Recap of fractions:

A fraction is defined as a part of a whole number that has been divided into an equal number of parts.

 

A fraction is written as a/b where a and b are whole numbers. a is known as the numerator and b is known as the denominator.

 

Equivalent fractions

Most of the time, students find the concept of equivalent fractions quite confusing. To ingrain the concept of equivalent fractions lucidly in the student’s mind, we have created an equivalent fractions worksheet that will help the children to grasp the concept of fractions effortlessly.

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Equivalent fractions are those fractions that have the same value. In other words, equivalent fractions represent the same parts of a whole.

 

Consider the following fractions

In the above figure:

The shaded parts (a), (b) and (c) represented by fractions 1/2 , 2/4 and  6/12 are equal. As the shaded parts cover the same area, this means that the fractions 1/2 , 2/4 and  6/12 represent the same part of the whole. Therefore, they are equivalent fractions.

 

Similarly, the shaded parts (d) and (e) represented by fractions  1/3 and 2/6  are equal. Therefore, 1/3 and 2/6 are equivalent fractions.

 

You can find equivalent fractions of a given fraction by multiplying or dividing both the numerator and the denominator of the original fraction by the same number. Note that this number cannot be 0.

 

  • Finding equivalent fractions by multiplication

To find the equivalent fractions of 2/3 we can multiply both the numerator 2 and the denominator 3 by the same number i.e.  2*2 ÷ 3*2  = 4/6

Hence, 4/6 is an equivalent fraction of 2/3

Similarly, if we multiply the numerator and the denominator by the numbers 3, 4, 5 we get the following equivalent fractions respectively: 
6/9, 8/12, 10/15

 

  • Finding equivalent fractions by division

To find the equivalent fractions of 12/30 we can divide both the numerator 12 and the denominator 30 by the number 3 as it is a common divisor of 12 and 30 i.e.  12/30 ÷ 30/3 = 4/10

Hence, 4/10  is an equivalent fraction of 12/30

Similarly, if we divide the numerator and the denominator by the numbers 2 and 6 we get the following equivalent fractions respectively:

6/15 , 2/5

 

 

Lowest form of a fraction

 

When the numerator and denominator of a fraction have no common factor other than 1 then the fraction is said to be in its lowest or simplest form. In order to find the simplest form of a fraction you must divide the numerator and the denominator by the Highest Common Factor.

 

For example: Find the simplest form of the fraction 12/30

The HCF of 12 and 30 is 6

Therefore, the simplest form is 12/6 ÷ 30/6 = 2/5

 

 

 

 

 

Equivalent Fractions worksheets:

Q1: Find the first four equivalent fractions of 3/7

A1: The first four equivalent fractions of  3/7 are:

3*2/7*2 , 3*3/7*3 , 3*4/7*4 , 3*5/7*5 

= 6/14 , 9/21, 12/28, 15/35 

 

Q2. Find an equivalent fraction of 5/8 with the numerator 25.

A2: We know that 5 * 5 = 25, hence the equivalent fraction of  5/8  with the numerator 25 can be obtained by multiplying the numerator and denominator by 5

= 5*5 / 8*5 =25/40 

 

Q3. Find an equivalent fraction of 3/4 with the denominator 40.

A3: We know that 4 * 10 = 40, hence the equivalent fraction of 3/4 with the denominator 40 can be obtained by multiplying the numerator and denominator by 10

= 3*10 / 4*10   =  30/40

 

Q4. Identify which of the following are equivalent fractions

  1.  3/8 and 21/56 
  2.  4/17 and 1/5
  3.  7/12 and 14/24
  4.  6/13 and 6/14

 

A4. Pairs of equivalent fractions are (a) and (c).

 

Q5. Reduce the fraction 35/63 to its simplest form.

A5. HCF of 35 and 63 is 7

Therefore, simplest form of 35/63 = 35/7 ÷ 63/7  = 5/9

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