Addition is one of the four basic operations in mathematics. It involves taking two or more numbers and adding them together. The result of adding two or more numbers is called their sum. The numbers which are added together are called addends. For example if we add the number 1 to the number 2 the result will be 3. Here 1 and 2 are the addends, and 3 is the sum.
An addition operation can be represented in an equation form as,
1 + 2 = 3, where “+” is the symbol used to represent addition of 2 or more numbers.
We will now learn about the addition of single digit numbers in detail.
When you add 0 to a number, the sum is that number itself.
For example, if we have 4 mangoes in the first basket, and 0 mangoes in the second basket, then the total number of mangoes will be 4.
4 + 0 = 4
Similarly, if we have 0 apples in the first basket, 3 apples in the second basket then the total number of apples will be 3.
3 + 0 = 3
When you add 1 to a number, the sum is the next number in counting.
For example, if a child had 4 balloons and she took 1 more balloon from her friend, then she will now have 5 balloons in total (as 5 is the next number in counting after 4).
4 + 1 = 5
When you add the same numbers, the sum is double of that number. In this case the addends are the same.
1 + 1 = 2 , 2 + 2 = 4 , 3 + 3 = 6, 4 + 4 = 8 and 5 + 5 = 10 are examples of doubles.
We can use doubles to find the sum of 2 different addends.
Let’s find 3 + 4 using doubles.
3 + 4 is equal to 3 + 3 and 1 more, that is, double of 3 and 1 more. Double of 3 is 6 and adding 1 more to 6 is 7.
So 3 + 4 equals 7 or 3 + 4 = 7
You can add numbers in any order. Any change in the order of the addends does not alter the sum.
Count on strategy is very useful in adding 2 numbers. We can add 2 numbers using this strategy on a number line. A number line is a straight line with equally spaced intervals. On each interval, numbers 0 to 10 are marked along the length of the line.
Let’s understand how the count on strategy works.
First, we draw a number line that has numbers from 0 through 10. Then we start from one of the addends and to add, we simply count on from there.
For example, to add 3 to 5, start at 5 on the number line and count 3 more.
On counting 3 more, we reach the number 8. So the sum is 8.
We can use the concept of addition to find the unknown addend, when the sum is given.
For example, let’s find what should be added to 5 to get 7?
Draw 5 dots. Draw more dots till you get 7 dots in total . Count the number of dots drawn.
We see that 2 more dots are drawn to get a total of 7 dots. So the missing addend is 2.
Let’s take an example to understand this.
We have 2 balls in one box and 4 balls in the second box, we need to find the number of balls we have in total. We will simply add the number of balls in each box:
So 2 + 4 = 6
We can use addition to compare two numbers. This comparison will tell us by how much one number is larger or smaller than the second number. We use a bar model to solve such problems.
A bar model is a pictorial representation of numbers using bars or rectangular figures. To represent numbers using bars we draw longer bars for large numbers and smaller bars for smaller numbers.
Let’s take an example: your sister has 5 balloons. You have 1 more balloon than your sister. How many balloons do you have?
Let’s use a bar model to represent this comparison. The smaller bar represents 5 balloons, add 1 to it, to get the total number of balloons you have. This is represented by the larger bar.
So you have 6 balloons.
Here we will find the missing addend that makes the sum 10.
Find, 7 + ? = 10
Here we have to find which number added to 7 gives 10?
To find the missing addend, draw 10 boxes. Then draw as many dots as the given addend, that is, 7. Then count the empty boxes, which is 3.
We can use this concept of getting to 10 to add any number to 9 and 8.
To add 9, express the other addend as a sum of 1 and another number. Then add 1 to 9 which will become 10. Then 10 and the remaining number can be added easily.
For example, you can find 9 + 5 as,
5 can be written as 4 + 1. 9 is added to 1 to get 10. Now 10 can be added easily to the remaining number that is 4. So the sum is 14.
Similarly we can 8 to any number.
For example, lets find 8 + 5 .
A fact family is a set of related addition equations that include the same numbers.
2 + 3 = 5
3 + 2 = 5
They are related because they have the same 3 numbers (2, 3, 5) and they all use addition. This method is useful for finding subtraction equations where we can subtract one part from the total to get the other part.
Add the numbers in any order. You get, 2 + 3 = 5 , 3 + 2 = 5
Subtract each part from the whole. You get, 5 – 3 = 2, 5 – 2 = 3
List the 4 equations to get a fact family.
To add three numbers, first we add any 2 numbers, and to their sum we add the third number to get the final sum. We can pick the numbers in any order, the final answer remains the same.
For example, you can find 5 + 2 + 3 as,
In the first case, 5 and 3 are added to get 8. Then 8 and 2 are added to get 10.
In the second case, 2 and 3 are added to get 5. Now, 5 is added to 5 to get 10
As you can see in both the cases, the final answer remains the same.
Example 1: Use pictures to write an equation:
Example 2: Find the sum.
We add 4 to 4, the double of 4 is obtained,
4 + 4 = 8.
Example 3: Find the missing number.
Draw dots in the first box till you get 8 dots in total. Count the dots drawn.
You draw 3 dots, so the missing number is 3.
Example 4: Complete the fact family.
Add two numbers in any order. Then, subtract each number from 9.
Example 5: Add three numbers.
2 + 5 + 6
First, add any two numbers. Then add the sum to the third number.
Add 2 and 5, the sum is 7.
Then add 7 to the third number, that is, 5.
The sum is 13.
If we add 0 to a number, the sum is the number itself.
If we subtract 1 from a number, we get the previous number when counting. And
if we add 1, we get the next number when counting.