3 Ways to Multiply Fractions - wikiHow (2024)

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1Multiplying Simple Fractions

2Working with Mixed Numbers

3Using a Calculator

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Co-authored byMario Banuelos, PhD

Last Updated: April 7, 2024Fact Checked

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Multiplying fractions might seem a little daunting at first, but once you get the hang of setting up your equation, you’ll be able to get those answers in no time! Turn mixed numbers into improper fractions, multiply numerators and denominators, and simplify your fraction to get the final answer to the question. Take your time and work step by step so you can check your work as you go.

Method 1

Method 1 of 3:

Multiplying Simple Fractions

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  1. 1

    Write down the problem on a piece of paper. Being able to see your work will help you learn how to multiply fractions better. Plus, if you make a mistake, it’ll be easier to go back in your work to see the error. Each fraction has a numerator (the number on the top) and a denominator (the number on the bottom). Separate the numerator from the denominator with a straight, horizontal line.[1]

    • Try your best to keep your fractions in a straight line. This will just make it easier to stay organized and work efficiently.
  2. 2

    Multiply the numerators first.[2][3] For example, if you’re asked to solve for 5/6 * 2/3, the first thing you’ll need to do is multiply 5 * 2, which gives you 10. This will be the numerator for your answer.[4]

    • In another example, solve for the numerator of 3/4 * 1/3. Any number times 1 will be itself, so your new numerator is 3.

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  3. 3

    Figure out the new denominator by multiplying the current denominators. In the example given, 5/6 * 2/3, multiply 6 * 3 to get 18. This is your new denominator.[5][6]

    • For 3/4 * 1/3, multiply 4 * 3 to get the new denominator of 12. The answer to your multiplication problem is 3/12.
  4. 4

    Simplify your new fraction to get it in the lowest form possible. If the numerator and denominator share common factors (they can be divided equally by the same number), you can simply your answer. For the example of 5/6 * 2/3, the answer you got was 10/18. Both 10 and 18 are divisible by 2. Divide both numbers by 2 to get your final, simplified answer, which is 5/9.[7]

    • Simply the fraction 3/12. 3 goes into both itself and 12 evenly. The simplified answer is 1/4.

    EXPERT TIP

    3 Ways to Multiply Fractions - wikiHow (8)

    Joseph Meyer

    Math Teacher

    Joseph Meyer is a High School Math Teacher based in Pittsburgh, Pennsylvania. He is an educator at City Charter High School, where he has been teaching for over 7 years. Joseph is also the founder of Sandbox Math, an online learning community dedicated to helping students succeed in Algebra. His site is set apart by its focus on fostering genuine comprehension through step-by-step understanding (instead of just getting the correct final answer), enabling learners to identify and overcome misunderstandings and confidently take on any test they face. He received his MA in Physics from Case Western Reserve University and his BA in Physics from Baldwin Wallace University.

    3 Ways to Multiply Fractions - wikiHow (9)

    Joseph Meyer
    Math Teacher

    Simplifying a fraction just changes the way the fraction is written. To simplify a fraction, you can cancel out the greatest common factor from the numerator and denominator or convert an improper fraction to a mixed number. This doesn't change the inherent value of the fraction.

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Method 2

Method 2 of 3:

Working with Mixed Numbers

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  1. 1

    Write the problem down on paper so you can keep track of your work. You may be tempted to solve math problems in your head, but when you’re first starting out it’s a good idea to write everything down, step by step. This way, if you make a mistake, it’s easy to go back and see what happened so you can fix it moving forward.

