Subtraction means taking away something or reducing the count.

In a subtraction problem, there is the minuend, subtrahend, and difference. For example, 7-4=3 is a subtraction problem in which 7 is a minuend; 4 is a subtrahend and 3 is the difference.

Note, that in subtraction we always subtract a smaller number with a larger number to get the correct answer. There are a number of techniques in which we can subtract two numbers. One of which is to countback.

**Count Bank**: Countback is a technique in which we count backward from the minuend.

Let’s understand it by taking up an example,

We need to subtract 3 from 7 so we start from 7 and start counting back 3 times as we have to subtract 3

so we get 7-3=4.

**Vertical Subtraction:**

We can subtract numbers vertically.

To subtract 8-2 vertically we write it as

8

-2

—-

6

—-

So what we have done we have written the two numbers one under another and then did the subtraction.

Now, let’s take the case of two-digit numbers; In two digits numbers, there are two places of the digits ones and tens so we write the numbers one below according to their place of digit.

Say, we need to add 64-24

T O

6 4

– 2 4

————

4 0

————

Similarly, we can do for three-digit numbers;

H T O

2 2 8

-1 1 6

——————

1 1 1

——————-

And for four digits

H T O

4 2 2 8

– 2 1 1 6

————————

2 1 1 2

————————-

Subtraction using Borrowing:

Let’s say now we need to subtract 86-47

T O

8 6

-4 7

————-

So, what we can see while subtracting 6 is smaller than 7, so what we do we take 1 borrow from the tens column and make 6 as 16, and then subtract 16-7

T O

8 16

-4 7

———-

8

As we have borrowed 1 from the tens place now 8 becomes 7 as we subtract 1 from 8, so,

T O

7 8 16

-4 7

———-

3 8

————

So, 86-47=38.

We have done it till now for two digits this method can be applied for 3 and 4 digits. Examples:

1. Subtract 865-276

H T O

78 1 56 15

-2 7 6

————-

5 8 9

————–

2. Subtract 864-135

H T O

8 5 6 15

-1 3 6

————-

7 2 9

————–

3. Subtract 7956-2347

Th H T O

7 9 45 16

-2 3 4 7

———————-

5 6 0 9

———————–

Practise Questions:

1. 357-126

2. 976-125

3. 758-245

4. 704-256

5. 6522-5320

6. 4291-3081

7. 6333-2111

8. 2631-430

9. 59-17

10.91-59

**Solutions:**

In the above way, we write the numbers and their number name after 100.

Place Value and Face value: The place value of a number means the value of the digit in its position. For example 2 in the place of tens so its place value will be 20.

The face value of a number means the actual value of the digit, For example, 2 in tens place will have its face value as 2 only.

Let’s take another example;

Find out the place value and face value of 2 in 2037.

As the 2 is in the thousands place so its place value is 2000 and its face value is 2. Expanded form:

Expanded form is a way of writing numbers by adding the value of the digits. Say, expanded form of 235 will be “200+30+5” as 2 is in hundreds place we multiply it by 100,3 is in tens place we multiply it by 10 and 5 in ones place so by 1 Let’s take another example; 1234 so the expanded form will be “1000+200+30+4” Comparing numbers:

When we write two numbers, there will be one number that is bigger than the other or lesser than the other or equal to each other.

Finding out which number is bigger or smaller or the numbers are equal is said to be as comparing numbers.

- If the number is bigger than the other number we said that the number is greater than and show it by the sign “>”
- If the number is smaller than the other number we said that the number is lesser than and show it by the sign “<”
- If the numbers are equal then we show it by the sign “=”

Let’s see some examples:

59>48

15<99

75 = 75

**Ordering Numbers**

Once you know how to compare the numbers you can arrange a set of numbers in the order of either highest to lowest or lowest to highest.

Arranging numbers from lowest to highest is known as Ascending order and arranging numbers from highest to lowest is known as descending order.

Let’s see an example of each type:

a) Arrange the numbers in ascending order: 56,15,13,28,49

Ans: 13,15,28,49,56

b) Arrange the numbers in descending order: 115,248,63,845,125

Ans: 845,248,125,115,63.

**Rounding Off**

Rounding off means changing a number near to its tens, hundreds or thousands. There are two rules for rounding off:

1. If the unit’s place digit is less than 5 we will round it off to the previous tens, hundreds or thousands. For example, we need to round off 73, as we can see 3 is less than 5 so we round it to 70. Similarly, for 743, we will round it to 740.

2. If the unit’s place digit is equal to or greater than 5 we will round it off to the next tens, hundreds or thousands. For example, we need to round off 88, as we can see 8 is greater than 5 so we round it to 90. Similarly, for 855, we will round it to 860.

**Practise Questions:**

1. Find the place values of

a. 3 in 7838

b. 8 in 38

c. 0 in 5840

d. 7 in 507

e. 1 in 316

2. Find the face values of

a. 9 in 2958

b. 8 in 383

c. 9 in 97

d. 3 in 3116

e. 7 in 7366

3. Write the following in expanded form:

a. 5057

b. 7684

c. 2152

d. 6058

e. 2381

4. Compare the following numbers and put the correct sign “<,>’=”

a. 354_255

b. 463_463

c. 150_199

d. 675_885

e. 777_777

5. Arrange in Ascending orders:

a. 1326,875,1020,364

b. 1624,1267,878,1312

c. 794,1120,618,1114,1388

d. 2378,909,2370,916,1897

e. 790,776,765,714

6. Arrange in descending order:

a. 879,846,825,833

b. 1116,1524,1423,1119

c. 6470,6102,6363,6599

d. 745,820,615,509

e. 937,528,634,769

7. Round off the following numbers:

861

826

415

549

699

**Solutions:**

1.

a. 30

b. 8

c. 0

d. 7

e. 10

2.

a. 9

b. 8

c. 9

d. 3

e. 7

3.

a. 5057=5000+000+50+7

b. 7684=7000+600+80+4

c. 2152=2000+100+50+2

d. 6058=6000+000+50+8

e. 2381=2000+300+80+1

4.

a. 354>255

b. 463=463

c. 150<199

d. 675<885

e. 777=777

5.

a. 364,875,1020,1326

b. 878,1267,1312,1624

c. 618,794,1114,1120,1388

d. 909,916,1897,2370,2378

e. 714,765,776,790

6.

a. 879,846,833,825

b. 1524,1423,1119,1116

c. 6599,6470,6363,6102

d. 820,745,615,509

e. 937,769,634,528

7.

a. 860

b. 830

c. 420

d. 550

e. 700

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