To solve decimal subtraction using regrouping, follow the instructions below:
Step 1: Organize the numbers with the decimal point in the order they should be.
Step 2: When the lengths of the decimal numbers vary, insert zeroes.
Step 3: Using the same methods as for the remaining digits, subtract the decimal numbers and find the result of subtracting.
Subtract 5.624 from 98.6542, for example.
Practice Problems Subtraction with Regrouping
1. Shelly paid $1699 for a bedsheet. She handed over $2000 in cash to the shopkeeper. What is the amount of the merchant’s refund?
2. Brad answered 483 of 500 questions correctly. How many unsolved questions remained?
3. Class V had 473 pupils; 461 passed and advanced to the next class. How many kids did not progress?
4. The library had 746 volumes. 242 of these books were misplaced. How many books are still on the library’s shelves?
5. Sam covered 8473 kilometers. He took the train for 4253 kilometers and then drove the rest. How many kilometers did he drive?
6. What is the difference between a five-digit and a four-digit number?
7. Derek must travel 1456 kilometers to his hometown, 1152 kilometers by train, and the rest by bus. In all, how far does he travel via bus?
8. What is the distinction between 4897 and 6123?
9. What is the difference between the numbers 698 and 553?
10. Mike had $4,776 in his savings account. He took out $1,873 from the ATM. How much money does he currently have in his savings account?
11. 1307 is the difference between two numbers. Find the lower number if the greater number is 9577.
12. The library has 4500 books. They are written in either English or French. How many French novels are there if there are 2894 in English?
13. A school has 1348 female students. If there are 2900 pupils, how many guys are there in total?
14. A basket contains 55 oranges. The merchant owns a total of 65 oranges. What is the maximum number of oranges that may be placed in the basket?
15. What is the distinction between 3756 and 5433?
16. Shelly went grocery shopping and bought 568 cookies. The bakery only gave her 233 cookies. How many more cookies does she need?
17. Rosy produced 452 dark chocolates and 183 vanilla chocolates on July 27. Which taste is weaker, and how many more chocolates are needed to equal both flavors?
18. The festival drew 23,948 young people, with 573 of them being guys. How many females attended the festival?
19. Mike must learn the meanings of 353 words. He had completed memorizing 120 words. How many more words does he need to know?
20. Jerry plans to read a book of 1762 pages in five days. How many pages are left to read if she can read 1143 in three days?
21. Adriana’s garden has 346 apples. She handed her pal two apples. She received 135 apples. In all, how many apples did she give to her friend?
22. Sara’s monthly salary is $6955. She saves $1565 every month. What is her budget for the month?
23. Nathalie has 3 hours to complete a 6500-word essay. If she can write 4895 words in two hours, how many words does she need to write in one hour to finish her piece?
24. During a vaccination campaign in the hamlet, 13026 children were immunized out of 13567. How many youngsters have yet to get vaccinated?
25. A cement merchant’s godown had 8436 sacks of cement. He sold 3565 cement sacks in all. How many bags are still in the godown?
26. Ron has 1846 marbles in his possession, 547 of which he has donated to his sister. So, how many marbles does he still have?
27. Jane took 356 minutes to do her English and Math assignments. Her English class lasted 204 minutes. How long did she take to finish Math?
28. There are 45 residences on the street. A total of twenty-one dwellings have been whitewashed. How many houses still need to be painted?
29. Only 6989 of the town’s 8797 students attend school. How many kids do not go to school?
30. My father wishes to purchase an $8580 washing machine. But he only has $7560. How much more cash does he require?
31. Tom has a $7800 sum in his bank account. On Monday, he withdrew $2340, and on Tuesday, he started $2670. How much money is remaining in his bank account?
32. I had a total of $500,000 in my possession. The total amount spent was $3585. How much money do I have now?
33. Sandy scored 785 points in a Saturday game. On Sunday, he was down 213 points. How many points did he still have?
34. While a television costs $7,069, a bicycle costs $2,359. What is the difference in price between the tv and the cycle?
35. What’s the distinction between 3162 and 2526?
36. Vanilla would want to spend $975 on a pair of jeans and $1699 on a shirt. With $2000, will she be able to purchase both the blouse and the pants? If not, how much more money does she require?
37. A grain dealer has 9736 kg of wheat on hand. He sold a total of 6859 kilograms of wheat. How much wheat does he have on hand right now?
38. The Olympiad exam drew a total of 24.790 students. 248 students sat the Math Olympiad test, while the remaining pupils took the Science Olympiad exam. What was the total number of pupils that competed in the Science Olympiad?
3. 12 students
5. 4220 km
7. 304 km
13. 1552 boys
14. 10 oranges
17. Vanilla; 269
25. 4871 bags
27. 102 minutes
28. 24 houses
29. 1808 children
36. $674 more needed
37. 2877 kg
Frequently asked questions on Subtraction with Regrouping
Q1. Why is it important to learn subtraction with regrouping?
Whether it is addition or subtraction, regrouping numbers helps deal with real-life mathematical calculations. If you visit a shop and do not know how to add or subtract quickly, you will be doomed. You must learn how to regroup numbers to speed up your calculations. Moreover, if you are not familiar with the regrouping concept, it will be difficult for you to calculate large numbers or a large amount of data.
Q2. Does learning subtraction with regrouping help clear SAT?
Yes, mastering the problems based on subtraction with regrouping will help score more in the SAT exam. The SAT math exam is not too hard. You can crack the SAT math exam by practicing regrouping in addition and subtraction. If your calculations are good and quick, you can correctly attempt 15-20 questions out of 58 in the SAT exam. Since there are 15 questions in the no-calculator section, you can attempt all of them within 25 minutes.
Q3. How much can I score on the ACT by practicing subtraction with regrouping?
The math section in ACT has the highest raw points of 60. Out of 60, you can easily score 60 if your command of mathematics is firm. If you practice regrouping, particularly subtraction with regrouping, you can score more than average, which is 21 marks in the ACT exam. To step ahead of your friends, you must practice word problems on subtraction 3 digits with regrouping and 2 digit subtraction with regrouping in mind daily.