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.

Properties of Operations

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.

Example : 

9 + 0  =  0 + 9  =  9

7. Identity Property of Multiplication :

Multiplying a number by one does not change its value.

Example : 

1 x 7  =  7 x 1  =  7

Practice Questions

Question 1 :

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

Tell which property you used.

Answer :

The operation in the expression is addition.

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

x + 3  =  3 + x

Question 2 :

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

Tell which property you used.

Answer :

Equivalent expression : a(bc)

Property used : Associative Property of Multiplication

Question 3 :

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

Tell which property you used.

Answer :

Equivalent expression : y(3 + 4)

Property used : Distributive Property

Question 4 :

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

Tell which property you used.

Answer :

Equivalent expression : n + 6

Property used : Commutative Property of Addition

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