Repeated Addition: Overview, Properties, Examples

Repeated Addition: In the olden days of the development in the number concept, around \(10,000\) years ago, people were using only the whole numbers. It may be that the earliest forefather of what is now multiplication was, in fact, repeated addition.

However, this was all about \(10,000\) years ago, and things have been replaced a lot since then. For example, the term repeated addition is nothing but known as multiplication today. Furthermore, repeated addition comes in handy while learning multiplication facts. In this article, we will provide detailed information on the process of repeated addition or multiplication.

What are Addition and Multiplication?

Definition: Addition means summing up two or more numbers or values to get another number, and the symbol representing addition is \(\left( + \right)\).

For example: If you add the numbers \(4\) and \(5\), we get \(9\) as a result.

\(4 + 5 = 9\)

Here, let us understand the sum of \(4\) and \(5\) practically. Suppose you have \(4\) oranges in a basket, and \(5\) more oranges are added to the same basket. So, how many oranges are there altogether?

\(4 \to 1 + 1 + 1 + 1\)
\(5 \to 1 + 1 + 1 + 1 + 1\)
\(4 + 5 = 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1\)

Now, if we count each orange, then it is equal to \(9\).

Multiplication: Multiplication is used to find the product of two or more numbers. Multiplication is also known as repeated addition.

Example: When you want to multiply the numbers \(4 \times 12 = 48\) or \(12 + 12 + 12 + 12 = 48\).

The primary explanation of the multiplication is adding the number concerning another number repeatedly.

For example, if we multiply the number \(2\) by the number \(3\), then \(3\) is said to be two times, i.e., \(3 + 3 = 6\). In the same few other numbers are given below:

\(3\) by \(3 = 3 + 3 + 3 = 9\)

\(4\) by \(4 = 4 + 4 + 4 + 4 = 16\)

\(5\) by \(5 = 5 + 5 + 5 + 5 + 5 = 25\)

Define Repeated Addition

Definition: Adding equal groups together is known as repeated addition or multiplication. If the same number appears, then you can write in the form of multiplication.

Example: \(4 + 4 + 4 + 4 + 4\)

Here the number \(4\) is repeated for \(5\) times, so you can write this addition as \(5 \times 4\).

In the same way, when you want to solve the multiplication problem through the repeated addition, you group that number repeatedly and then add the same number again and again to get the answer.

\(3 \times 3\)

\(3 + 3 + 3 = 9\) or \(3 \times 3 = 9\)

\(5 \times 4\)

\(5 + 5 + 5 + 5 = 20\) or \(5 \times 4 = 20\)

See here in the below diagram; there are five groups of chickens, and in each group, you can see three chickens.

You can see five groups, and there are three chickens in each group.

When you want the addition statement, it will be \(3 + 3 + 3 + 3 + 3 = 15\).

And when you want to write in multiplication, the statement will be \(5 \times 3 = 15\).

Hence, in total, you have \(15\) chickens.

As you know the multiplication is known as repeated addition, so each repeated addition can be written in two ways:

Example: \(6 + 6 + 6 + 6 = 24\) can be written as \(6 \times 4 = 24\) or \(4 \times 6 = 24\). You can see the product was the same when the numbers were interchanged.

\(6 + 6 + 6 + 6 = 24\) and multiplication is \(4 \times 6 = 24\)
\(4 + 4 + 4 + 4 + 4 + 4 = 24\) and the multiplication is \(6 \times 4 = 24\)

Facts of Repeated Addition

The repeated addition can also be helpful for us to learn the multiplication facts like:

1. If you are not aware of the \(8 \times 5\) facts yet, then you can find it easy when you write it in this way \(5 + 5 + 5 + 5 + 5 + 5 + 5 + 5\) or \(8 + 8 + 8 + 8 + 8\) and then add them to get the answer.
2. You can even add the large numbers in the same way \(6 \times 50\); you will write it as \(50 + 50 + 50 + 50 + 50 + 50\) and then add them on tens.
3. There are \(6\) groups of \(3\) cherries each. The total number of cherries of \(6\) groups can be written as \(3\) in \(6\) groups or by adding \(3\) for six times as shown \(3 + 3 + 3 + 3 + 3 + 3 = 18\).
4. Now, the number \(30\) can also be identified with the help of multiplication \(5 \times 6\). Thus, \(6 + 6 + 6 + 6 + 6 + 6 = 30\) and another multiplication sentence is \(3 \times 10\) which can be written as \(10 + 10 + 10 = 30\).
5. Hence, the repeated addition of \(6\) five times is equal to \(6\) multiplied by the number \(5\).
6. Similarly, eight groups of \(7\) balls \(7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 = 56\).
7. Here, the addition fact \(7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 = 56\) is similar to the multiplication fact \(7 \times 8 = 56\).
8. Thus, \(7 \times 8 = 56\) that \(7\) multiplied by the number \(8\) is equal to \(56\), or \(7\) into \(8\) is similar to \(56\), or product of the numbers \(7\) and \(8\) is \(56\).
9. \(7 \times 8 = 56\) is known as the multiplication fact.
10. So, this whole process \(7 \times 8 = 56\) is the multiplication process.
11. The symbol or sign \(‘ \times ‘\) is the sign of the operation multiplication.

Similarly:

1. \(5 + 5 + 5 + 5 + 5 + 5 + 5 = 35\) is the addition sentence or the fact.
2. \(5 \times 7 = 35\) is the multiplication fact.
3. For the exact numbers, addition fact \( = \) multiplication fact..
4. The number \(5\) multiplied by the number \(7\) is \(35\) or \(5\) into \(7 = 35\) or the product of the numbers \(5\) and \(7\) is \(35\).
5. The symbol  \(‘ \times ‘\) is the sign of multiplication.

