**Category : **4th Class

**LEARNING OBJECTIVES**

**This lesson will help you to:—**

- be able to find the sum of two numbers.
- be able to solve real life problems based on addition.
- explore various facts of addition.
- be able to define addition.
- be able to define the terminology of addition.
- be able to explain the properties of addition.

** **

**Real** **Life** **Example**

Addition is used in every sphere of our life. It is used in our daily activities like purchasing grocery, all monetary transactions like in banks etc.

** **

**QUICK CONCEPT REVIEW**

**WHAT IS ADDITION?**

Combining two or more objects of same kind is known as addition. It is bringing two or more numbers (or things) together to make a new total. Addition is finding the total, or sum, by combining two or more numbers.

Some other names used in addition are Sum, Plus, Increase & Total.

** **

**TERMINOLOGY**

**Sum**

The result obtained after addition is called sum. It the result obtained after adding one number to another.

** **

**Addend**

The numbers that are to be added are called addends.

ADDEND + ADDEND = SUM

**For example: **50 + 20 = 70

Here, 50 = Addend

20 = Addend

70 = Sum

**PROPERTIES OF ADDITION**

**When we add 1 to any number, the answer is always its successor**

**For Example:** Tina had 1 fish in her fish tank.

Her mom gave her another fish on her birthday.

How many fish are there in all?

There was 1 fish in the fish tank. One more is added to it.

Therefore, total number of fish in the fish tank = 1 + 1 = 2

**When we add zero to a number, the answer is the number itself.**

That is, 29 + 0 = 29

Hence, we can say that when we add zero to a number, the answer is the number itself.

- If we change the order of numbers while adding, the sum does not change.

**For example:** 25 + 34 s 59

Here, Addend 1= 25

Addend 2 =3 4

Sum =59

If we interchange the addends with each other, that is 34 becomes addend 1 & 25 becomes addend 2. The sum remains the same.

That is, 34 + 25 = 59

Hence, we can say that if the order of the numbers to be added is changed, the sum will remain the same.

**DIFFERENT WAYS TO MAKE A NUMBER**

Let us find out different ways to form the number 50. AII the petals of the flower represent ways to form the number 50. We can add many more petals to this flower.

**Amazing Facts **

The sum is always greater than the numbers being added except when one of the numbers being added is zero.

If you add up the numbers 1 to 100. Consecutively (1 + 2 + 3 + 4 + 5….) the total is 5050.

Opposite sides of a die always add up to seven (7).

**Activity Time**

Add 4 more petal to the flower given below.

**ADDITION WITH NUMBER LINE**

Example,

45 27 =?

Break the smaller number as shown above and reach to the answer.

**Step 1:** 45 + 5 = 50

**Step 2:** 50 + 20 = 70

**Step 3:** 70+2 = 72

Therefore, 45 + 27 = 72

**ADDITION WITHOUT REGROUPING**

Lily went to the zoo, she found that there were 1163 animals & 824 birds. She wants to know what, is the total number of animals & birds in the zoo. Let us help her to do so.

Number of animals in the zoo = 1163

Number of birds in the zoo = 824

Total number of animals & birds in the zoo = 1163 + 824

We can also write this in columnar form as follows:

\[\underline{\begin{align}

& \,\,\,\,\,\,Th\,\,H\,\,T\,\,O \\

& +\,\,\,\,1\,\,\,\,\,1\,\,\,\,\,6\,\,\,\,\,3\, \\

& \,\,\,\,\,\,\,\,\,\,\,\,\,8\,\,\,\,\,2\,\,\,\,\,4 \\

\end{align}}\]

