Fluency and Strategies for the Addition of Numbers
Adding two numbers is very simple. You have two blue toffees and three red toffees. If you are asked the total number of toffees that you have, you need to add the numbers together.
The addend is the name given to the two numbers that are added together. Let’s discuss what addition is all about. We are given 2 blue toffees and three red toffees. If you are asked the total number of toffees, what do you do?
2 + 3 = 5
So, there are a total of five toffees. If the two blue toffees are added to the three red ones, the answer will be ‘5’. Even if the three red toffees are added to the blue ones, the answer will still be five. So, the order of adding the two numbers does not matter as the answer stays the same.
3 + 2 = 5
3 + 2 = 2 + 3
= 5
Now, you can add any of the two numbers that belong to the line of numbers marked in blue to the line of numbers marked in green. If you trace your index fingers along the line of the numbers of each color, you can find the sum at the point where your index fingers meet. Try to find the sum of six and seven. Keep your right index finger and scroll down the set of numbers below ‘6’. Scroll the index finger of your left hand towards the left of ‘7’. We can see that both the fingers meet at ‘13’.
You can try this out for the other numbers as well. Add a number by itself and let’s see what the result looks like.
1 + 1 = 2
2 + 2 = 4
3 + 3 = 6
By adding the numbers together, we get double the value. Now we will trace the result along with this table like we did before and see what we get.
As you can see, the line cuts the entire table in the middle.
Take a look at the sum of these numbers.
3 + 3 = 6
We already know that three added to itself gives six. Now, if we wish to obtain 7, we can add one to the sum of three plus three.
3 + 3 + 1 = 7
In other words, the double of three plus one is greater than the double of three.
3 + 4 = 3 + 3 + 1
= 7
In order to obtain 5, we deduct one from the sum of three plus three.
3 + 3 – 1 = 5
In other words, the double of three, minus one, is less than the double of three.
3 + 3 – 1 = 5
You can add more than two numbers together. Let’s see what the answer looks like if we had violet toffees also added to what we have.
2 + 3 + 5 = 10
This gives us a total of ten toffees.
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Solved Examples
Example 1: Solve the following problems using addition.
There are eight blue mugs and six red mugs. Adding eight and six together, we get 14. So the answer is 14.
12 + 18 = ____
Answer:
12 + 18 = 30
18 + 12 = ____
Answer:
18 + 12 = 30
55 + 67 = ____
Answer:
55 + 67 = 122
67 + 55 = ____
Answer:
67 + 55 = 122
13 + 16 + 22 = ___
Answer:
13 + 16 + 22 = 51
54 + 65 + 99 = ____
Answer:
54 + 65 + 99 = 218
Example 2: Alan bought 5 toys from a garage sale and later bought five more from a toy shop. Later, Alan gave away one of his toys to his best friend. How many toys does Alan have now?
Answer:
Initially, Alan bought five toys from a garage sale. Later, he bought five more toys from the store, so,
5 + 5 = 10
As Alan gave away one toy to his best friend, we can remove one toy from the total number of toys.
5 + 5 – 1 = 10 – 1
= 9
So the answer is 9 toys.
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Addition is one of the most basic mathematical operations. For something as simple as calculating the total amount to be paid at the mall to complex mathematical calculations where the speed and velocity of rocket ships are calculated, addition is constantly used.
In simple words, multiplication is repeated addition. If one has to find out three multiplied by two, the other way of phrasing the question is what is the answer we get when three is added to itself twice?