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 Circle Worksheet | Free Worksheet with Answer |Practice Math

    Jul 11, 25 02:14 PM

    Radii of the circRadii, Chords, Diameters, Semi-circles
    In 5th Grade Circle Worksheet you will get different types of questions on parts of a circle, relation between radius and diameter, interior of a circle, exterior of a circle and construction of circl…

    Read More

  2. Construction of a Circle | Working Rules | Step-by-step Explanation |

    Jul 09, 25 01:29 AM

    Parts of a Circle
    Construction of a Circle when the length of its Radius is given. Working Rules | Step I: Open the compass such that its pointer be put on initial point (i.e. O) of ruler / scale and the pencil-end be…

    Read More

  3. Combination of Addition and Subtraction | Mixed Addition & Subtraction

    Jul 08, 25 02:32 PM

    Add and Sub
    We will discuss here about the combination of addition and subtraction. The rules which can be used to solve the sums involving addition (+) and subtraction (-) together are: I: First add

    Read More

  4. Addition & Subtraction Together |Combination of addition & subtraction

    Jul 08, 25 02:23 PM

    Addition and Subtraction Together Problem
    We will solve the different types of problems involving addition and subtraction together. To show the problem involving both addition and subtraction, we first group all the numbers with ‘+’ and…

    Read More

  5. 5th Grade Circle | Radius, Interior and Exterior of a Circle|Worksheet

    Jul 08, 25 09:55 AM

    Semi-circular Region
    A circle is the set of all those point in a plane whose distance from a fixed point remains constant. The fixed point is called the centre of the circle and the constant distance is known

    Read More