Product Definition

Product is actually the result that we will get by multiplying two numbers. In different fields, this word has different meanings. In Mathematics, it shows the result that we will get after the multiplication of two numbers or variables.

Note:

You can read about Variables here.

We all know that multiplication is one of the basic operations of Mathematics. In this operation, you can multiply two or more terms to find the output. In two numbers multiplication, the two factors are termed Multiplier and Multiplicand.

Note:

You can read about Factors, Multipliers, and Multiplicands here.

In Mathematics, it is generally denoted by a symbol “x” between the factors. It has great importance in multiple fields related to this subject from basic to advance.

How to find a product of two numbers?

It is simple to find the product of two numbers. You only have to count the table of the first number equal to the second number. Let us show you an example for better understanding.

Example 1:

Find the product of 2 and 6.

Solution:

We only have to multiply 2 by 6 by reading its table.

2 x 6 = 12

So, the product of the above-given numbers is 12.

How to find the Product of two fractions?

When it comes to finding the product of two fractions, you can follow some tricks. Here are some tips that you can follow in this regard.

  • You can multiply the numerator with the numerator and denominator with the denominator of the given fractions.
  • You can divide two fractions in cross format i.e. denominator of the first fraction will be divided by the numerator of the second fraction and vice versa.
  • You can convert the improper fraction that comes as the product into a mixed fraction.

Note:

You can read about Improper Fraction and Mixed Fraction here.

Let us now show you an example for better understanding.

Example 2:

Find the Product of the following fractions.

2/7, 6/11

Solution:

To find the Product, we will first write them in multiplication format.

2/7 × 6/11

Now, we will multiply the denominator with the denominator and numerator with the numerator as these are not divisible in cross format.

2/7 × 6/11 = 12/77

As the product is a Proper Fraction, so, it is considered the final answer.

Note:

You can Read about Proper Fraction here

How to find the Product of two decimals?

The multiplication of two decimals is considered to be a difficult process by beginners. It is because of the involvement of the decimal. Let us show you the easiest way to multiply such factors to find the product.

  • Write the given decimals side by side
  • Count the digits after the decimal on the right side of both factors
  • Remove the decimals and multiply them as the integers
  • Start counting digits from the right side of the product and put a decimal just after the counted digits from Step # 2
  • You have got the product of the two decimals

Let us show you an example to understand the above steps.

Example 3:

Find the product of 1.7 and 1.4.

Solution:

First of all, we will count the digits after decimals of the given factors

= 1.7 x 1.4

There are two digits on the right side of the decimals.

Now, remove those decimals and multiply the integers.

= 17 x 14
= 238

Now, count the digits from the right side of the output and put the decimal after two digits as we have seen that factors have only two digits on the right side of the factors.

= 2.38

So, this is the Product of the decimals that we have got in the question.

Fun Facts of Product

  • The product of a number with 0 will be 0.
  • The product of a number with 1 will result in the number itself.

Note:

You can read about Multiplicative Inverse here.

  • The product of two negative numbers will be a positive number.
  • The product of two same reciprocal fractions will be equal to 1 and is called Multiplicative Inverse.
  • The product of two positive numbers will always be positive.

FAQ's

What are multiplicands and multipliers?

These are two factors that make the product as the output of a multiplication process.

Can we multiply two negative numbers?

Yes, you can multiply two negative integers but the product of such integers will be positive.

What is the output of the multiplication of a number with 0?

The product of a number with 0 will be 0.

What do you mean by Multiplicative Inverse?

It is the reciprocal of any number or fraction. As it answers product 1, that’s why it is called the Multiplicative Inverse of the particular number or fraction.

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