What is the Product in Math? - Definition & Overview

What is the Product in Math? - Definition & Overview
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  • 0:00 What Is a Product?
  • 0:20 How to Find the Product
  • 1:35 Properties of Multiplication
  • 2:45 Special Products
  • 3:20 Lesson Summary
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Lesson Transcript
Instructor: Jennifer Beddoe
In mathematics, the term 'product' refers to the answer to a multiplication problem. This lesson will define the term in more detail and give some examples of how it is used. Then, there will be a quiz to test your understanding.

What Is a Product?

When speaking mathematically, the term product means the answer to a multiplication problem.

For example:

5 * 3 = 15

15 is the product

The term product first showed up in England in the 1400s and comes from the Latin word productum, which means 'to produce.'

How to Find the Product

Multiplication is often referred to as repeated addition because what the multiplication problem is telling you is that you have a certain number of groups of something, all containing a specific number. Confused yet? Here's an example.

You have 3 bags of candy, and each bag contains 5 pieces of candy. How many pieces of candy do you have?

There are two ways to solve this problem. The first is by adding up the pieces of candy:

5 + 5 + 5 = 15

The other way to solve is to use multiplication, because you have 3 groups of candy with 5 pieces of candy in each bag.

3 * 5 = 15

The answer to this multiplication problem is the product, which in this case is 15.

Here's another example. The classroom has 8 rows of chairs and each row has 7 chairs in it. How many chairs are there?

Again, you could add:

7 + 7 + 7 + 7 + 7 + 7 + 7 + 7 = 56

Or, you can find the product by multiplying:

7 * 8 = 56

Properties of Multiplication

There are four basic properties of multiplication that are true no matter what is being multiplied together.

1. Commutative property: When two numbers are multiplied together, the product is the same regardless of the order in which they are written.

For example:

5 * 7 = 7 * 5

2. Associative property: When three or more numbers are multiplied together, the product is the same regardless of which two are multiplied first.

For example:

(2 * 4) * 6 = 2 * (4 * 6)

8 * 6 = 2 * 24

48 = 48

3. Multiplicative identity property: The product of any number and 1 is that number.

For example:

3 * 1 = 3

4. Distributive property: The sum of two numbers times a third number is equal to the sum of each addend times the third number.

For example:

2 * (3 + 4) = 2 * 3 + 2 * 4

2 * 7 = 6 + 8

14 = 14

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