# WRITING EQUIVALENT EXPRESSIONS USING PROPERTIES

## About "Writing equivalent expressions using properties"

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 twonumbers, 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 twonumbers, 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

## Writing equivalent expressions using properties - Examples

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".

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6