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If you see this message, it means were having trouble loading external resources on our site. If you are behind a web filter, make sure the *.kastatic.org and *.kasandbox.org domains are unblocked. When subtracting fractions, you must first check that the denominators are equal. Subtracting fractions with the same denominator Fractions with the same denominator are called like fractions. To subtract fractions with the same denominator, subtract the numerator and write the difference in the denominator. 5 7 - 4 7 = 1 7 Example: Find 4 5 - 2 5 . Since the denominators are the same, subtract the numerator. = 4 - 2 5 = 2 5 You can get a result that is not the lowest even if the fractions you added and subtracted were equal. In this case, you need to shorten the fraction. 8 9 - 2 9 = 6 9 = 6 3 9 3 = 2 3 Subtracting Fractions with Different Denominators If the denominators do not match, you must use equivalent fractions that have a common denominator. To do this, you need to find the least common multiple (LCM) of the two denominators. To subtract fractions with different denominators, rename the fractions with a common denominator. Then subtract and simplify. Suppose you want to add: 6 7 - 2 3 The LCM of 3 and 11 equals 33 . So we need to find fractions equal to 6 7 and 2 3 that have 21 in the denominator. Multiply the numerator and denominator of the number 6 7 3 and multiply the numerator and denominator by 2 3 7 . 6 x 3 7 x 3 - 2 x 7 3 x 7 = 18 21 - 14 21 Now we have the same denominators and can subtract as above. = 4 21 You can read adding fractions first. To subtract fractions, you need to do 3 simple steps. Step 1: Make sure the bottom numbers (denominators) match. Step 2. Subtract the highest numbers (numerators). Put the answer above the same denominator. Step 3. Simplify the fraction (if necessary). Step 1. The numbers below already match. Go straight into stepStep 2: Subtract the larger numbers and give the result the same denominator: 3 4 - 1 4 = 3 - 1 4 = 2 4 Step 3: Simplify the fraction: 2 4 = 1 2 (See Equal Fractions if youre not sure about the last step .) Step 1. The numbers below are different. See how the pieces are different sizes? We have to make them equal before continuing because we cant subtract them like this: 1 2 - 1 6 = ? To make the bottom numbers equal, multiply the top and bottom numbers of the first part (12) by 3, like this: x 3 x 3 And now our question looks like this: 3 6 - 1 6 The bottom numbers ( Denominators ) are the same, so you can go to the 2nd act. Step 2. Subtract the larger numbers and put the result over the same denominator: 3 6 - 1 6 = 3 - 1 6 = 2 6 In the picture it looks like this: 3 6 - 1 6 = 2 6 Step 3. Simplify one Fraction: 2 6 = 1 3 with pen and paper Heres how to do it with pen and paper (press the play button): Try subtracting the fractions shown. Subtraction of mixed fractions I have a special page for adding and subtracting mixed fractions. In the previous example, making the common denominators equal was easy, but it can be tricky... so you may need to use either the common denominator method or the least common denominator method. Both work, use whichever you prefer! Example: cookies. You want to sell cupcakes at the market: you get paid 2 5 of total sales, but you have to pay 1 4 of total sales per stall. How much do they get? We need to subtract 1 4 from 2 5 2 5 - 1 4 = ? ? Reduce the smaller numbers (denominators) first. Multiply the top and bottom of 25 by 4: 2 x 4 5 x 4 - 1 4 = ? ? And multiply the top and bottom 14 by 5: 2 x 4 5 x 4 - 1 x 5 4 x 5 = ? ? Now lets calculate: 8 20 - 5 20 = 8 - 5 20 = 3 20 Answer: You should keep 3 20 of the total sales. Copyright ©ï¸ 2020 MathsIsFun.com Subtracting fractions, especially fractions with different denominators, can be tricky at first. However, once you receiveAs long as you follow a few basic rules, its pretty easy. First, we need to understand the composition of a fraction. Here the two parts - the numerator and the denominator - are separated by a dividing line. The denominator is the bottom number. This tells us how many equal parts the whole was divided into. The numerator is the largest number that tells you how many parts of the whole. To effectively subtract one fraction from another, we must make sure that the whole we are dealing with is divided into the same number of equal parts in both cases, that is, that the denominators are the same. There are some quick tricks you can use when subtracting fractions with different denominators. We will explain the traditional method below as you should use it 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). Step 1. Find the lowest common denominator. The least common denominator (LCD) is the least common multiple of the two denominators you are working with. For example, if we are asked to subtract 23 from 26, we know that 6 is a multiple of 3, so 6 is our LCD. Step 2: Find the equivalent fraction Once you have found the LCD, you should keep the fractions the same. So if you change the denominator, you must apply the same change to the numerator. To convert the denominator to 6 in the example above, we multiply 3 by 2. To get the fraction equal to the value, we also need to multiply 2 (the numerator) by 2. This gives the equivalent fraction 46. Repeat this process for the second fraction. In our example, we already have a denominator of 6, so no changes are required. Now we have the corrected equation 46 - 26. Step 3: Subtract New Counters The next step is easy: just subtract

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