**Step 1:** Start with ones column & proceed towards the left.

Adding 3 & 4 on ones column gives 7 as shown below:

\begin{align}

& \underline{\begin{align}

& \,\,\,\,\,\,Th\,\,H\,\,T\,\,O \\

& +\,\,\,\,1\,\,\,\,\,1\,\,\,\,\,6\,\,\,\,\,3\, \\

& \,\,\,\,\,\,\,\,\,\,\,\,\,8\,\,\,\,\,2\,\,\,\,\,4 \\

\end{align}} \\

& \underline{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,7} \\

\end{align}

**Step 2:** Now moving to the tens column, 6+2=8

\begin{align}

& \underline{\begin{align}

& \,\,\,\,\,\,Th\,\,H\,\,T\,\,O \\

& +\,\,\,\,1\,\,\,\,\,1\,\,\,\,\,6\,\,\,\,\,3\, \\

& \,\,\,\,\,\,\,\,\,\,\,\,\,8\,\,\,\,\,2\,\,\,\,\,4 \\

\end{align}} \\

& \underline{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,8\,\,\,\,7\,} \\

\end{align}

**Step 3:** In the hundreds column, 1+8 = 9

\begin{align}

& \underline{\begin{align}

& \,\,\,\,\,\,Th\,\,H\,\,T\,\,O \\

& +\,\,\,\,1\,\,\,\,\,1\,\,\,\,\,6\,\,\,\,\,3\, \\

& \,\,\,\,\,\,\,\,\,\,\,\,\,8\,\,\,\,\,2\,\,\,\,\,4 \\

\end{align}} \\

& \underline{\,\,\,\,\,\,\,\,\,\,\,\,\,9\,\,\,\,\,8\,\,\,\,\,7\,} \\

\end{align}

**Step 4:** Lastly, in the thousands column, bring 1 as it is.

\begin{align}

& \underline{\begin{align}

& \,\,\,\,\,\,Th\,\,H\,\,T\,\,O \\

& +\,\,\,\,1\,\,\,\,\,1\,\,\,\,\,6\,\,\,\,\,3\, \\

& \,\,\,\,\,\,\,\,\,\,\,\,\,8\,\,\,\,\,2\,\,\,\,\,4 \\

\end{align}} \\

& \underline{\,\,\,\,\,\,\,1\,\,\,\,9\,\,\,\,\,8\,\,\,\,\,7\,} \\

\end{align}

Hence, total number of animals <& birds in the zoo = 1987.

This kind of addition is known as addition without regrouping. Now we will learn how to do addition with regrouping.

**ADDITION WITH REGROUPING**

In a month, 7125 men & 3799 women went to the beach.

Find out the total number of people who visited the beach.

Number of men = 7125

Number of women = 3799

Total number of people = 7125 + 3799

Let us write it in columnar form:

\[\underline{\begin{align}

& \,\,\,\,\,\,Th\,\,H\,\,T\,\,\,O \\

& +\,\,\,\,7\,\,\,\,\,1\,\,\,\,\,2\,\,\,\,5\, \\

& \,\,\,\,\,\,\,3\,\,\,\,\,7\,\,\,\,\,9\,\,\,9 \\

\end{align}}\]

**Historical Preview**

Plus (+) and minus (–). Nicole d’ Oresme (1323 – 1382) may have used a figure which looks like a plus symbol as an abbreviation for the Latin et( meaning “and”) in Agorismus proportionum, believed to have been written between 1356 and 1361. The symbol appears in a manuscript of this work believed to have been written in the fourteenth century.

The plus symbol as an abbreviation for the Latin et, though appearing with the downward stroke not quite vertical, was found in a manuscript dated 1417 (Cajori).

** **

**An Interesting Poem on Addition**

Add at a circus.

Come along with me.

Add at a circus.

Math is fun you see!

3 + 3 is 6; 8 + 2 is 10; 2 + 1 is 3.

Even clowns add. It’s easy.

5 + 2 is 7; 10 + 10 is 20; 12 + 3 is 15;

3 + 1 is 4; 6 + 2 is 8

I love the circus! It was great!

Add at a circus.

Come along with me.

Add at a circus.

Math is fun you see!

No clowing around now.

You put in the answers.

