Loading [MathJax]/jax/output/HTML-CSS/jax.js

Equivalent Fractions

Equivalent fractions are the fractions having the same value. Same fraction can be represented in many ways. Let us take the following example.

Equivalent Fractions

In picture (i) the shaded part is represented by fraction 12

The shaded part in picture (ii) is represented by fraction 24. In picture (iii) the same part is represented by fraction 48. SO, the fraction represented by these shaded portions are equal. Such fractions are called equivalent fractions.

We say that 122448

Hence, for a given fraction there can be many equivalent fractions.


Making Equivalent Fractions:

We have seen in the above example that 1224 and 48 are equivalent fractions.

Therefore, 12 can be written as 121×22×21×32×31×42×4 and so on.

Hence, an equivalent fraction of any given fraction can be obtained by multiplying its numerator and denominator by the same number.

Same way, when the numerator and denominator of a fraction are divided by the same number, we get its equivalent fractions.

12 = 1÷12÷1 = 24 = 2÷24÷2 = 36 = 3÷36÷3 

We have,

2/4 = (1 × 2)/(2 × 2)

3/6 = (1 × 3)/(2 × 3)

4/8 = (1 × 4)/(2 × 4)
We observe that 2/4, 3/6 and 4/8 are obtained by multiplying the numerator and denominator of 1/2 by 2, 3 and 4 respectively.

Thus, an equivalent fraction of a given fraction can be obtained by multiplying its numerator and denominator by the same number (other than zero).

2/4 = (2÷ 2)/(4 ÷ 2) = 1/2

3/6 = (3÷ 3)/(6 ÷ 3) = 1/2

4/8 = (4 ÷ 4)/(8 ÷ 4) = 1/2


We observe that if we divide the numerators and denominators of 2/4, 3/6 and 4/8 each by their common factor 2, we get an equivalent fraction 1/2.

Thus, an equivalent fraction of a given fraction can be obtained by dividing its numerator and denominator by their common factor (other than 1), if ant.

Note:

(i) Multiplying its numerator (top) and denominator (bottom) by the same number (other than 0).

(ii) Dividing its numerator (top) and denominator (bottom) by their common factor (other than 1).


For Example:

1. Write three equivalent fraction of 3/5.

Equivalent fractions of 3/5 are:

(3 × 2)/(5× 2) = 6/10,

(3 × 3)/(5 × 3) = 9/15,

(3 × 4)/(5 × 4) = 12/20


Therefore, equivalent fractions of 3/5 are 6/10, 9/15 and 12/20.

2. Write next three equivalent fraction of 23.

We multiply the numerator and the denominator by 2.

We get, 2×23×2 = 46

Next, we multiply the numerator and the denominator by 3. We get

2×33×3 = 69.

Next, we multiply the numerator and the denominator by 4. We get

2×43×4 = 812.

Therefore, equivalent fractions of 23 are 46, 69 and 812.



3. Write three equivalent fraction of 1/4.

Equivalent fractions of 1/4 are:

(1× 2)/(4× 2) = 2/8,

(1 × 3)/(4 × 3) = 3/12,

(1× 4)/(4× 4) = 4/16


Therefore, equivalent fractions of 1/4 are 2/8, 3/12 and 4/16.



4. Write three equivalent fraction of 2/15.

Equivalent fractions of 2/15 are:

(2× 2)/(15 × 2) = 4/30,

(2 × 3)/(15 × 3) = 6/45,

(2× 4)/(15 × 4) = 8/60


Therefore, equivalent fractions of 2/15 are 4/30, 6/45 and 8/60.



5. Write three equivalent fraction of 3/10.

Equivalent fractions of 3/10 are:

(3× 2)/(10× 2) = 6/20,

(3 × 3)/(10 × 3) = 9/30,

(3× 4)/(10× 4) = 12/40


Therefore, equivalent fractions of 3/10 are 6/20, 9/30 and 12/40.

● Fraction

Representations of Fractions on a Number Line

Fraction as Division

Types of Fractions

Conversion of Mixed Fractions into Improper Fractions

Conversion of Improper Fractions into Mixed Fractions

Equivalent Fractions

Interesting Fact about Equivalent Fractions

Fractions in Lowest Terms

Like and Unlike Fractions

Comparing Like Fractions

Comparing Unlike Fractions

Addition and Subtraction of Like Fractions

Addition and Subtraction of Unlike Fractions

Inserting a Fraction between Two Given Fractions





Numbers Page

6th Grade Page

From 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. Dividing 3-Digit by 1-Digit Number Video | Long Division | Worksheet

    Apr 03, 25 12:09 AM

    Dividing 3-Digit by 1-Digit Number
    Dividing 3-Digit by 1-Digit Numbers are discussed here step-by-step. How to divide 3-digit numbers by single-digit numbers? Let us follow the examples to learn to divide 3-digit number by one-digit nu…

    Read More

  2. Division of Two-Digit by a One-Digit Numbers | Dividing Larger Numbers

    Apr 03, 25 12:03 AM

    Divide 2-Digit Number by 1-Digit Number
    In division of two-digit by a one-digit numbers are discussed here step by step. How to divide 2-digit numbers by single-digit numbers?

    Read More

  3. Subtracting 2-Digit Numbers Video | How to Subtract Two Digit Numbers?

    Apr 01, 25 02:15 AM

    Subtracting 2-Digit Numbers
    In subtracting 2-digit numbers we will subtract or minus a two-digit number from another two-digit number. To find the difference between the two numbers we need to ‘ones from ones’ and ‘tens from

    Read More

  4. PEMDAS Rule | Steps to Simplify the Order of Operation | Simple Rules

    Apr 01, 25 02:10 AM

    Easy and simple way to remember PEMDAS rule!! P → Parentheses first E → Exponent (Powers, Square Roots, Cube Roots, etc.) MD → Multiplication and Division (start from left to right) AS →

    Read More

  5. Worksheet on Simplification | Simplify Expressions | BODMAS Questions

    Apr 01, 25 01:59 AM

    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