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Addition of Numbers With Number Line and Downward Method

Maths Query > Unit > Arithmetic > Arithmetic Operations > Addition of Numbers With Number Line and Downward Method

Add numbers using number line

Let’s understand first what a number line is. It is a straight line with marked numbers on it at equal distances. The numbers on a number line start from left from 0 and increase towards the right side. It is like the one shown shown as below.

Number line from 0 to 10
Number line from 0 to 10

Steps to add numbers on number line

Step 1: To add two numbers, take the first number. Start from 0 on number line and move to the right until you reach the given number.
Step 2: Take the second number. On the number line, start from the first number drawn on number line. Jump to the right one by one by number of steps equal to the second number.

Example

Add 14 and 5 using number line.
To add 14 and 5, draw a number line from 0 to 20.
Number line from 0 to 20


Step 1:Start from 0 on number line then move to the right until we reach 14, which is the first number.
Step 1: Number line representing number 14


Step 2: Take second number 5, jump to the right one by one by 5 steps the second number.
Step 2: Number line representing sum of 14 and 5

Finally, after jumping by 5, we reach 19, which is the answer of sum of 14 and 5.
∴ 14 + 5 = 19


Downward addition of numbers

In this method, the numbers are added up after arranging the numbers in order of places like ones, tens, hundreds, thousands and so on. Let’s first take a short look at what are the places in a number

The digits in a number have their own positions namely ones, tens, hundreds, thousands and so on which are called places. These places start from the digit which is at the very right end of the number and moves from right to left. The digit which is at the rightmost side in a number is at place “Ones” and second from right is at “Tens”. Following is the chart to know the different place names in a number written in an increasing order from right to left.

Chart of place names of a number
Chart of place names of a number

The places of the digits in a number 4936 are 6 at ones place, 3 at tens place, 9 at hundreds place and 4 at thousands place. They can be easily understood from the following figure also.

Places of digits chart of 4936
Places of digits chart of 4936

How to know place and place value of a digit in a number have been explained with examples in the chapter Digit, Face, Place Values and Comparison of Numbers.

Steps to add numbers downwards

Following steps can be used to add numbers downward.
Step 1: Write all the given numbers in an order of places of ones, tens, hundreds, thousands and so on.
Step 2: Add all digits under a same place in downward direction starting from first column or ones place to the second column or tens place and so on.
Let’s understand it with an example.

Example

Add the numbers 14 and 25
Step 1: Write 4 under ones place and 1 under tens place from 14. Write 5 under ones place and 2 under tens place from 25.
Write 14 and 25 at ones and tens places


Step 2: Add all digits at ones place i.e. 4 and 5. So, 4 + 5 = 9.
add 4 and 5 digits at ones place


Also, add all digits at tens place i.e. 1 and 2. So, 1 + 2 = 3. add 1 and 2 digits at ones place

So, addition of 14 and 25 is equal to 39.

Addition of numbers with carryover

When adding numbers, there may be a case when the sum of two digits in a column is more than 9, eventually a 2 digit number.
In such cases, the digit at tens place of the sum carried over to the next column. Then the carried over digit is added up to the rest of the digits in that column.
In the above example of adding 14 and 25, the sum of first column digits 4 and 5 is 9, which means it is less than 9, so this example is without any carryover digit.

Steps to add numbers with carryover

Step 1: Write the 3 digits numbers at their ones, tens and hundreds places
Step 2: Add the digits at each place starting from ones and moving to tens then hundreds and so on. If at any place, the total of digits obtained is more than 9 then the digit at tens place of the total is carried over to the next upper place. This carried over digit is added up to the rest of digits at that place of given numbers.


Lat’s take an example to add three digit numbers with carryover.
Example

Add 386 and 978
Step 1: Write the 3 digits numbers 386 and 978 at their ones, tens and hundreds places.
Write 386 and 978 at ones, tens and hundreds places


Step 2: Add the digits of first column or at ones place i.e. 6 and 8. So, 6 + 8 = 14.
Now, 14 is a two digit number. So, here, 1 is at tens place, which is a carryover digit. Write the carryover 1 at the top of tens place digits or second column i.e. 8 and 7.
add first column digits of 386 and 978


Add all digits at tens place i.e. 1, 8 and 7. So, 1 + 8 + 7 = 16.
Again, 16 is a two digit number. So, write the carryover 1 at the top of hundreds place digits or third column i.e. 3 and 9.
add second column digits of 386 and 978


Add all digits at hundreds place i.e. 1, 3 and 9. So, 1 + 3 + 9 = 13.
The total 13 of last place digits i.e. 1, 3 and 9, is written as it is.
add third column digits of 386 and 978

So, addition of 386 and 978 is equal to 1364.

Worksheet 1

Addition of two digits numbers using number line

Number line from 0 to 20
1) 7 + 5 =
2) 4 + 9 =
3) 3 + 7 =
4) 5 + 6 =
5) 17 + 1 =
6) 15 + 2 =

Worksheet 2

Downward addition of one digit numbers

1)
TO
8
+2
2)
TO
9
+4
3)
TO
2
+6
4)
TO
8
+6
5)
TO
5
+4
6)
TO
9
+9
7)
TO
7
+5
8)
TO
3
+6
9)
TO
5
+5
10)
TO
6
+0

Worksheet 3

Downward addition of two digits numbers without carryover

1)
TO
32
+52
2)
TO
43
+24
3)
TO
56
+31
4)
TO
12
+83
5)
TO
76
+23
6)
TO
84
+14
7)
TO
36
+32
8)
TO
24
+15
9)
TO
10
+10
10)
TO
43
+55

Worksheet 4

Downward addition of two digits numbers with carryover

1)
TO
47
+34
2)
TO
56
+35
3)
TO
26
+44
4)
TO
84
+18
5)
TO
45
+36
6)
TO
16
+67
7)
TO
28
+16
8)
TO
34
+57
9)
TO
57
+23
10)
TO
77
+17

Worksheet 5

Downward addition of three digits numbers with carryover

1)
HTO
143
+657
2)
HTO
482
+327
3)
HTO
274
+237
4)
HTO
357
+565
5)
HTO
208
+115
6)
HTO
666
+244
7)
HTO
517
+245
8)
HTO
419
+381
9)
HTO
732
+198
10)
HTO
436
+358
Last updated on: 31-08-2025
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