How to Find the Product of Fractions?

A fraction is a mathematical term that signifies the division of a whole into parts. It contains two parts– a numerator and a denominator. The numerator is the number at the top of the fraction, and the denominator the number written at the bottom. To find the product of fractions, you need to multiply them. The process of multiplying fractions can seem a little confusing for students because, unlike fraction addition or subtraction, it doesn’t need the denominators to be the same. The product of two or more fractions is equal to the multiplication of all numerators over the multiplication of all denominators.  

Students usually learn the concept of fractions from an elementary school level. With the rising complexity of the topic, they often feel dreaded and start losing interest in it. By establishing a thorough practice of the important concepts, students can easily establish the necessary foundation required to master this important skill. 

Breaking the process of fractions multiplication into a few simple steps will help students to better comprehend and understand the process. Since fractions are composed of two parts: the numerator and the denominator, it is simple to perform fraction multiplication by multiplying numerators and denominators separately to obtain the final result. 

Here are the stepwise instructions for finding the product of fractions.

Multiplying Two Fractions

To multiply two fractions, simply multiply the numerators of the first and second numbers to each other and denominators to each other. The product of the two numerators becomes the numerator of the resultant fraction, and the product of the two denominators becomes the denominator of the resultant fraction. For instance, to multiply fraction 3/7 with 2/3 first, multiply three by two, and then multiply seven by three. Thus, the resultant fraction will become 6/21, i.e., 3/7 x 2/3= 6/21.

Simplifying Fractions

The next step is to check if the resultant fractions can be simplified further to derive the answer. This can be done by dividing both the numerator and the denominator by the same number. For example, we can further simplify 6/21 as both of them are exactly divisible by 3, that is, 6 / 3 = 2 and 21/ 3 = 7. Sp, the simplified answer is 2/7. Since 2 and 7 can not be divided with the same number any further, so 2/7 is the final answer. In some cases where the denominator is completely dividing the numerator, the resultant fraction becomes a whole number. For example, when we simplify the product of fraction 4/2 and 6/4, which is 4/2 x 6/4 = 24/8 = 3

Multiplication of Fractions with Whole Numbers

To multiply a fraction to a whole number, simply multiply the fraction numerator by the whole number and write the denominator as it is. Any whole number can be represented in a fractional form by using one as its denominator. For instance, we can write the given whole number, say ’9’ as the numerator and one as the denominator. I.e., 9/1. Consider the example of multiplying whole number 9 with fraction 5/2. find the product of 9 and 5 to produce the new numerator, which is 45, and the denominator remains the same: 9 x 5/2 = 9/1 x 5/2 = 45/2


Fractions are not just a math topic– it is an extremely important concept used in our everyday life, from reading a clock to baking a cake. Learning the concept of fractions multiplications forms the foundation for various math topics and is also an essential life skill. Therefore, it is highly recommended that students implement the conceptual clarity of fractions multiplication through practice. Cuemath offers math worksheets for 3rd grade and 4th grade students to efficiently master the vital skill of finding the product of two or more fractions. 

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