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Fractions are an integral part of mathematics, and understanding how to multiply and divide them is fundamental in various real-life scenarios. Whether you’re trying to split a recipe in half, calculate probabilities, or solve complex mathematical problems, knowing how to multiply and divide fractions accurately is crucial. However, this concept can often seem intimidating and confusing to many people. In this guide, we will break down the process of multiplying and dividing fractions into simple, easy-to-follow steps. By the end, you will have a clear understanding of the fundamental rules and techniques needed to multiply and divide fractions effectively. So, let’s delve into the world of fractions and discover how to manipulate them using multiplication and division.
This article was co-written by Mario Banuelos, PhD. Mario Banuelos is an assistant professor of mathematics at California State University, Fresno. With over eight years of teaching experience, Mario specializes in mathematical biology, optimization, statistical modeling for genome evolution, and data science. Mario holds a bachelor’s degree in mathematics from California State University, Fresno, and a doctorate in applied mathematics from the University of California, Merced. Mario teaches at both the high school and college levels.
This article has been viewed 188,248 times.
To multiply fractions, all you need to do is find the product of the numerators as well as the denominators and then simplify the result. And if you want to divide a fraction, you just need to inverse the numerator and denominator of one of those two fractions, then multiply the inverse fraction by the other fraction and then reduce the result. The following article will guide you through the steps to perform multiplication and division of fractions quickly.
Steps
Fractional Multiplication
![Image titled Divide and Multiply Fractions Step 1](https://www.wikihow.com/images/thumb/8/8c/Divide-and-Multiply-Fractions-Step-1-Version-3.jpg/v4-728px-Divide-and-Multiply-Fractions-Step-1-Version-3.jpg)
![Image titled Divide and Multiply Fractions Step 2](https://www.wikihow.com/images/thumb/5/55/Divide-and-Multiply-Fractions-Step-2-Version-3.jpg/v4-728px-Divide-and-Multiply-Fractions-Step-2-Version-3.jpg)
![Image titled Divide and Multiply Fractions Step 3](https://www.wikihow.com/images/thumb/d/dc/Divide-and-Multiply-Fractions-Step-3-Version-3.jpg/v4-728px-Divide-and-Multiply-Fractions-Step-3-Version-3.jpg)
- If both are even, you can start by dividing them by 2 and so on. 12/96 ÷ 2/2 = 6/48 ÷ 2/2 = 3/24. At this point, it is easy to see that 24 is divisible by 3, so you can divide both the numerator and the denominator by 3 to get an answer of 1/8. 3/24 ÷ 3/3 = 1/8.
Fraction division
![Image titled Divide and Multiply Fractions Step 4](https://www.wikihow.com/images/thumb/b/bd/Divide-and-Multiply-Fractions-Step-4-Version-3.jpg/v4-728px-Divide-and-Multiply-Fractions-Step-4-Version-3.jpg)
![Image titled Divide and Multiply Fractions Step 5](https://www.wikihow.com/images/thumb/d/d1/Divide-and-Multiply-Fractions-Step-5-Version-3.jpg/v4-728px-Divide-and-Multiply-Fractions-Step-5-Version-3.jpg)
Advice
- Check the post again.
- Don’t forget to shorten your answer.
- Remember: all natural numbers can be converted to fractions: 2 and 2/1 are the same.
- The cross reduction method can be used at any time to omit the final reduction step. Cross reduction is dividing two numbers on the diagonal (one numerator with the other denominator and vice versa) by a common divisor. For example, the calculation of two fractions (8/20)*(6/12) after cross reduction becomes (2/10)*(3/3).
- Always check your work. If you have any questions, ask your teacher right away.
Warning
- Take it one step at a time to limit errors.
- In mathematics, a problem can be solved in many ways. However, just because you find the right answer when solving a problem in a different way doesn’t mean that it always works. For example, another way to do fractional division is cross multiplication (multiply one numerator by the other and vice versa).
- Don’t forget to put your answer in the simplest fraction form. An incompletely truncated result will not score maximum.
This article was co-written by Mario Banuelos, PhD. Mario Banuelos is an assistant professor of mathematics at California State University, Fresno. With over eight years of teaching experience, Mario specializes in mathematical biology, optimization, statistical modeling for genome evolution, and data science. Mario holds a bachelor’s degree in mathematics from California State University, Fresno, and a doctorate in applied mathematics from the University of California, Merced. Mario teaches at both the high school and college levels.
This article has been viewed 188,248 times.
To multiply fractions, all you need to do is find the product of the numerators as well as the denominators and then simplify the result. And if you want to divide a fraction, you just need to inverse the numerator and denominator of one of those two fractions, then multiply the inverse fraction by the other fraction and then reduce the result. The following article will guide you through the steps to perform multiplication and division of fractions quickly.
In conclusion, mastering the skills to multiply and divide fractions is crucial for a strong foundation in mathematics. By following the steps outlined in this guide, individuals can confidently tackle problems involving fraction multiplication and division. It is important to simplify fractions before multiplying or dividing to ensure accurate results. Additionally, understanding the concept of reciprocals and how to use them in division can simplify the process further. With practice, individuals can become proficient in multiplying and dividing fractions, enabling them to confidently solve complex mathematical problems and apply these skills in various real-life scenarios.
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