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Finding the fraction of a number is the same as multiplying the number and the fraction. This simple method can be used for any kind of number (percent, fraction, mixed number, decimal), but is easiest with whole numbers. To solve the problem, you will need to know basic multiplication and division .
Steps
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Write out the problem. If the problem you are working with is a word problem, first you need to write out all of the numbers involved in the calculation. If you were given the numbers written out already, you can skip this step.
- For example: What is one-third of seven?
- When you see “of” written between two numbers in a word problem, think of it as meaning multiply. Thus, one-third of seven actually means one-third multiplied by seven.
- Writing out the problem gives you ( 1 / 3 ) x 7.
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Multiply the whole number by the numerator. When working with whole numbers, you will only multiply the number by the numerator (the top number) of the fraction. The denominator remains the same throughout the multiplication process. [1] X Research source
- For example: ( 1 / 3 ) x 7 = 7 / 3 .
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Divide by the denominator. Divide the product by the denominator (the bottom number) of the fraction. At this stage, the fraction might be an improper fraction , meaning that the numerator is larger than the denominator, or it will just need to be reduced . [2] X Research source
- For example: After multiplying, the fraction is 7 / 3 . Three doesn’t divide evenly into seven so you will have a remainder. Three goes into seven twice with one leftover; therefore, the final answer is the mixed number 2 1 / 3 .
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Simplify the improper fraction. An improper fraction is one where the numerator is a larger number than the denominator. Always simplify an improper fraction before writing the final answer. To simplify, divide the numerator by the denominator and write the remainder as a fraction. [3] X Research source
- For example: 10 / 3
- Divide: 10/3 = 9 remainder 1
- Write the remainder as a fraction: 1 / 3
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Write the mixed number . A mixed number contains both a whole number and a fraction. It is the simplest form of an improper fraction. To write the mixed number, simply write the whole number and the fraction that was created by the remainder. [4] X Research source
- For example: 10 / 3 , 3 goes into 10 3 times with a remainder of 1. The mixed number is 3 1 / 3 .
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Reduce a fraction to its simplest form. Once you have multiplied through, you need to reduce the fraction. You can divide by a smaller number until the fraction is completely reduced. [5] X Research source
- For example: Simplify the fraction 4 / 8 . Divide both numbers by four to simplify. The simplest form of 4 / 8 is 1 / 2 .
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EXPERT TIP
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.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.
Community Q&A
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QuestionJack has $48, he spends $18. What fraction of his money is left?DonaganTop AnswererThere is 30 left. 30 is 30/48 of 48. 30/48 = 5/8.
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QuestionIf Susan works 10 hours a day, and her boss allows her to use (1/8) of the 10 hours for lunch. How long is her lunch break?DonaganTop AnswererFind the answer with this equation: 10 x 1/8 = 10/8 = 1¼ = 1 hour and 15 minutes.
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QuestionWhat fraction represents 3 x 3/2?DonaganTop AnswererMultiply the whole number by the numerator, and keep the denominator.
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Expert Interview
Thanks for reading our article! If you’d like to learn more about fractions, check out our in-depth interview with Grace Imson, MA .
References
- ↑ http://www.bbc.co.uk/schools/gcsebitesize/maths/number/fractionsrev1.shtml
- ↑ https://www.mathsisfun.com/improper-fractions.html
- ↑ https://www.calculatorsoup.com/calculators/math/fractionssimplify.php
- ↑ https://edu.gcfglobal.org/en/fractions/comparing-and-reducing-fractions/1/
- ↑ https://www.purplemath.com/modules/fraction.htm
About This Article
Article Summary
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To find a fraction of a whole number, multiply the whole number by the numerator of the fraction. Divide the product by the denominator of the fraction, then reduce the answer to a mixed number in its simplest form. If you want to learn how to reduce the fraction into its simplest form, keep reading the article!
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