**Writing equivalent expressions using properties :**

There are some properties of operations which we can use to write an expression equivalent to another expression.

The same properties of operations can be used to identify equivalent expressions.

**1. Commutative Property of Addition : **

When adding, changing the order of the numbers does not change the sum.

**Example : **

3 + 4 = 4 + 3

**2. Commutative Property of Multiplication : **

When multiplying, changing the order of the numbers does not change the product.

**Example : **

2 x 4 = 4 x 2

**3. Associative Property of Addition : **

When adding more than twonumbers, the grouping of the numbers does not change the sum.

**Example : **

(3 + 4) + 5 = 3 + (4 + 5)

**4. Associative Property of Multiplication : **

When multiplying more than twonumbers, the grouping of the numbers does not change the product.

**Example : **

(2 × 4) × 3 = 2 × (4 × 3)

**5. Distributive Property : **

Multiplying a number by a sum or difference is the same as multiplying by each number in the sum or difference and then adding or subtracting.

**Examples : **

6(2 + 4) = 6(2) + 6(4)

8(5 - 3) = 8(5) - 8(3)

**6. ****Identity Property of Addition :**

Adding zero to a number does not change its value.

**Examples : **

9 + 0 = 0 + 9 = 9

**7. ****Identity Property of Multiplication :**

Multiplying a number by one does not change its value.

**Examples : **

1 x 7 = 7 x 1 = 7

**Example 1 :**

Use a property to write an expression that is equivalent to x + 3.

Tell which property you used.

**Solution :**

The operation in the expression is addition.

We can use the Commutative Property of Addition to write an equivalent expression:

x + 3 = 3 + x

**Example 2 :**

Use a property to write an expression that is equivalent to (ab)c.

Tell which property you used.

**Solution :**

Equivalent expression : a(bc)

Property used : Associative Property of Multiplication

**Example 3 :**

Use a property to write an expression that is equivalent to 3y + 4y.

Tell which property you used.

**Solution :**

Equivalent expression : y(3 + 4)

Property used : Distributive Property

**Example 4 :**

Use a property to write an expression that is equivalent to 6 + n.

Tell which property you used.

**Solution :**

Equivalent expression : n + 6

Property used : Commutative Property of Addition

After having gone through the stuff given above, we hope that the students would have understood "How to write equivalent expressions using properties".

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