How to Find Equivalent Fractions?

We need to simplify the given fractions to calculate whether they are equivalent or not. Simplification to get equivalent numbers can be done to a point where both the denominator and numerator should still be whole numbers. There are different methods to identify if the given fractions are equivalent. Some of them are as follows:

• Making the denominator the same 
• Calculate the decimal form of both the fractions.
• Visual method
• Cross multiplication method

Let us identify whether 2/12 and 3/18 are equivalent fractions by each of these methods.

Making the denominator the same

The denominators of the given fractions, 2/12and 3/18 are 12 and 18. The (LCM) of the denominators 12 and 18 is 36. Making the denominators of both fractions 36, by multiplying them with suitable numbers.

• 2/12=2×3/12×3=6/36
• 3/18=3×2/18×2=6/36

We can identify that both the fractions are equivalent to the same fraction 6/36. Thus, the given fractions are equivalent.

Calculate the decimal form of both fraction 

Let us calculate the decimal form of both the fractions 2/12 and 3/18 to see if they give the same value.

• 2/12=0.166..
• 3/18=0.166..

The decimal result of both the fractions are the same and hence, they are equivalent.

Cross Multiplication method

To identify whether 2/12 and 3/18 are equivalent, we cross multiply them. If both given fractions the products are the same, the fractions are equivalent.

Since both fractions of the products here are 36, the given fractions are said to be equivalent fractions.

Visual method

Let us denote each of the fractions 2/12 and 3/18pictorially on identical shapes and check if the shaded portions of both are equal.

it can be seen that the shaded parts in both the figures denote the same portion if seen as a whole. Hence, the given fractions are equivalent.

Summary

• Two fractions are said to be equivalent if their values graphical value, decimal value are the same.
• We usually multiply the denominator and numerator of a fraction by the same number to get its equivalent fraction.
• The ‘Cross multiplication method is used to determine whether any two fractions are equivalent or not.
•  the denominators making the same’ is another method used to determine if two or more fractions are equivalent.