Properties of Equivalent Fractions

The properties of equivalent fractions are discussed here step-by-step.


1. If the numerator and denominator of a fraction is multiplied by the same number, except zero, the value of the fraction remains the same and an equivalent fraction is obtained. 

As:

(i) 2/3 = 2 x 2/3 x 2 = 4/6; 2 x 3/3 x 3 = 6/9; 2 x 4/3 x 4 = 8/12;

2 x 5/3 x 5 = 10/15

So, 2/3, 4/6, 6/9, 8/12, 10/15, etc., are equivalent fractions.


(ii) 5/6 = 5 x 3/6 x 3 = 15/18; 5 x 7/6 x 7 = 35/42; 5 x 4/6 x 4 = 20/24;

5 x 9/6 x 9 = 45/54

So, 5/6, 15/18, 35/42, 20/24, 45/54, etc., are equivalent fractions.

2. If the numerator and denominator of a fraction is divided by the same number, except zero, the value of the fraction remains the same and an equivalent fraction is obtained. 

(i) 60/90 = 60 ÷ 10/90 ÷ 10 = 6/9; 60 ÷ 2/90 ÷ 2 = 30/45;

60 ÷ 3/90 ÷ 3 = 20/30, 60 ÷ 5/90 ÷ 5 = 12/18

So, 60/90, 6/9, 30/45, 20/30, 2/3 etc., are equivalent fractions.

32/72 = 32 ÷ 2/72 ÷ 2 = 16/36, 32 ÷ 4/72 ÷ 4 = 8/18, 32 ÷ 8/72 ÷ 8 = 4/9

So, 32/72, 16/36, 8/18, 4/9 are equivalent fractions.



3. In case of two equivalent fractions, the product of the numerator of one fraction and denominator of the second fraction is equal to the product of the denominator of the first fraction and numerator of the second fraction.

Accordingly, the two fractions are equivalent if:

numerator of the first fraction × denominator of the second fraction = denominator of the first fraction × numerator of the second fraction

As:

1/3 = 2/6

5/7 = 15/21

So, 1 x 6 = 3 x 2 = 6

So, 5 x 21 = 7 x 15 = 105


4. A fraction may be reduced to its lowest term. If a factor or factors is / are common to numerator and denominator of a fraction, then the common factor or factors may be removed to get it in its lowest term.

If there is a fraction 12/18 and we have to reduce it to its lowest term,

Since, 12 = 2 x 2 x 3 and 18 = 2 x 3 x 3, thus, 2 x 3 = 6 is a common factor in numerator and denominator of 12/18

So, 12 ÷ 6/18 ÷ 6 = 2/3

By dividing both 12 and 18 by 6, we get the fraction 2/3 as the lowest of 12/18.


These are the properties of equivalent fractions explained along with the examples.

Related Concept

Fraction of a Whole Numbers

Representation of a Fraction

Equivalent Fractions

Properties of Equivalent Fractions

Like and Unlike Fractions

Comparison of Like Fractions

Comparison of Fractions having the same Numerator

Types of Fractions

Changing Fractions

Conversion of Fractions into Fractions having Same Denominator

Conversion of a Fraction into its Smallest and Simplest Form

Addition of Fractions having the Same Denominator

Subtraction of Fractions having the Same Denominator

Addition and Subtraction of Fractions on the Fraction Number Line







4th Grade Math Activities

From Properties of Equivalent Fractions to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. 5th Grade BODMAS Rule Worksheet | PEMDAS | Order of operations|Answers

    Apr 03, 25 03:11 PM

    5th Grade BODMAS Rule Worksheet
    In 5th Grade BODMAS Rule Worksheet you will get different types of problems on mathematical expressions involving different operations, mathematical expression with 'brackets' and 'of' and simplifying…

    Read More

  2. Worksheet on Simplification | Simplify Expressions | BODMAS Questions

    Apr 03, 25 02:58 PM

    Worksheet on Simplification
    In worksheet on simplification, the questions are based in order to simplify expressions involving more than one bracket by using the steps of removal of brackets. This exercise sheet

    Read More

  3. Divisible by 2 Video |Test of Divisibility by 2 Trick| Rules| Examples

    Apr 03, 25 10:25 AM

    Divisible by 2
    A number is divisible by 2 if the digit at unit place is either 0 or multiple of 2. So a number is divisible by 2 if digit at its units place is 0, 2, 4, 6 or 8.

    Read More

  4. BODMAS Rule | Order of Operation | Definition, Examples, Problems

    Apr 03, 25 10:22 AM

    What is BODMAS Rule in Math?
    Easy and simple way to remember BODMAS rule!! B → Brackets first (parentheses) O → Of (orders i.e. Powers and Square Roots, Cube Roots, etc.) DM → Division and Multiplication

    Read More

  5. Before and After Video | Math Worksheets on Number | Before and After

    Apr 03, 25 12:44 AM

    before and after number worksheet
    Free math worksheets on numbers before and after help the kids to check how much they are good at numbers. The purpose of this math activity is to help your child to say a number in order and also hel

    Read More