Solved Examples on Repeated Addition

Q.1. If Rahul has four boxes which contain four balls in each box, how many balls does he have in total?
Ans: Given,
Number of boxes Rahul has \( = 4\)
Number of balls in each box \( = 4\)
The total number of balls \( = \)?

You can see the diagram above, which has:
The addition sentence will be \(4 + 4 + 4 + 4 = 16\) and the multiplication sentence will be \(4 \times 4 = 16\)
Hence, the total number of balls Rahul has is \(16\).

Q.2. A teacher has two boxes of badges of smilies, and in each box, there are \(12\) smilies. How many smilies does she have in total?
Ans: Given,
Number of boxes teacher has \( = 2\)
Number of smilies in each box \( = 12\)
The total number of smilies \( = \)?

From the above diagram we can see that:

The addition sentence will be \(12 + 12 = 24\) and the multiplication sentence will be \(2 \times 12 = 24\). Hence, the total number of smilies teacher has is \(24\).

Q.3. There are three stars in each circle. What is the total number of stars?
Ans: Given,
Number of circles \( = 3\)
Number of stars in each circle \( = 3\)
The total number of stars \( = \)?

As you can see in the above diagram:
The addition sentence will be \(3 + 3 + 3 = 9\) and the multiplication sentence will be \(3 \times 3 = 9\).
Hence, the total number of stars is \(9\).

Q.4. Multiply the numbers and write the answer: \(400 + 400 + 400 + 400 + 400 = \)_____.
Ans: Given that the addition sentence given to us is \(400 + 400 + 400 + 400 + 400\)
Now, count the number of times the number \(400\) is added.
So, the number \(400\) is added \(5\) times which means \(400 \times 5 \to 5 \times 4 = 20\) now, add two more zeroes to it \(400 \times 5 = 2000\).
Thus, \(400 + 400 + 400 + 400 + 400 = 2000\)
Multiplication sentence will be \(400 \times 5 = 2000\)
Hence, the required answer is \(2000\).

Q.5. Multiply the numbers and write the answer: \(142 + 142 + 142 + 142 = \)_____.
Ans: Given,
The addition sentence given to us is \(142 + 142 + 142 + 142\)
Now, count the number of time the number \(142\) is added.
So, the number \(142\) is added \(4\) times which means \(142 \times 4\).
Thus, \(142 + 142 + 142 + 142 = 568\)
Multiplication sentence will be \(142 \times 4 = 568\)
Hence, the required answer is \(568\).

Q.6. Multiply the numbers and write the answer: \(89 + 89 + 89 + 89 + 89 + 89 + 89 = \)______.
Ans: Given,
The addition sentence given to us is \(89 + 89 + 89 + 89 + 89 + 89 + 89\)
Now, count the number of time the number \(89\) is added.
So, the number \(89\) is added \(7\) times which means \(89 \times 7\).
Thus, \(89 + 89 + 89 + 89 + 89 + 89 + 89 = 623\)
Multiplication of the sentence will be \(89 \times 7\)
Hence, the required answer is \(623\).

Q.7. Multiply the numbers and write the answer: \(350 + 350 + 350 = \)_____.
Ans: Given,
The addition sentence given to us is \(350 + 350 + 350\)
Now, count the number of times the number \(350\) is added.
So, the number \(350\) is added \(3\) times which means \(350 \times 3\).
Thus, \(350 + 350 + 350 = 1050\)
Multiplication sentence will be \(350 \times 3 = 1050\)
Hence, the required answer is \(1050\).

Summary

The addition is defined as summing up two or more numbers or values to get another number. Repeated addition is defined as adding equal groups together. It is also important to note that repeated addition helps us in learning multiplication facts. Repeated addition is important as it is the more straightforward way to go from the additive to the multiplicative understanding.

Furthermore, repeated addition is also known as multiplication. For instance, if the exact number is repeated then, we can note that down in the form of expansion. In this article, we learned about the important facts of repeated addition along with the solved examples for better understanding.

FAQs on Repeated Addition

Q.1. How do you teach repeated addition?
Ans: You can explain to students that repeated addition is nothing but adding the number of equal groups known as multiplication, then telling them to write the addition sentence and the multiplication sentence and then cross-check the same, making them use pictures for better understanding.

Q.2. What is the fastest way to write the repeated addition of the same number?
Ans: When you want to write the short sentence instead of the repeated addition sentence, you write the multiplication sentence for the same.
Example: The addition sentence is \(8 + 8 + 8 = 24\) and the multiplication sentence will be \(3 \times 8 = 24\).
The addition sentence is \(7 + 7 + 7 + 7 + 7 + 7 + 7 = 49\) and the multiplication sentence will be \(7 \times 7 = 49\).

Q.3. Explain repeated addition with an example.
Ans: Adding equal groups together is known as repeated addition or multiplication. If the same number appears, then you can write in the form of multiplication.
Example: \(4 + 4 + 4 + 4 + 4\)
Here the number \(4\) is repeated for \(5\) times, so you can write this addition as \(5 \times 4\).

Q.4. Why is repeated addition important?
Ans: It is essential because the repeated addition is the more straightforward way to going from the additive to the multiplicative understanding.

Q.5. Is multiplication a repeated addition?
Ans: Repeated addition is adding equal groups together. It is also known as multiplication. If the exact number is repeated then, we can write that in the form of expansion.

We hope this detailed article on Repeated Addition helped you in your studies. If you have any doubts or queries regarding this, feel to ask us in the comment section and we will answer you at the earliest.