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This article was co-written by David Jia. David Jia is a tutoring teacher and founder of LA Math Tutoring, a private tutoring facility based in Los Angeles, California. With over 10 years of teaching experience, David teaches a wide variety of subjects to students of all ages and grades, as well as college admissions counseling and prep for SAT, ACT, ISEE, etc. scoring 800 in math and 690 in English on the SAT, David was awarded a Dickinson Scholarship to the University of Miami, where he graduated with a bachelor’s degree in business administration. Additionally, David has worked as an instructor in online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math.

This article has been viewed 3,561 times.

Fractional subtraction can look a bit confusing at first, but with some basic multiplication and division you should get simple subtraction. If the fractions are less than 1, make sure their denominators are the same before subtracting the numerators. If there are mixed numbers and whole numbers, convert them to fractions greater than 1. You also need to make sure the denominators are the same before subtracting the numerators.

## Steps

### Find the least common multiple and subtract

**List multiples of the denominator**

**if necessary.**If the denominators of the fractions are different, you need to make them the same. List the multiples of each denominator so you can find the common multiple of both denominators. For example, if you are doing the calculation 1/4 – 1/5, list all the multiples of 4 and 5 and you will find 20.

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- Since multiples of 4 include 4, 8, 12, 16, 20, and multiples of 5 include 5, 10, 15, and 20, 20 is their least common multiple.
- If the denominators are already the same, you can skip to subtract the numerators.

**Multiply both the numerator and the denominator to get the same denominator.**After finding the least common multiple for dissimilar fractions, multiply the fractions so that their denominators become the least common multiple.

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- For example, multiply 1/4 by 5 to get a denominator of 20. You also need to multiply the numerator by 5, so 1/4 becomes 5/20.

**Generate equivalent fractions for all fractions in the equation.**Remember that if you adjust 1 fraction in the problem, you need to adjust all the fractions so that they are equivalent.

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- For example, if you adjusted 1/4 to become 5/20, multiply 1/5 by 4 to get 4/20. The original 1/4 – 1/5 problem becomes 5/20 – 4/20.

**Subtract the numerators and keep the denominators the same.**If the original problem had the same denominator or you created equivalent fractions with the same denominator, subtract the numerators. Write the result and then write the denominator below.

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- Remember not to subtract the denominators.
- For example, 5/20 – 4/20 = 1/20.

**Shorten the results.**After you have the answer, check to see if you can shorten it further. Find the greatest common divisor of the numerator and denominator and divide both the numerator and the denominator by this number. For example, if your answer is 24/32, then the greatest common divisor is 8. Divide both the numerator and the denominator by 8 to get 3/4.

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- Depending on the result, you may not be able to further shorten it. For example, 1/20 cannot be reduced any further.

### Subtract mixed numbers

**Convert mixed numbers to fractions greater than 1.**Mixed numbers are numbers that include whole numbers and fractions. To make subtraction easier, convert all mixed numbers to fractions. This means that the numerator will be larger than the denominator.

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- For example, 2 3/4 – 1 1/7 would be 11/4 – 8/7.

**Find a common denominator if necessary.**Find the least common multiple of both denominators to find the same denominator for fractions. For example, if you are doing the calculation 11/4 – 8/7, list all the multiples of 4 and 7, you will get 28.

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- Since multiples of 4 include 4, 8, 12, 16, 20, 24, 28 and multiples of 7 include 7, 14, 21, and 28, then 28 is their least common multiple.

**Make fractions equal if you have to change the denominator.**You need to convert the denominator to the least common multiple. To do this, multiply whole fractions.

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- For example, for the denominator of 11/4 to become 28, you need to multiply the whole fraction by 7. The fraction becomes 77/28.

**Adjust all the fractions in the problem to their equivalent fractions.**If you changed the denominator of 1 of the fractions in the problem, you need to adjust the other fractions so that their proportions remain the same as the original problem.

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- For example, if you adjusted 11/4 to 77/28, multiply 8/7 by 4 to get 32/28. The problem 11/4 – 8/7 becomes 77/28 – 32/28.

**Subtract the numerators and keep the denominator.**If the denominators are the same from the start or you’ve converted to equivalent fractions, you can subtract the numerators too. Write the result and place it on top of the denominator. Remember not to subtract the denominator.

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- For example, 77/28 – 32/28 = 45/28.

**Shorten the results found.**You need to convert the result to a mixed number. Let’s start by dividing the numerator by the denominator to get an integer. Then write the rest out. This will be the numerator. Put the numerator above the denominator. Simplify fractions if possible.

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- For example, 45/28 becomes 1 17/28 because 45 divided by 28 gives 1 remainder 17.

## Advice

- If you want, you can calculate mixed numbers without having to convert to fractions greater than 1. Subtract the whole numbers and then subtract the numerator if the fractions have the same denominator.

This article was co-written by David Jia. David Jia is a tutoring teacher and founder of LA Math Tutoring, a private tutoring facility based in Los Angeles, California. With over 10 years of teaching experience, David teaches a wide variety of subjects to students of all ages and grades, as well as college admissions counseling and prep for SAT, ACT, ISEE, etc. scoring 800 in math and 690 in English on the SAT, David was awarded a Dickinson Scholarship to the University of Miami, where he graduated with a bachelor’s degree in business administration. Additionally, David has worked as an instructor in online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math.

This article has been viewed 3,561 times.

Fractional subtraction can look a bit confusing at first, but with some basic multiplication and division you should get simple subtraction. If the fractions are less than 1, make sure their denominators are the same before subtracting the numerators. If there are mixed numbers and whole numbers, convert them to fractions greater than 1. You also need to make sure the denominators are the same before subtracting the numerators.

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