Addition Tricks

Addition Tricks are are the techniques that helps to calculate sum in a very quick manner. It is fundamental to learn all the addition tricks in the mathematics to perform quick addition. In this article, we will learn addition tricks for performing sum of large numbers without use of pen and paper. This article also has solved examples and practice questions to help the students thoroughly with the concept.

Addition is the process of calculating the total number by adding two or more numbers. It is a fundamental arithmetic operation that is utilized in a variety of applications, ranging from simple counting to more complicated calculations. It is widely used in counting total marks, total number of items that you purchased and total bill of your shopping. It is such fundamental concept without which you can’t imagine your daily life. Let’s understand it with a very simple example given below:

Suppose you have 3 apples, and a friend gives you 4 more apples. To find out how many apples you have in total, you perform the addition:

• You start with 3 apples.
• You receive 4 more apples.

The total number of apples is 3 + 4 = 7 Apples.

Now, for this you might have used fingers to count the number of total apples. But what if you have 345 apples and your friend has given you 406 more apples. Then this counting would not be possible on fingers. For this you would do conventional method of addition that you have learned in your junior classes when you started learning arithmetic.

Now, its time to go ahead and calculate these complex additions in seconds in your mind without using pen and paper. For this you need to learn some tricks which are useful in quick addition. These addition tips and tricks are mentioned in detail below along with their examples.

Additions tricks are nothing but a quick way to calculate sum of numbers even for complex and larger number. These tricks will help you in help in increasing you speed. Below are some useful tricks for performing addition quickly and efficiently, along with examples for each:

Commutative Property

The order of addends can be changed without affecting the sum.

a + b = b + a

Example:

7 + 13 = 13 + 7 = 20

Here, if you can’t add 7 with 13 then you can quickly reverse their order and add which will make you feel easy.

Associative Property

Grouping of addends can be changed without affecting the sum.

(a + b) + c = a + (b + c)

Example :

(13 + 11) + 9 = 13 + (11 + 9)

24 + 9 = 13 + 20

30 = 30

Here, if we have three or more numbers we can choose pair of number which is more easy to add. Like it is easy to add 11 with 9 and then with 13 rather than 13 with 11 and then with 9.

Adding Zero

Adding zero to a number leaves it unchanged.

a + 0 = a

Example : 9 + 0 = 9

Breaking Down Numbers (Decomposition)

Break down numbers into parts that are easier to add.

Example :
47 + 25
= (40 + 7) + (20 + 5)
= (40 + 20) + (7 + 5)
= 60 + 12
= 72

Rounding and Compensating

Round one addend to a nearby number that is easier to add, then adjust the result.

Example:
68 + 27
Round 68 to 70 (add 2), then subtract 2 at the end:
70 + 27 = 97
97 – 2 = 95

Using the Tens Complement

Find the complement to the next multiple of ten and adjust. Complement means just to find how much the number is lagging or exceeding the nearest round off number.

Example:
48 + 37
48 to 50 (complement is 2)
37 – 2 = 35
50 + 35 = 85

Counting Up

Start with the larger number and count up by the smaller number.

Example:
23 + 6
Start with 23:
24, 25, 26, 27, 28, 29
So, 23 + 6 = 29

Using Known Sums

Use commonly known sums, such as doubles or sums of ten.

Example:
8 + 7
8 + 8 = 16
7 is 1 less than 8, so 16 – 1 = 15

Splitting for Easier Addition

Split numbers to make the addition easier, especially useful for multi-digit numbers.

Example :
123 + 456
Split into hundreds, tens, and units:
(100 + 400) + (20 + 50) + (3 + 6)
= 500 + 70 + 9
= 579

Using Number Lines

Visualize addition on a number line.

Example :
5 + 3
Start at 5, move 3 steps to the right:
5 to 6, 7, 8
So, 5 + 3 = 8

Vertical Addition (Column Addition)

Line up numbers by place value and add vertically, carrying over if necessary.

Example :

[Tex]\begin{array}{ccccc} & & 4 & 5 & 6 \\ +& & 7 & 8 & 9 \\ \hline & 1 & 2 & 4 & 5 \\ \end{array}[/Tex]

1. Add units: \(6 + 9 = 15\) (write 5, carry 1)
2. Add tens: \(5 + 8 + 1 = 14\) (write 4, carry 1)
3. Add hundreds: \(4 + 7 + 1 = 12\) (write 2, carry 1 to the next thousand)
4. Result: 1245

Mental Math for Near-Doubles

If two numbers are nearly the same, use the double and adjust.

Example :
49 + 52
Think of 50 + 50:
50 + 50 = 100
Adjust for the difference:
49 + 52 = 100 – 1 + 2 = 101

Addition with Place Value Splitting

Add numbers by their place values separately.

Example :
345 + 678
= (300 + 600) + (40 + 70) + (5 + 8)
= 900 + 110 + 13
= 900 + 110 + 10 + 3
= 1023

Using these tricks can make addition quicker and more intuitive, especially when dealing with larger numbers or performing mental math.

Also, Check

• Addition of Algebraic Expressions
• Arithmetic Operations
• Addition of Fractions

Example 1: Add 35 and 47.

Solution:

Break down into tens and units:

35 = 30 + 5

47 = 40 + 7

(30+40) + (5+7) = 70+12 = 82

Example 2: Add 58 and 34.

Solution:

Round 58 to 60 (add 2), then subtract 2 at the end:

60 + 34 = 94

94 − 2 = 92

Example 3: Add 67 and 29.

Solution:

67 is close to 70, so we can round it up and adjust:

67→70(complement is 3)

29 − 3 = 26

70 + 26 = 96

Example 4: Add 128 and 345.

Solution:

Split into hundreds, tens, and units:

(100 + 300) + (20 + 40) + (8 + 5)

= 400 + 60 + 13

= 473

Example 5: Add 53 and 51.

Solution:

Think of 52 + 52:

52 + 52 = 104

Adjust for the difference:

53 + 51 = 104 + 1 − 1 = 104

Try to solve the following questions using the addition tricks mentioned in the article

Q1. Add numbers by their place values separately.

• 246+789
• 357+864
• 468+975

Q2. If two numbers are nearly the same, use the double and adjust.

• 49+48
• 52+51
• 39+40

Q3. Split numbers to make the addition easier, especially useful for multi-digit numbers.

• 123+456
• 234+567
• 345+678

Q4. Find the complement to the next multiple of ten and adjust.

• 58+27
• 68+35
• 77+19

What is the commutative property of addition?

Commutative property of addition states that the order of the numbers being added does not affect the sum. For example, a + b = b + a.

How does the associative property help in addition?

Associative property allows you to group numbers in any way to simplify the addition process. It states that (a+b)+c=a+(b+c).

What is breaking down numbers or decomposition in addition?

Breaking down numbers, or decomposition, involves splitting numbers into parts that are easier to add. For example, to add 47+26, you can break them down as 40+7 and 20+6.

What does rounding and compensating mean in addition?

Rounding and compensating is a technique where you round one number to the nearest ten to make the addition simpler, and then adjust the result.

How can the tens complement be used to simplify addition?

Tens complement method involves finding the complement of a number to the next multiple of ten and adjusting.

Where can I get all addition tricks?

You can get all addition tricks at w3wiki.