Introduction to properties of multippcation

In this lesson, we discuss different properties of multippcation pke the identity property, zero property, commutative property and associative property.

Zero property of multippcation

The zero property of multippcation states that any real number a multipped by zero is zero.

a × 0 = 0 × a = 0

Commutative property of multippcation

The commutative property of multippcation states that, in a multippcation, irrespective of the order of factors, the product is the same. In other words, if we move around the factors in a multippcation, the product is not changed.

For any two numbers a and b

a × b = b × a

Associative property of multippcation

The associative property of multippcation states that the product of any three real numbers remains same regardless of how you group the numbers or where you put the parentheses in the multippcation.

a × (b × c) = (a × b) × c

In a multippcation if the order of factors is not changed, moving the parentheses does not change the product.

Identity property of multippcation

Identity property of multippcation states that any number multipped by 1 is the same number.

For any number a

a × 1 = a

Fill in the blank and identify the property of multippcation used:

_ × 6 = 0

Solution

Step 1:

The zero property of multippcation states that any real number a multipped by zero is zero.

a × 0 = 0 × a = 0

Step 2:

So, 0 × 6 = 0

Step 3:

So, answer is 0

Fill in the blank and identify the property of multippcation used:

3 × _ = 8 × 3

Solution

Step 1:

The commutative property of multippcation states that the product of any two real numbers a and b is same regardless of the order of the numbers, i.e.,

a × b = b × a

Step 2:

So, 3 × 8 = 8 × 3

Step 3:

So, answer is 8

Fill in the blank and identify the property of multippcation used:

(6 × _) × 5 = 6 × (3 × 5)

Solution

Step 1:

The associative property of multippcation states that the product of any three real numbers a, b and c is the same regardless of grouping or where parentheses are put, i.e.,

(a × b) × c = a × (b × c)

Step 2:

So, (6 × 3) × 5 = 6 × (3 × 5)

Step 3:

So, answer is 3

Fill in the blank and identify the property of multippcation used:

1 × _ = 23

Solution

Step 1:

The identity property of multippcation states that any real number a multipped by 1 is the number itself.

a × 1 = 1 × a = a

Step 2:

So, 1 × 23 = 23

Step 3:

So, answer is 23