How To Subtract Fractions With Different Denominators Step By Step

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This article was co-written by copywriter Jessica Gibson. Jessica Gibson has been a contributing writer and editor since 2014. After completing a year of art studies at Emily Carr University in Vancouver, she graduated from Columbia College with a BA in History. Jessica also completed a Masters in History from the University of Oregon in 2013.

How To Subtract Fractions With Different Denominators Step By Step

Subtracting mixed numbers can seem challenging at first, but doing some simple conversions will make it easier. Once you’ve identified the parts of a mixed number, decide whether you want to convert the mixed numbers to improper fractions, or whether you want to subtract whole numbers and fractions separately. Make the denominators of the fractions equal, then subtract the numerators.

Ways To Add And Subtract Fractions

When subtracting mixed numbers, multiply the whole number by the denominator and add the numerator to get an improper fraction. If the improper fractions have different denominators, find the lowest common denominator and convert the fractions. When the denominators are the same, subtract the numerators and convert the result to a mixed number to get your final answer. If you want to learn more, how to subtract whole numbers and fractions separately, keep reading! We use cookies to make it great. By using our website, you accept our cookie policy.Cookie settings

This article was co-written by David Jia and copywriter Jessica Gibson. David Jia is an academic tutor and founder of LA Math Tutoring, a private tutoring company based in Los Angeles, California. With over 10 years of teaching experience, David works with students of all ages and grades in a variety of subjects, as well as counseling for college admissions and SAT, ACT, ISEE test preparation and more. After earning a perfect score of 800 in math and a score of 690 in English on the SAT, David received the Dickinson Scholarship from the University of Miami, where he majored in Business Administration. Additionally, David has worked as an online video instructor for textbook companies such as Larson Texts, Big Ideas Learning and Big Ideas Math.

How To Subtract Fractions From Whole Numbers: 10 Steps

Subtracting fractions can seem a little confusing at first, but with basic multiplication and division, you’ll be ready for simple subtraction. If the fractions are suitable, check that the denominators are the same before subtracting the numerators. If fractions are mixed and you have whole numbers, convert them to improper fractions. You’ll also need to make sure the denominators are the same before subtracting the numerators.

To subtract fractions, first check that the denominators are the same. If they are not, find the least common multiple of the 2 denominators. Then multiply each denominator to equal the least common multiple. Then multiply the numerator by the same number you multiplied the denominator by. Finally, subtract the numerators and leave the denominator as the least common multiple. To learn how to subtract mixed numbers, scroll down! Subtracting fractions, especially those with different denominators, can seem complex at first. However, once you familiarize yourself with a few basic rules, it’s pretty easy.

Adding And Subtracting Fractions With Different Denominators

First, we need to understand the composition of a fraction. Here there are two parts, the numerator and the denominator, separated by a dividing line.

The denominator is the bottom figure. This tells us how many equal parts a whole has been divided into. The numerator is the top figure and represents how many parts of the whole are present.

To successfully remove one fraction from the other, we must ensure that the whole we are dealing with in both cases is divided into the same number of equal parts, that is, that the denominators are equal.

How To Add Fractions With Different Denominators

There are some quick tricks you can use when subtracting fractions with unlike denominators. Below we explain the traditional method as this is what you will need to apply when you are asked to show your work in an official exam.

The same rules apply whether you are working with proper fractions (where the numerator is less than the denominator) or improper fractions (where the numerator is greater than the denominator).

$How To Subtract Fractions With Different Denominators Step By Step$

4 easy steps on how to subtract fractions with different denominators: Step 1: Find the lowest common denominator

Adding Fractions With Unlike Denominators Introduction (video)

For example, if we’re asked to subtract 2/3 from 2/6, we know that 6 is a multiple of 3, so 6 is our LCD.

Once you find the LCD screen, you must keep the same value of your fractions. So when changing the denominator you need to apply the same change to the numerator.

Using the example above, to replace the denominator with 6, we multiply 3 by 2. To keep a fraction equal in value, we must also multiply 2 (the numerator) by 2. This gives us a fraction equivalent to 4/6. 🇧🇷

Awesome Activities For Adding And Subtracting Fractions With Like Denominators

Repeat this process for the second fraction as well. In the case of our example, we already have the denominator 6, so no changes are needed.

The next step is easy: just subtract the numerators you have in your new equation. In this case, 4 – 2 = 2.

The last step is to simplify the fraction if possible. To do this, you’ll need to find the greatest common factor that both parts of the fraction share and divide by that.

Learn How To Add Fractions

In the case of 2/6, the greatest common factor is 2. Since 2 ÷ 2 = 1 and 6 ÷ 2 = 3, our simplified fraction is 1/3.

Below you will find two example questions that ask you to reduce fractions with different denominators. The former is expressed as a standard equation, the latter as a more complex word problem.

Start by finding the LCD screen. In this example it’s not that easy, so it might be useful to write multiples of the current largest denominator to help you: 25, 50, 75, 100, 125, 150…

How To Multiply Fractions In Four Easy Steps

Now we can see that the first multiple of 25 divisible by 6 is 150, so this is our LCD.

6 x 25 = 150, so we need to use the same value to multiply the numerator, giving 5 x 25 = 125. So our first equivalent fraction is 125/150.

$How To Subtract Fractions With Different Denominators Step By Step$

Emma is training for a marathon and has set herself a distance goal to reach by the end of the week. On Monday he runs 7/15 of the distance. On Wednesday he runs 4/5 of the distance.

Adding Fractions With Unlike Denominators.

To solve this problem, we need to subtract the distance Emma ran on Monday from the distance she ran on Wednesday, so we would write our equation as: 4/5 – 7/15.

Then we find our LCD, which we can see is 15. We find the equivalent of our first fraction by multiplying both sides by the same value: 5 x 3 = 15 and 4 x 3 = 12.

Now we can subtract our numerators (12 – 7 = 5) and put our answer over the denominator: 5/15.

How To Multiply Fractions

Finally, we identify the greatest common divisor of 5 and 15 as 5 and divide the two parts of the fraction for simplicity: 5 ÷ 5 = 1 and 15 ÷ 5 = 3.

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