    • Fractions are made up of 2 parts, the numerator (the top number) and the denominator (the bottom number), and they are separated with a straight, horizontal line. To write a mixed number, put the whole number on the left-hand side of the fraction.
  2. 2

    Change the mixed number to an improper fraction. For example, let’s say the problem you’re solving for is 1 and 3/4 * 7 and 1/5. The first thing you need to do is change both of those mixed fractions into improper fractions, meaning that the numerator will be greater than the denominator. Here’s how to do this: [8]

    • 1 and 3/4 = 7/4 when it’s made into an improper fraction. The denominator will always stay the same when making improper fractions. Multiply the denominator by the whole number (4 *1) and add that answer to the current numerator (3). (4*1) + 3 = 7.
    • For 7 and 1/5, multiply the denominator by the whole number (5*7) and add that answer to the current numerator (1). (5*7) + 1 = 36. Put the new numerator over the original denominator for your improper fraction. 7 and 1/5 = 36/5.
  3. 3

    Simplify the improper fractions to make the numbers easier to multiply.[9] In the example given, we are left with 7/4 * 36/5. While you could just multiply the numerators and the denominators, it will be easier to do the math if you can simplify the fractions first. When simplifying, check to see if the cross numerator and denominator can be divided equally by the same number.[10] 7 and 5 cannot be, but 36 and 4 are both equally divisible by 4. To get your simplified fraction:[11]

    • Divide 4 by 4 to get 1, changing the first fraction from 7/4 to 7/1.
    • Divide 36 by 4 to get 9, changing the second fraction from 36/5 to 9/5.
    • You can also simplify single fractions if the numerator and denominator have a common factor. For example, if 7/4 were instead 8/4, you could simplify that fraction to 2/1.
  4. 4

    Solve for the problem by multiplying the numerators and the denominators. Now all you have to do is solve for your fraction by multiplying 7 * 9 to get 63 for the new numerator. Multiply 1 * 5 to get 5 for the new denominator. The final improper fraction is 63/5.[12]

    Tip: Remember to keep writing down your work step by step so you don’t get lost in the process. Mixed numbers and improper fractions can be a little tricky, but with practice, you’ll get the hang of it.

  5. 5

    Convert the fraction back to a mixed number get the final answer. To get back to a mixed number, you just need to do some simple division.[13] Divide the numerator by the denominator, so 63/5. 5 goes into 63 12 times, with 3 left over. 12 becomes the whole number and 3 becomes the new numerator. The denominator of 5 stays the same. In the end, 1 and 3/4 * 7 and 1/5 = 12 and 3/5.[14]

    • If you can’t do the division in your head for the whole number, write it out on your piece of paper.
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Method 3

Method 3 of 3:

Using a Calculator

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  1. 1

    Make a fraction into a decimal to solve equations on the calculator. Enter your fractions individually into the calculator to get their decimal equivalents. For example, to solve for 3/4 * 1/2, 3/4 would be entered as 3 divided by 4, giving you the answer of 0.75. Enter the next fraction in the equation, 1/2, as 1 divided by 2 to get the answer of 0.5.[15]

    • Some calculators have functions that allow you to enter the fraction as a fraction so that you don’t have to deal with decimals at all. Check out your calculator’s instruction manual to see if that’s an option that is available to you.
  2. 2

    Use mixed numbers by putting the whole number in front of the decimal. It’s really easy to use mixed numbers in your calculator, even if your calculator doesn’t have a fraction function. Simply follow the step to turn the fraction into a decimal and then place the whole number in front of the decimal point to continue with your equation.[16]

    • For example, to turn the mixed number 3 and 3/4 into a decimal, all you have to do is divide 3 by 4 on your calculator, getting 0.75. Then, place the 3 in front of the decimal point to get 3.75.
  3. 3

    Multiply the decimals on the calculator. For the example of 3/4 * 1/2, punch 0.75 * 0.5 into your calculator. You get the decimal 0.375 as the answer. It can really help to write down your answers on a piece of paper as you work, just in case you forget something or accidentally clear away your calculator screen.[17]

    • If your calculator has parentheses, you could also put the equation into the calculator all at once by typing: (3/4) * (1/2). The “/“ stands for the division button.
  4. 4

