This article was coauthored by Grace Imson, MA. Grace Imson is a math teacher with over 40 years of teaching experience. Grace is currently a math instructor at the City College of San Francisco and was previously in the Math Department at Saint Louis University. She has taught math at the elementary, middle, high school, and college levels. She has an MA in Education, specializing in Administration and Supervision from Saint Louis University.
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To multiply fractions, all you have to do is multiply the numerators and denominators and simplify the result. To divide fractions, you simply have to flip the numerator and denominator of one of the fractions, multiply the result by the other fraction, and simplify. If you want to know how to divide and multiply fractions in no time at all, just follow these steps.
Steps
Method 1
Method 1 of 2:Multiplying Fractions
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1Multiply the numerators of the fractions. The numerator is the number on the top of a fraction and the denominator is the number on the bottom.^{[1] X Expert Source Grace Imson, MAMath Instructor, City College of San Francisco Expert Interview. 1 November 2019. } The first step to multiplying fractions is to line them up so that their numerators and denominators are next to each other. If you're multiplying the fraction 1/2 by 12/48, then the first thing you want to do is multiply the numerators, 1 and 12. 1 x 12 = 12. Write the product, 12, in the numerator of the answer.

2Multiply the denominators of the fractions. Now, you'll just have to do the same thing with the denominators.^{[2] X Expert Source Grace Imson, MAMath Instructor, City College of San Francisco Expert Interview. 1 November 2019. } Multiply 2 and 48 to find the new denominator. 2 x 48 = 96. Write this answer in the denominator of the new fraction. Therefore, the new fraction is 12/96.Advertisement

3Simplify the fraction. The last step is to simplify the result if it can be done. To simplify a fraction, you have to find the greatest common factor (GCF) of both the numerator and the denominator. The GCF is the largest number that can be evenly divided into both numbers.^{[3] X Research source } In the case of 12 and 96, 12 happens to evenly divide into 96. So, divide 12 by 12 to get 1, and divide 96 by 12 to get 8. Therefore, 12/96 ÷ 12/12 = 1/8.
 If both numbers are even, you can also start by dividing them both by 2 and keep going. 12/96 ÷ 2/2 = 6/48 ÷ 2/2 = 3/24. Then you may notice that 3 goes evenly into 24, so you can divide both the numerator and denominator by 3 to get 1/8. 3/24 ÷ 3/3 = 1/8.
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Method 2
Method 2 of 2:Dividing Fractions
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1Reverse the numerator and denominator of the second fraction and change the division sign to a multiplication sign.^{[4] X Research source } Let's say you're dividing the fraction 1/2 by 18/20. Now, find the reciprocal of 18/20 which is 20/18 and change the division sign to a multiplication sign. So, 1/2 ÷ 18/20 = 1/2 x 20/18.

2Multiply the numerators and denominators of the fractions and simplify your answer. Now, do the same thing you would do to multiply.^{[5] X Research source } If you multiply the numerators, 1 and 20, you get the result of 20 in the numerator. If you multiply the denominators, 2 and 18, you get 36 in the numerator. The product of the fractions is 20/36. 4 is the largest number that is evenly divisible by both the numerator and the denominator of this fraction, so divide each by 4 to get the simplified answer. 20/36 ÷ 4/4 = 5/9.Advertisement
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QuestionCan I simplify fractions before multiplying/dividing them?Grace Imson, MAGrace Imson is a math teacher with over 40 years of teaching experience. Grace is currently a math instructor at the City College of San Francisco and was previously in the Math Department at Saint Louis University. She has taught math at the elementary, middle, high school, and college levels. She has an MA in Education, specializing in Administration and Supervision from Saint Louis University.
Math Instructor, City College of San Francisco 
QuestionCan you clarify Step 1, please?Community AnswerStep 1 says to multiply the numeratorsthat means multiply the top number in both fractions. For example, if you want to multiply 2/3 (two thirds) and 1/2 (one half), I would start by multiplying 2 and 1 together.

QuestionHow do I divide negative fractions?Community AnswerThe same way you would positive fractions. If both fractions have the same sign your answer will be positive regardless of whether they are both negative or both positive. But if your fractions have different signs, you will get a negative answer.

QuestionHow do I divide and multiple negative fractions?DonaganTop AnswererSame as with positive fractions, except the sign of the answer may be affected. If one of the fractions is negative, the answer will be negative. If both of the fractions are negative, the answer will be positive.

QuestionWhat are the steps to multiplying fraction with common and different denominators?Community AnswerMultiply the numerator by the other numerator, and multiply the same number with each of the denominators. You then can divide to the smallest whole values for each.

QuestionHow do I know when to reduce?DonaganTop AnswererReduce whenever you can divide a whole number into both the numerator and denominator. It's easiest to recognize when you can divide a small integer (like 2, 3 or 5) into both the numerator and denominator.

QuestionHow do I multiply mixed fractions that are in brackets?Community AnswerFirst change each mixed fraction into an improper fraction. For example, change 1 1/2 to 3/2. Then follow the steps given to multiply the improper fractions.

QuestionHow do you add and subtract fractions?Community AnswerFirst, make the denominator of the fractions equivalent. Then add the numerators or subtract them.

QuestionHow do I multiply and divide negative fractions?DonaganTop AnswererIgnore signs while multiplying/dividing. Once you have the final number, count the negative signs among the original fractions. If there is an odd number of negative signs, the answer has a negative sign. If there is zero or an even number of negative signs, the answer has a positive sign.

QuestionWhat does "of" mean when using fractions?Community AnswerIn word problems, the word "of" typically indicates multiplication. Threefifths of two hundred women means (3/5)x200 or 120 women.
Video
Tips
 Double check your work.Thanks!
 Remember: Whole numbers can be expressed as a fraction: 2 is the same as 2/1 .Thanks!
 Always double check your work. Have a doubt ? Ask your teacher .Thanks!
 Crosscancelling can be used at anytime to save yourself work simplifying. Crosscancelling is dividing the diagonals by a common factor. For example, the problem (8/20)*(6/12) can be crosscancelled to (2/10)*(3/3).Thanks!
 Make sure you cross simplify.Thanks!
 Don't ever forget to simplify.Thanks!
Warnings
 Remember to simplify completely. An incomplete simplification might as well be no simplification at all.Thanks!
 There is always more than one way to do something in math. However, just because you get the right answer once doing a problem a different way doesn't mean that it will always work. Another way to divide fractions, for example, is crossmultiplication, which is multiplying the diagonals.Thanks!
 Do it one step at a time. This will minimize the chances of a mathematical error.Thanks!
References
 ↑ Grace Imson, MA. Math Instructor, City College of San Francisco. Expert Interview. 1 November 2019.
 ↑ Grace Imson, MA. Math Instructor, City College of San Francisco. Expert Interview. 1 November 2019.
 ↑ https://www.mathsisfun.com/greatestcommonfactor.html
 ↑ http://www.math.com/school/subject1/lessons/S1U4L5DP.html
 ↑ http://www.math.com/school/subject1/lessons/S1U4L5DP.html
About This Article
To multiply fractions, start by multiplying the numerators, or top number of each fraction. For example, if you want to multiply 1/12 × 3/4, first multiply 1 × 3 = 6. Then, multiply the denominators, which would be 12 × 4 = 48, making our example fraction 6/48. After you've multiplied the top and bottom, simply the fraction by finding the greatest common factor, or GCF. Often, you can start with 2 if it is an even number. Once you have the GCF, divide the numerator and denominator to reduce the fraction. When divided by 6, the example fraction would reduce to 1/8. To learn how to divide fractions, read on!
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