**Step 1:** Adding the digits on ones column, 5 + 9 = 14.

We will write 4 in the ones column & 1 will be regrouped to tens column as shown below:

\begin{align}

& \underline{\begin{align}

& \,\,\,\,\,\,Th\,\,H\,\,T\,\,\,O \\

& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,1 \\

& +\,\,\,\,7\,\,\,\,\,1\,\,\,\,\,2\,\,\,\,5\, \\

& \,\,\,\,\,\,\,3\,\,\,\,\,7\,\,\,\,\,9\,\,\,9 \\

\end{align}} \\

& \underline{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,4} \\

\end{align}

**Step 2:** In the tens column, add 1, 2, & 9.

1 + 2 + 9 = 12

Again I will be regrouped to hundreds column.

\begin{align}

& \underline{\begin{align}

& \,\,\,\,\,\,Th\,\,H\,\,T\,\,\,O \\

& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,1\,\,\,\,\,1 \\

& +\,\,\,\,7\,\,\,\,\,1\,\,\,\,\,2\,\,\,\,5\, \\

& \,\,\,\,\,\,\,3\,\,\,\,\,7\,\,\,\,\,9\,\,\,9 \\

\end{align}} \\

& \underline{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,2\,\,\,4\,\,\,} \\

\end{align}

**Step3:** 1+1+7 = 9 in the hundreds column.

\begin{align}

& \underline{\begin{align}

& \,\,\,\,\,\,Th\,\,H\,\,T\,\,\,O \\

& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,1\,\,\,\,\,1 \\

& +\,\,\,\,7\,\,\,\,\,1\,\,\,\,\,2\,\,\,\,5\, \\

& \,\,\,\,\,\,\,3\,\,\,\,\,7\,\,\,\,\,9\,\,\,9 \\

\end{align}} \\

& \underline{\,\,\,\,\,\,\,\,\,\,\,\,\,\,9\,\,\,\,\,2\,\,\,4\,\,} \\

\end{align}

**Step4: **Moving to the thousands column, 7 + 3 =

\begin{align}

& \underline{\begin{align}

& \,\,\,\,\,\,Th\,\,H\,\,T\,\,\,O \\

& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,1\,\,\,\,\,1 \\

& +\,\,\,\,7\,\,\,\,\,1\,\,\,\,\,2\,\,\,\,5\, \\

& \,\,\,\,\,\,\,3\,\,\,\,\,7\,\,\,\,\,9\,\,\,9 \\

\end{align}} \\

& \underline{\,1\,\,\,\,0\,\,\,\,\,9\,\,\,\,\,2\,\,\,4\,\,} \\

\end{align}

Therefore, total number of people = 10924

This form of addition is known as addition with regrouping.

**AMAZING ADDITION FACTS**

- Sums of three consecutive numbers differ by 3.

1 + 2 + 3 = 6

2 + 3 + 4 = 9

3 + 4 + 5 = 12

4 + 5 + 6 = 15........

- Sums of 5 consecutive numbers differ by 5.

1 + 2 + 3 + 4 + 5 = 15

2 + 3 + 4 + 5 + 6 = 20

3 + 4 + 5 + 6 + 7 = 25..........

- 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55

Sum of 1 to 10 = 55

11 to 20 = 155

21 to 30 = 255

31 to 40 = 355............

- 1 + 3 = 4\[\left( 2Addends\times 2=4 \right)\]

1 + 3 + 5 = 9\[\left( 3Addends\times 3=9 \right)\]

1 + 3 + 5 + 7 = 16\[\left( 4Addends\times 4=16 \right)\]

1 + 3 + 5 + 7 + 9 = 25....... \[\left( 5Addends\times 5=25 \right)\]

**Addition Trick**

** **Aim for ten

If you see any number close to

ten, then break the other number

so that you reach ten.

For example, 8 + 5 =?

8 is 2 away from 10. So 8 + 2 = 10.

Now 5 becomes 3.

Therefore, 8 + 2 + 3 = 13.

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