    Turn decimals back into fractions. On a piece of paper, write the decimal over the denominator of 1, so for the example of 3/4 * 1/2, you would write 0.375/1 on a piece of paper. Multiply the numerator and denominator by however many places there are after the decimal point. 0.375 has 3 digits after the decimal point, so multiply the decimal and the denominator of 1 by 1000 (use your calculator to help if needed). You end up with 375/1000.[18]

    • If your calculator has the fraction function, you can usually convert the decimal to a fraction just using your calculator.
  5. 5

    Simplify your fraction to get the final answer. All that’s left once you’ve turned the decimal into a fraction is to simplify your answer. For big numbers, you might have to simplify more than once to get the smallest possible fraction. For 375/1000, the number 5 goes into both 375 and 1000, simplifying the fraction to 75/200. That fraction can simplify again by the number 5, which gives you 15/40. Do it one more time to get the final answer of 3/8.[19]

    • It’s totally okay if it takes you a few steps to simplify a fraction. Take your time, don’t rush your work, and you will get there in the end!
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  • Question

    How do you multiply a hard fraction?

    Grace Imson, MA
    Math Instructor, City College of San Francisco

    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.

    Grace Imson, MA

    Math Instructor, City College of San Francisco

    Expert Answer

    Try to simplify the fractions as much as you can before multiplying them so you're working with smaller numbers. For example, 6/8 can be reduced down to 3/4.

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  • Question

    Tess is 5 1/2 feet tall; Ben is 3/4 as tall as Tess. How do I calculate?

    3 Ways to Multiply Fractions - wikiHow (24)

    Donagan

    Top Answerer

    Change the mixed number to an improper fraction, then multiply numerator times numerator and denominator times denominator. Simplify if possible.

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  • Question

    How do I multiply a fraction by a whole number?

    3 Ways to Multiply Fractions - wikiHow (25)

    Community Answer

    To multiply fractions by a whole number, you just multiply the numerator (top number) by the whole. Once you find that, divide the numerator by the denominator (bottom number), and you get a decimal version of the answer. If you don't know how to convert decimals to fractions, you can look it up on wikiHow.

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      • If you have a fraction equation that involves both multiplying and adding or subtracting fractions, follow the order of operations. Multiply before you add or subtract anything else. For example, if you have 7/13 + 5/8 * 8/9, solve for 5/8 * 8/9 first, and then add that answer to 7/13.

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      References

      1. https://youtu.be/CTKMK1ZGLuk?t=12
      2. Grace Imson, MA. Math Instructor, City College of San Francisco. Expert Interview. 1 November 2019.
      3. Mario Banuelos, PhD. Associate Professor of Mathematics. Expert Interview. 11 December 2022.
      4. https://youtu.be/CTKMK1ZGLuk?t=12
      5. Grace Imson, MA. Math Instructor, City College of San Francisco. Expert Interview. 1 November 2019.
      6. https://youtu.be/CTKMK1ZGLuk?t=42
      7. https://youtu.be/CTKMK1ZGLuk?t=61
      8. https://www.mathsisfun.com/mixed-fractions-multiply.html
      9. Grace Imson, MA. Math Instructor, City College of San Francisco. Expert Interview. 1 November 2019.

      More References (10)

      About This Article

      3 Ways to Multiply Fractions - wikiHow (41)

      Co-authored by:

      Mario Banuelos, PhD

      Associate Professor of Mathematics

      This article was co-authored by Mario Banuelos, PhD. Mario Banuelos is an Associate Professor of Mathematics at California State University, Fresno. With over eight years of teaching experience, Mario specializes in mathematical biology, optimization, statistical models for genome evolution, and data science. Mario holds a BA in Mathematics from California State University, Fresno, and a Ph.D. in Applied Mathematics from the University of California, Merced. Mario has taught at both the high school and collegiate levels. This article has been viewed 547,054 times.

