Subtracting Mixed NumbersDate: 01/23/98 at 14:24:02 From: Sean Ferguson Subject: Subtracting mixed numbers I don't really get subtracting mixed numbers. Date: 01/27/98 at 16:35:49 From: Doctor Loni Subject: Re: Subtracting mixed numbers Subtracting mixed numbers can be tough to understand at first, but once you understand how to set them up, they get easier. Let's try a couple of examples: 2 2/3 - 1 1/6 Write it down like this: 2 2/3 - 1 1/6 --------- Just as in any other subtraction problem, start at the far right of the problem. You would begin with 2/3 - 1/6. You would do this just as you would any other subtraction of fractions. First you find a common denominator (a number, preferably the smallest one, that both denominators will divide into evenly) In this case the common denominator is 6. First you change 2/3 into sixths. 2/3 = ?/6 Ask yourself, "how many times does 3 go into 6?" The answer is 2. Now take 2 times the numerator of the original fraction (in this case 2) You will get 4. So: 2/3 = 4/6 4/6 and 2/3 are equivalent fractions, which means they are equal 1/6 is already in sixths so there is no need to change it. Now your problem looks like this: 2 4/6 - 1 1/6 -------- Again starting at the right 4/6 - 1/6 = 3/6 2 4/6 - 1 1/6 -------- 1 3/6 Now move to the next number to the left and subtract 1 from 2. The answer to your problem so far is 1 3/6 However, the fraction, 3/6, is not in lowest terms. If you divide both the top and bottom of 3/6 by 3 you get 1/2. So the answer to this problem is: 1 1/2 Let's try one where you will have to borrow. 5 1/3 - 3 1/2 ----------- Starting at the right you have 1/3 - 1/2. You need to find the common denominator. In this case the least common denominator is 6. 1/3 = 2/6 1/2 = 3/6 Now you have: 5 2/6 - 3 3/6 ----------- Here we have a problem. We can't take 3/6 away from 2/3 because 3/6 is a bigger number. So just like any other subtraction problem, we have to borrow from the next column over. We cross off the 5 and write 4 because we are borrowing 1. Here comes the tricky part. We have actually borrowed 1. However, our fractions are written as parts of a whole (in this case sixths). So 1 expressed in sixths is 6/6 (remember 6/6 = 1; we are just writing it differently). When we borrow, we add what we borrowed to the next column over - just as in regular subtraction: 4 2/6 + 6/6 - 3 3/6 ---------------- Remember it's now 4 instead of 5 because we borrowed 1. 2/6 + 6/6 = 8/6, so 4 8/6 - 3 3/6 ---------- Now we can do the subtraction. 8/6 - 3/6 = 5/6 and 4 - 3 = 1 so: 4 8/6 - 3 3/6 --------- 1 5/6 If you are still having trouble or are confused about common denominators, let me know! -Doctor Loni, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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