What is Repeated Addition?
Repeated addition is a concept taught to children to learn about multiplication. Its fundamentals branch out from simple addition. You can understand the process of repeated addition if you know the basics of addition. This knowledge is fundamental in linking the concepts of addition and multiplication.
Repeated Addition
Have you ever tried adding the same numbers over and over again? Do you see a pattern in which the numbers appear? If you have, this is what you call repeated addition. Repeated addition is the addition of the same number multiple times. This process is also called multiplication.
For example: Let us take the sum of 3 + 3 + 3 + 3
We would solve this sum by adding the 3’s one by one. We notice that 3 repeats 4 times. Ultimately, after solving, the answer you get is 12.
However, it is inefficient to add the numbers one by one. Thus, we introduce the concept of multiplication. Here, we can write the same sum as 3 * 4 = 12. However, we have to add the number 3 four times in this method. Hence, we will repeat the number 3 four times.
In this way, multiplication helps children to improve their counting and become more efficient. On the other hand, multiplication tells us that if 3 * 4 = 12, then 4 * 3 is also = 12. It means that if 4 is the number and it is repeated 3 times, the outcome is still 12. It is similar to saying,
3 + 3 + 3 + 3 = 12 and 4 + 4 + 4 = 12
Thus, 3 + 3 + 3 + 3 = 4 + 4 + 4 = 12
Hence, 3 * 4 = 4 * 3 = 12
Using repeated addition, we can ascertain this fact and render it true.
We can perform repeated addition on the number line by skipping the same number of steps every time we add. It helps us to understand by visualizing the number of times we must repeat the same number. We will try this for the above example.
We can do it by counting the number and skipping each time. Thus, we count till 4 and add 4 three times to get 12.
Now, let us try a few more sums using the traditional and the multiplication method.
1} (i) 2 + 2 + 2 + 2 + 2 + 2 + 2 = 4 + 4 + 4 + 2 = 8 + 6 = 14
(ii)2 * 7 = 14. This is because we repeat 2 seven times.
2} (i) 5 + 5 + 5 + 5 + 5 = 10 + 10 + 5 = 20 + 5 = 25
(ii)5 * 5 = 25. This is because we repeat 5 five times.
3} (i) 7 + 7 + 7 = 14 + 7 = 21
(ii)7 * 3 = 21. This is because we repeat 7 three times.
4} (i)1 + 1 + 1 + 1 = 2 + 2 = 4
(ii)1 * 4 = 4. This is because we repeat 1 four times.
The last example illustrates the identity property of multiplication. Any number multiplied by 1 will give itself. In simple terms, when we add a number to 0, the result is the number itself.
Similarly, when a number is multiplied by 0 the result is always 0. It means that when there is no number taken, the result is nothing which is 0. For example:
(i) 250 * 0 = 0
(ii) 1 * 0 = 0
This property of multiplication is known as the zero property.
Thus repeated addition builds the framework of multiplication which is essential.