      35 votes - 69%

      Co-authors: 56

      Updated: April 7, 2024

      Views:547,054

      Categories: Fractions

      Article SummaryX

      To multiply fractions, start by multiplying the numerators together, which are the numbers at the top of the fractions. For example, if you’re trying to solve 2/3 × 3/4, you’d multiply 2 by 3 and get 6. Then, multiply the denominators together, which are the numbers at the bottom of the fractions. In this example, you’d multiply 3 by 4 and get 12. Therefore, your new fraction would be 6/12. Once you've gotten your new fraction, simplify it to the lowest terms. To simplify the fraction, just divide the numerator and denominator by the largest number that can go into them evenly, also known as the largest common factor. So, in this case, since 6 is the largest number that can go into the top and bottom number, you’d divide 6 by 6 and 12 by 6 and get 1/2. If you want to learn how to simplify your fractions before multiplying them, keep reading the article!

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      3 Ways to Multiply Fractions - wikiHow (2024)

      FAQs

      What are three ways to multiply fractions? ›

      There are 3 simple steps to multiply fractions
      • Multiply the top numbers (the numerators).
      • Multiply the bottom numbers (the denominators).
      • Simplify the fraction if needed.

      How to do 3 way fraction multiplication? ›

      To multiply any 3 fractions, multiply the three numerators and then multiply the three denominators. After multiplying the numerators and denominators, write them as fractions. This will give the product of 3 fractions in fractional form.

      What are the 4 ways to multiply? ›

      There are many methods for multiplication. Here are four of those methods: repeated addition, long multiplication (traditional algorithm), grid method, and drawing lines.

      What are the 3 steps to multiply mixed numbers? ›

      Step 1: Convert all the mixed numbers in the given problem into improper fractions. Step 2: Rewrite the problem using the new improper fraction. Step 3: Multiply the numerators. Write the result as the numerator of the answer.

      What are the three forms of multiplication? ›

      There are three properties of multiplication: commutative, associative, and distributive.

      Which way do you multiply fractions? ›

      You multiply the numerators (the top numbers) together, and then multiply the denominators (the bottom numbers) together. After putting the two results together as a new fraction, you may need to simplify the fraction in order to express it in its lowest terms.

      How to multiply 3 algebraic fractions? ›

      Step 1: Multiply the numerators of the fractions together straight across the top of the fraction. This product will be the new numerator. Step 2: Multiply the denominators of the fractions together straight across the bottom of the fraction.

      What three steps should be followed when multiplying fractions? ›

      Step 1: Multiply the numerators. Step 2: Multiply the denominators. Step 3: Simplify the end result. To simplify means to make the fraction into the smallest numbers possible by finding the largest number that can divide both the numerator and denominator.

      What are the 4 steps to multiplying fractions? ›

      The correct procedure for multiplying fractions is: find a common denominator, multiply the numerators, multiply the denominators, and simplify if necessary.

      What is the easiest multiplication method? ›

      One of the best and easy multiplication tricks for large numbers is to find the tens of one of the numbers, and multiply with that quickly. Adding the remaining leftovers will be easier to calculate fully. E.g., 22 X 83 can be rewritten as (20 X 83) + (2 X 83) which gives us 1660 + 166 = 1826.

      What are 3 ways to multiply fractions? ›

      Rule 1: The first rule is to convert mixed fractions to improper fractions if any. Then, multiply the numerators of the given fractions. Rule 2: Multiply the denominators separately. Rule 3: Simplify the value obtained to its lowest term.

      What are the 3 parts of a mixed fraction? ›

      Parts of a Mixed Number

      A mixed number is formed by combining three parts: a whole number, a numerator, and a denominator. The numerator and denominator are part of the proper fraction that makes the mixed number.

      What are multiplication strategies for 3? ›

      To multiply any number by 3, double it and then add one more set of that number. To multiply any number by 4, double the number and then double that product. To multiply any number by 5, multiply it by 10 and then divide the result in half.

      What can you multiply by 3? ›

      The first 10 multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27 and 30.

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