- Properties of Real Numbers
- Home
- Identifying Like Terms
- Combining like terms: Whole number coefficients
- Introduction to properties of addition
- Multiplying a constant and a linear monomial
- Distributive property: Whole Number coefficients
- Factoring a linear binomial
- Identifying parts in an algebraic expression
- Identifying equivalent algebraic expressions
- Introduction to properties of multiplication

# Introduction to properties of multiplication

Properties of Multiplication | |
---|---|

8 × 0 = 0 | Zero property |

3 × 7 = 7 × 3 | Commutative property |

2 × (5 × 9) = (2 × 5) × 9 | Associative property |

1 × 4 = 4 | Identity property |

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

**Zero property of multiplication**

The zero property of multiplication states that any real number a multiplied by zero is zero.

*a × 0 = 0 × a = 0*

**Commutative property of multiplication**

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

For any two numbers *a* and *b*

*a × b = b × a*

**Associative property of multiplication**

The associative property of multiplication 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 multiplication.

*a × (b × c) = (a × b) × c*

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

**Identity property of multiplication**

Identity property of multiplication states that any number multiplied by 1 is the same number.

For any number a

*a × 1 = a*

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

_ × 6 = 0

### Solution

**Step 1:**

The zero property of multiplication states that any real number a multiplied 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 multiplication used:

3 × _ = 8 × 3

### Solution

**Step 1:**

The commutative property of multiplication 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 multiplication used:

(6 × _) × 5 = 6 × (3 × 5)

### Solution

**Step 1:**

The associative property of multiplication 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 multiplication used:

1 × _ = 23

### Solution

**Step 1:**

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

a × 1 = 1 × a = a

**Step 2:**

So, 1 × 23 = 23

**Step 3:**

So, answer is 23