What Does Product Mean in Math? Definition, Examples, and Easy Explanation

There are many math terms that help us describe and solve problems in everyday life. One of these terms is “product,” which is the basis for understanding multiplication. But what does product mean in math, and why is it so important? Simply put, a product results from multiplying two or more numbers. For example, if you multiply 2 and 3, the product is 6. This concept is one of the foundations of math, especially for kids who are just starting to learn multiplication.

In this article, we will explore the product meaning in math, how to find the product in math, the product of fractions and decimals, and help you better understand the concept with solved examples of product. Whether you are a student, parent, or teacher, this guide will make understanding products in math simple and easy.

What Does Product Mean in Math?

Here is the definition of a product: In math, a product is the result obtained by multiplying numbers. The numbers being multiplied are called factors. Therefore, when we multiply factors together, whether they are whole numbers, fractions, or decimals, the final result of the multiplication operation is called the product. This concept is at the heart of many areas in math, which is why understanding the definition of product is so important.

For example, if you multiply 6 by 3, the product is 18.

How to find the product in math?

To calculate the product of two or more numbers, multiply them together. The product of 9 and 3 is 27 because 9 × 3 = 27. The product of 9, 3, and 4 is 108 because 9 × 3 = 27 and 27 × 4 = 108. Since multiplication is an exchange operation, the numbers in the calculation can be in any order.

Consider a simple example:

To calculate the product of 2, 3, and 4, you can multiply them in any order. You can multiply 2 and 3 to get 6, then multiply 6 by 4 to get 24. Alternatively, you can multiply 4 and 2 to get 8, then multiply 8 by 3 to get 24. This flexibility is due to the commutative nature of multiplication, which means that the order of the numbers does not change the product.

It is also important to remember that the mathematical product of any number and zero is always zero. This is the zero property of multiplication.

When calculating fractions or decimals, the process is essentially the same. You can directly multiply fractions or decimals. However, calculating these operations may require extra steps or a good grasp of fractions and decimals.

Why is understanding the concept of product important?

The concept of “product” is an essential math skill. Familiarity with the concept of “product” helps to make it easier to understand more advanced topics.

Moreover, the “product” also has a wide range of applications in daily life, from calculating the price of multiple items to calculating the area of a room. Therefore, understanding “product” is not only useful for learning, but also for daily life!

Explain Product When Different Properties of Multiplication are Used

There are 4 properties of multiplication:

• Commutative property
• Associative property
• Multiplicative identity property
• Distributive property

Commutative property

According to this property of multiplication, the order of the multiplier and the product does not matter. The product remains the same regardless of the order.

The property is given as: a x b = b x a

Let’s find the product in the example given below:

For example, a = 4 and b = 11

The product of a and b is a x b = 4x 11 = 44

If the order of a and b is exchanged, the product is b x a = 11 x 4 = 44

Associative property

When three or more numbers are multiplied together, the product remains the same irrespective of the order of the numbers. The property is given as: (a x b) x c = (b x c) x a = (a x c) x b

For example, a = 3, b = 5, and c = 7

The product of a, b, and c is a x b x c = 3 x 5 x 7 = 105

1. If initially a and b were multiplied and then c was multiplied, the product would be given as
   

   (a x b) x c = (3 x 5) x 7 = 15 x 7 =105

2. If initially b and c were multiplied and then a was multiplied, the product would be given as
   

   (b x c) x a = (5 x 7) x 3 = 35 x 3 = 105

3. Similarly, If initially a and c were multiplied and then b was multiplied, the product would be given as
   

   (a x c) x b = (3 x 7) x 5 = 21 x 5 = 105

Multiplicative identity property

By this property, any number multiplied by 1 gives the number itself.

The property is as follows: a x (1) = a

For example, when 2 is multiplied by 1, the product is 2, which is the number itself.

