Multiplication is a repeated addition as if we add a group of numbers or a single number again and again then actually we are doing multiplication. Let us understand it with an example:
Table of 2
2 × 1 =2 2 × 2 = 4 2 × 3 = 6 2 × 4 = 8 2 × 5 = 10 |
2 × 6 =12 2 × 7 =14 2 × 8 = 16 2 × 9 = 18 2 × 10 = 20 |
Now this table can also be written as repeated addition.
2 + 2 = 4
2 + 2 + 2 = 6
2 + 2 + 2 + 2 = 8
2 + 2 + 2 + 2 + 2 = 10
2 + 2 + 2 + 2 + 2 + 2 = 12
2 + 2 + 2 + 2 + 2 + 2 + 2 = 14
2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 = 16
2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 = 18
2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 = 20
So here we can clearly see that multiplication is nothing but repeated addition. Instead of doing 2 × 8 = 16, we are adding 8 times 2 i.e. 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 = 16.
However it is evident and clear that adding numbers many a times makes the calculation complicated and time consuming as well hence instead of doing repeated addition we simply multiply to get the answer easily in one step.
Here are few other examples to show that multiplication is a repeated addition:
1. Rohit cut a rope into 16
pieces. Each piece is of \(\frac{3}{4}\) mm. Find the total length of the rope.
Solution:
By repeated addition:
No. of pieces of rope = 16
Length of each piece of rope = \(\frac{3}{4}\) mm
Total length of the rope = \(\frac{3}{4}\) + \(\frac{3}{4}\) + \(\frac{3}{4}\) + \(\frac{3}{4}\) + \(\frac{3}{4}\) + \(\frac{3}{4}\) + \(\frac{3}{4}\) + \(\frac{3}{4}\) + \(\frac{3}{4}\) + \(\frac{3}{4}\) + \(\frac{3}{4}\) + \(\frac{3}{4}\) + \(\frac{3}{4}\) + \(\frac{3}{4}\) + \(\frac{3}{4}\) + \(\frac{3}{4}\) = 12 mm
By Multiplication:
No. of pieces of rope = 16
Length of each piece of rope = \(\frac{3}{4}\) mm
Total length of the rope = \(\frac{3}{4}\) × 16 = 12 mm
So, here we can see that this sum can also be done with repeated addition method but we do it by multiplication as it is very easy and less time consuming. Hence we actually in practice do this type of sums with the help of multiplication.
However, for the purpose of understanding we have to keep in mind that multiplication is nothing but repeated addition. If we add a number many a times we are actually doing multiplication. This understanding is very essential when we are solving story sums on multiplication, division, addition and subtraction. There we have to determine which operation is required to be carried out.
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