Equivalent Fractions

Fractions are defined as the part of the group or the region. To explain with example – Suppose 6 / 10 be any fraction. It is  read as “six-tenth”. So, 6 is the numerator and 10 is the denominator. Here, what does ‘10’ stand for? It is the number of equal parts in which the whole region is being divided. What does ‘6’ stand for? It is the number of equal parts taken out from the whole region. 

Equivalent Fractions

Equivalent fractions are fractions having the same value but the numerator and denominator might look different in values. An equivalent fraction represents the same proportion of the given fraction. All these fractions are the same.

Why are they the same or equal? They are the same because if you multiply both numerator and denominator by the same number then the resultant fraction will be the same value. To convert into equivalent fraction You can only multiply and divide but cannot add or subtract in numerator or denominator to get the equivalent fraction. 

Here , few equivalent fraction example are listed-

8 / 24 = 4 / 12= 2 / 6 = 1 / 3

Equivalent Fractions Examples

The example of equivalent fractions in real life are –

If we cut pizza, into four equal parts then it can be given by 4/4. If you eat one of the piece of pizza , then it is given by 1/4. The denominator shows there were 4 pieces of pizza and the numerator shows 1 piece was eaten. Hence, the fraction of pizza which is left is 3/4.

Here, the numerator tells that 3 pieces are left and the denominator tells that there are 4 pieces. 

Types of Fractions

Proper Fractions

Proper fraction is the fraction representing the part of the whole number. In the proper fraction, the denominator shows the number of parts into which the whole region is divided and the numerator shows the number of parts which can be taken. Therefore, to identify the proper fraction, the numerator is always less than the denominator. 

Improper and Mixed Fractions

The fraction where the numerator is bigger than the denominator is referred to as improper fraction. Thus, fractions like  18/5, 5/4 … etc.  is called improper fractions.

Fractions in the form of 212, 645… etc are called mixed fractions. 

Improper fraction can be expressed as a fixed fraction by dividing  the numerator by denominator to obtain quotient and remainder. Then , the mixed fraction can be written as 

quotient  Remainder/Divisor

Equivalent Fractions

Look at all the below given representation of fractions-

The fractions are 1/2, 2/4, 3/6 representing the parts taken from the total number of parts. If we draw the pictorial representation and place it one over the other, they all would be equal. These fractions are called equivalent fractions. 

1/2, 2/4, 3/6, , ….., 36/72, etc…are all equivalent fractions. They represent the same part of the whole region.. 

Why do equivalent fractions represent the same part of the whole region? How can  we obtain one from another? 

Observe, 1/2= 2/4= 1  /2 *2 / 2

Similarly, 1/2=3/6= 1 / 3 *2 / 3

1/2=4/8= 1 /4 *2 /4

To find an equivalent fraction of a given fraction, you have to multiply both the numerator and the denominator by  the same number of the given fraction. 

Examples:

1. Calculate equivalent fraction of 25with numerator 6. 

We know 2 × 3=6. It means, we need to multiply both the numerator and denominator by 3 to get the equivalent fraction. 

Hence, 2/5 =2× 5 /5×3=615 is the required equivalent fractions.

1. Calculate  the equivalent fraction of 15/35 with denominator 7.

We have 15/35= ?/7

We Observe the denominator and calculate 355=7.

We therefore, divide both the numerator and denominator of 1535by 5. 

Thus, 15/35=15  5/35  5= 3/7    

Methods to Determine Equivalent Fraction

What can we infer from the table?

When the product of the numerator of the first and the denominator of the second is equal to the product of the denominator of the first and the numerator of the second in the above cases. These two products are referred to as cross products. Hence, this rule is very useful in finding the equivalent fractions. 

Equivalent Fraction Cross-Multiplication

The method to determine the equivalent fraction is by cross multiplication-

When the product of the numerator of the first and the denominator of the second is equal to the product of the denominator of the first and the numerator of the second in the above cases. These two products are referred to as cross products. Hence, this rule is very useful in finding the equivalent fractions. 

Let us understand this with an example-

410=25

Above are the two given fractions-

In order to understand if the above fractions are equivalent , we have to use a cross multiplication method. 

Using the above rule, 4× 5=20.

10×2=20

Since both the values are equal. So, it is an equivalent fraction. 

Conclusion

As the topic we have discussed above talks about the equivalent fraction, how to find if the given fraction is the equivalent fraction or not, how equivalent fraction is relevant to understand  in the real-life and many more. Equivalent fraction is the fraction having the same value but the numerator and denominator might look different in values. An equivalent fraction represents the same proportion of the given fraction. These fractions are the same.

There are numerous methods to determine if the fraction is equivalent or not. One of the method has been described above in detail which is the cross multiplication method. This is the most easy and widely used method.