Wednesday, November 14, 2012

Multiplication as Repeated Addition


In elementary mathematics, there are two basic mathematical operations which are addition and multiplication. Though the other two operations subtraction and division are also said to be basic operations, they are actually the inverse of addition and multiplication, respectively. Even multiplication can be represented as repeated addition. Let us see about multiplication as repeated addition.

Multiplication

Multiplication is done between two numbers. The two numbers are termed as factors and the result obtained is termed as the product. The product is the same irrespective of the order in which the factors are multiplied. Symbolically, a cross i.e. x is used to represent multiplication.

Multiplication as Repeated Addition

Multiplication is generally a scaling operation of one number by another whole number. In other words, we can explain the scaling procedure of multiplication as the number of copies of the given number. Thus it is understood that by adding the given number many times, we get the product.  The product of whole numbers which are greater than one can be found out by repeated addition.

To understand better, let us consider an example of a school teacher distributing 2 T-shirts each to 11 students in a sports team.  Here, to find out the total number of t-shirts, we have to multiply 2 by 11. We can say this as 2 times 11.  We can Sum to Product 2 by 11 as we understand that there are 11 copies or multiples of 2 T-shirts distributed.

2 x 11 = 2+2+2+2+2+2+2+2+2+2+2 = 22

Thus, multiplication as addition repetition has converted Product to Sum of number of copies (11) of a given number (2).  Here 2 and 11 are factors and the result 22 is the product.

When to use Multiplication as Repeated Addition?

Multiplication as Repeated Addition is applicable only in certain cases such as multiplication of whole numbers.  In some cases multiplication of given two values will result in a new type of value. In such cases, direct multiplication is done. In some cases such as commutative property, addition repetition method is not applicable. Generally, multiplication as addition that is repeated is used best when counting numbers.

To understand better, let us consider an example of multiplication of two measurements. If the two measurements given are 5 meters/second and 4 seconds, the product obtained will be 20 meters.  Similarly multiplication of 2 meters and 5 meters will give 10 square meters. Here we can see that the factors had the unit meters whereas the product has the unit square meters.

We have seen multiplication as something as addition repeated. On the contrary, multiplication replaces addition repeated to reduce the complexity in addition. There are situations where a single number has to be repeatedly added for a larger number of times. For example, if a student has to distribute 2 chocolates to all the students in the school and the number of students in the school is 1440, then going on adding 2 for 1440 times is very tedious. Here multiplication replaces repeated addition and we get 2 x 1440 = 2880 chocolates.

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