Subtraction up to 10,000 With and Without Regrouping

Key Concepts

•   Subtraction without regrouping
•   Difference 
•   Subtraction with regrouping in hundreds and thousands.
•   Regroup
•   Subtraction with regrouping in ones, tens, hundreds, and thousands.
•   Subtraction across zeros.

Introduction

 This chapter will learn about the subtraction of numbers up to 10,000 and the terms used for subtraction.

4.1 Subtraction without Regrouping:

Subtraction without regrouping is when the digits subtract up to a number that is 9 (or) less. Here, the answer can be written below each place value column. 

Example: Find the difference of 8432 and 2321. 

Sol: Step 1: Subtract ones  

                       

  

Step 2: Subtract tens 

              

Step3: Subtract hundreds      

Step4: Subtract thousands 

             

4.1.1 Difference

The result obtained from the subtraction of two (or) more numbers are called the difference. 

Example: 150 – 40 = 110     Difference 

4.2 Subtraction with regrouping in hundreds and thousands.

Regrouping in subtraction is a process of exchanging one ten into ten ones. We use regrouping in subtraction when the minuend is smaller than the subtracted. We use subtraction with regrouping to work out different subtraction problems. 

Example: Find the difference between 8694 and 4843. 

Step 1: Subtract the ones      

 

Step 2: Subtract the tens  

 Step3: (1) You cannot take away 6 from 8 

(2) So, regroup thousands and hundreds 

Regroup: 8 thousand + 6 hundred 

        = 7 thousand + 16 hundred 

Step 4: Subtract the hundreds 

 

Step 5: Subtract the thousands 

7 thousand – 4 thousand = 3 thousand 

    The difference between 8694 – 4843 is 3851. 

4.2.1 Regroup

Regrouping can be defined as the process of making groups of tens when carrying out operations like addition and subtraction with two-digit numbers (or) larger numbers.

4.3 Subtraction with regrouping in ones, tens, hundreds, and thousands. 

Subtraction with regrouping is the process of making groups of ones, tens, hundreds, and thousands when carrying out operations like subtraction with 2 (or) more digits (or) larger. 

Example: Find the difference between 5678 and 3789. 

Sol: Step1: Subtract the ones 

          

Regroup the tens and ones                

=>6 Tens and 18 ones                         

Step2: Subtract the tens   

Regroup hundreds and tens       

=> 5 hundreds and 16 tens

Step3: Subtract the hundreds         

              

Regroup thousands and hundreds            

=> 4 thousand and hundred   

Step4: Subtract the thousands 

Regrouping is not required. 

4.4 Subtraction Across Zeros.

If you subtract 0 from any number, you get the same sum. 

Example: 4000 – 125 

Sol:

Step1: Regroup thousands and hundreds 

So, 4000 (4 thousand and 10 hundred) 

Step2: Regroup hundreds and tens   

So, (10 – 1) 9 hundred and 10 tens 

Step3: Subtract the ones        

10 ones – 5 ones                    

Step4: Subtract the tens 

9 tens – 2 tens 

Step5: Subtract the hundreds      

       

9 hundred – 1 hundred             

Step6: Subtract the thousand 

Remaining 3 in thousands 

Exercise:

1. Subtract 743 and 529.
2. Subtract 2991 and 745.
3. Find the difference of 4263 and 2528.
4. Find 299 – 197.
5. Find 395 – 182.
6. Find the difference of 10551 and 9721.
7. Find 41526 – 32486.
8. Find 5791 – 3426.
9. Find 73967 – 64521
10. In finding 3631 – 2987, what will be the first step.
11. Find 5937 – 4631.
12. Find the difference of 54311 and 43846.
13. There are 576 people in a colony. If 324 people left the colony, then how many people are remaining in the colony?

What we have learnt:

• Understood how to subtract 2 (or) more digits without regrouping place values and understood the term difference.
• Understood how to subtract 2 (or) more digits with regrouping in places of hundreds and thousands. Understood the term regrouping.
• Understood how to subtract 2 (or) more digits with regrouping all the place values from ones to thousand.
• Understood how to subtract the 2 (or) more digits a crossing zero from regrouping all place values.

Concept Map:

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