How to Multiply and Divide Fractions

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Multiplying and dividing fractions are fundamental operations in mathematics that are essential for solving a wide range of problems. Understanding how to accurately perform these operations is crucial for success in various fields, such as science, engineering, and finance. Fractions represent parts of a whole and are commonly used to express proportions, ratios, and percentages. In this guide, we will explore the step-by-step process of multiplying and dividing fractions, providing clear explanations, practical examples, and useful tips to ensure a solid understanding of these concepts. By the end, you will be equipped with the necessary knowledge and skills to confidently multiply and divide fractions, empowering you to solve complex mathematical problems with ease.

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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.

Table of Contents

Steps

Fractional Multiplication

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Multiply the numerators of the fractions together. The numerator is the number at the top of the fraction, and the denominator is the number at the bottom. The first step in multiplying fractions is to line them up so that the numerators and denominators are close together. For example, if you want to multiply 1/2 and 12/48, you first need to find the product of the numerators 1 and 12. 1 x 12 = 12. You have a numerator of 12.

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Continue multiplying the denominator. Do the same when you find the product of the numerators. Multiply 2 by 4. 2 x 48 = 96. This is the denominator of the answer. So, the new fraction will be 12/96.

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Simplify fractions . The final step is to reduce the result if the fraction is still not minimal. To reduce a fraction, you need to find the greatest common divisor (GCC) of the numerator and denominator in the fraction. The GCLN is the largest number that both the numerator and the denominator are divisible by. In this example, 96 is divisible by 12. We have: 12 divided by 12 is 1, 96 divided by 12 is 8. So, 12/96 ÷ 12/12 = 1/8.

• 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

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Reverse the numerator and denominator of the second fraction and change the division sign to the multiplication sign. For example, we have the calculation 1/2 ÷ 18/20. First, invert 18/20 to get the fraction 20/18, then change the division sign to the multiplication sign. The calculation will be rewritten as follows: 1/2 ÷ 18/20 = 1/2 x 20/18.

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Continue, multiply the numerators together to find the numerator, multiply the denominators together to find the denominator, and then simplify the answer. Do the same thing as multiplying fractions. Multiplying the two numerators together, 1 and 20, we get the numerator of the answer is 20. Multiplying the two denominators, 2 and 18, we get the denominator of the answer is 36. The provisional result is 20/36 . Simplify the fraction by dividing both the numerator and denominator by 4. So the final result is 20/36 ÷ 4/4 = 5/9.

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.

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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.

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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, understanding how to multiply and divide fractions is an essential skill in mathematics that provides a strong foundation for more complex calculations and problem-solving. By following a few simple rules and techniques, one can easily multiply and divide fractions accurately. It is crucial to remember that when multiplying, the numerators are multiplied together, and the denominators are multiplied together, resulting in a simplified fraction. Similarly, when dividing, the first fraction is multiplied by the reciprocal of the second fraction. To simplify the process, it is recommended to simplify the fractions before multiplying or dividing. Additionally, it is advisable to convert mixed numbers into improper fractions for easier calculations. By practicing these techniques and understanding the underlying principles, one can confidently solve problems involving fractions and apply this knowledge to real-life scenarios.

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