Product in Math

The concept of multiplication is an integral part of math and has a role to play in arithmetic, algebra, and geometry.

In this chapter, you will learn about the product of a number, as well as how to find a product.

Check-out the interactive simulations to know more about the lesson and try your hand at solving a few interesting practice questions at the end of the page.

Lesson Plan

Product in math is defined as the outcome obtained after arithmetic operation of multiplication.

Let us take an example to show the product in math.

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The arithmetic operation of multiplication can also be referred to as repetitive addition.

Let's say Joey went out on Halloween and received 3 bags of chocolates, and each bag contains 4 chocolates. How many chocolates does Joey have?

The number of chocolates can be calculated in two ways:

• Method 1: He could add the number of chocolates \( 4 + 4 + 4 = 12\)
• Method 2: He multiplies the number of chocolates in each bag to tht number of bags, i.e., \( 4 \times 3 = 12\)

The answer remains the same in both the cases.

To find the product in math, we always need a multiplicand and a multiplier. Multiplicand represents the number of objects in a group and multiplier represents the number of such equal groups. With reference to the example taken, number of objects in a group was 4 and number of such equal groups was 3

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 multiplicand and the multiplier does not matter. The product remains the same no matter what is the order.

The property is given as

Let's find the product in the example given below.

For example, a = 3 and b = 11

The product of a and b is \( a \times b = 3 \times 11 = 33\)

If the order of a and b is interchanged the product is \( b \times a = 11 \times 3 = 33\)

Associative Property

When three or more numbers are multiplied together, the product remains the same irrespective of the order of those numbers.

The property is given as

Let's see an example.

For example, a = 2, b = 4, and c = 5

The product of a, b, and c is  \( a \times b \times c = 2 \times 4 \times 5 = 40\)

If initially a and b were multiplied and then c was multiplied, the product would be given as \( (a \times b) \times c = (2 \times 4) \times 5 = 8 \times 5 = 40\)

If initially b and c were multiplied and then a was multiplied, the product would be given as \( (b \times c) \times a = (4 \times 5) \times 2 = 20 \times 2 = 40\)

Similarly, If initially a and c were multiplied and then b was multiplied, the product would be given as \( (a \times c) \times b = (2 \times 5) \times 4 = 10 \times 4 = 40\)

Multiplicative Identity Property

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

The property is given as

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 when multiplied to a third number can be expressed as sum of each one of the addends multiplied by the third number.

The property is given as

Let's try finding the product for this case.

For example, \(a = 5, b = 7, and c = 3\)

Applying distributive property, we get \( a \times ( b + c ) =  5 \times ( 7 + 3 ) = 5 \times 10 = 50\)

As per the property, \( (a \times b) + (a \times c) = (5 \times 7) + (5 \times 3) \\= 35 + 15 = 50\)

Example 2

 

 

Justin has to find the product of two numbers such that the multiplicand is the cube of 2 and the multiplier is a square root of 625

Solution

The multiplicand is cube of 2 which is given as \( 2^3 \), i.e., 8

The multiplier is a square root of 625 which is given as \( \sqrt{625} = 25\)

The product of the multiplicand and the multiplier is thereby given as \( 8 \times 25 = 200\)

\(\therefore\) Justin found that the product is 200

Example 3

 

 

What is the product of a number "n" by "(n+1)?" Help Amy find it.

Solution

Amy knows that in this case, number "n" is the multiplicand and "(n+1)" is the multiplier.

The product is given as \( n \times (n+1)\)

Applying distributive property of multiplication, she gets

\( n \times (n+1) \!=\! (n \times n) + (n \times 1) \!=\! n^2 + n\)

\(\therefore\) Amy found the product as n2 + n