Distributive Property

The sum of any two numbers multiplied by a third number can be expressed as the sum of each additive number multiplied by the third number. This property is expressed as: a x (b + c) = (a x b) + (a x c)

Let’s try finding the product for this case. For example, a = 2, b = 4, and c = 6

Applying distributive property, we get a x (b + c) = 2 x (4 + 6) = 2 x 10 = 20

As per the property, (a x b) + (a x c) = (2 x 4) + (2 x 6) = 8 + 12 = 20

Product of Fractions and Decimals

So far, we’ve learned how to calculate the product of whole numbers. Now we will learn how to find the product of fractions and decimals!

Product of fractions

Let us learn this concept with the help of an example.

Suppose we ask for the product of the fractions 5/2 and 3/4.

Step 1: Multiply the numerator by the numerator and the denominator by the denominator.

Step 2: If you get an improper fraction, you can convert this into a mixed number.

We can also use the same method to find the product of two mixed numbers, a fraction and a mixed number, or even a whole number and a fraction, just make sure to convert the multiplier and the multiplicand into fraction form first.

Products of decimals

What makes decimals different? The answer is the decimal point!

Multiplying two decimals is the same as multiplying two whole numbers, the difference being that we need to pay attention to the decimal point.

Here is an example to make it easier for you to understand: calculate the multiplication of 1.5 and 1.2.

• Step 1: Count the number of digits after the decimal point in both numbers.
  

  Both 1.5 and 1.2 are one digit after the decimal point.

• Step 2: So the total number of digits after the decimal point in our multiplication expression is 1 + 1 = 2.
• Step 3: Multiply the two numbers without the decimal point.
  

  15 x 12 = 180

• Step 4: In this product, starting from the right, place the decimal point after the same number of places as the total found in Step 2. This is the answer to multiplying decimals.
  

  Therefore, after 2 digits from the right of 180, the product is 1.80

Thus, the product of 1.5 and 1.2 will be 1.8.

Solved Examples of Product in Math

Example 1: Tom has 4 boxes of apples. If 1 box has 3 apples, how many apples does he have?

Solution: In this example, the multiplicand is 3 and the multiplier is 4.

Hence, the total number of apples Tom has = the product of 4 and 3, or 4 ✕ 3 = 12

Example 2: Calculate the product of 0.06 and 0.3.

Solution:

• First, let’s calculate the number of decimal places.
• Number of decimal places for 0.06 = 2
• Number of decimal places for 0.3 = 1
• Total number of decimal places in the final answer = 2 + 1 = 3
• Now let’s multiply the two numbers without the decimal point: 6 ✕ 3 = 18
• Putting the decimal point from the right after the 3 digits of this product, we get 0.018.

The final product is 0.06 ✕ 0.3 = 0.018.

Example 3: What is the product of the numbers “n” and “(n+1)”? Help Jake find it.

Solution: In this case, the number “n” is the multiplier, and “(n+1)” is the product.

The product is n x (n + 1)

Applying distributive property of multiplication, Jake will get

n x (n + 1) = (n x n) + (n x 1) = n² + n

Jake finds that the product is n² + n

Frequently Asked Questions

Q.1: Which two numbers have a sum of 15 and a product of 36?

The two numbers which have sum 15 and product 36 are 12 and 3.

Q.2: What happens when you calculate the product of a number and 0?

When you calculate the product of a number with 0, you get the answer as 0.

For instance, 7 ✕ 0 = 0; this is called the zero property of multiplication.

Q.3: What is the product of the first 50 whole numbers?

The product of the first 50 whole numbers is 0.

Conclusion

The concept of product in mathematics is a fundamental building block that students encounter throughout their studies. With this study, you will now be able to easily solve problems in math such as products, finding products, and what a product is.

For students, mastering this concept requires practice and familiarity with the rules of multiplication. Remember, the more you practice, the easier it will be to calculate and understand multiplication in math. So, keep practicing and soon, solving problems involving products will become easy!