### 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:

- Subtract 743 and 529.
- Subtract 2991 and 745.
- Find the difference of 4263 and 2528.
- Find 299 – 197.
- Find 395 – 182.
- Find the difference of 10551 and 9721.
- Find 41526 – 32486.
- Find 5791 – 3426.
- Find 73967 – 64521
- In finding 3631 – 2987, what will be the first step.
- Find 5937 – 4631.
- Find the difference of 54311 and 43846.
- 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.