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How to Subtract Fractions
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When fractions have the same denominator, subtraction is easy. You just
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Hi, I'm Zoya Popova for About.com, and today I'm going to show you how to subtract fractions.When fractions have the same denominator, subtraction is easy. You just subtract the numerators, and keep the denominators the same. So,1/7-5/7=(1-5)/7=-4/7. However, if the fractions have different denominators, such as 1/5-1/7, we first have to bring them to a common denominator. We do that by taking each of the fractions and multiplying the top and the bottom by the same number. 1/5 multiplied by 7/7 is the same value as 1/5. And 1/7 multiplied by 5/5 is the same value as 1/7. Now, with a common denominator, we can simply subtract the numerators:1/5-1/7=1/5*7/7-1/7*5/5=7/35-5/35=(7-5)/35=2/35.In this case, we acted intuitively. But for tougher cases, you should use the step-by-step process of finding the least common denominator, or the LCD. Let's say the problem is 7/18-3/14.First, write down your denominators: 18 and 14.Now, you must present each of these numbers as a product of prime numbers. As a reminder, prime numbers are numbers that can only be divided by themselves and by 1: 2, 3, 5, 7, 11, 13... Let's start with 18. What prime numbers can it be divided into? Always start with the lowest prime number. So, “Is 18 divisible by 2?” Yes. 2 is the first of our prime factors. 18 divided by 2 is 9. 9 is not divisible by 2, but is divisible by 3. 3 is our second prime factor. 9 divided by 3 is 3. And when the result of our division is itself a prime number, that means we've reached our final prime factor. So, for 18, prime factorization is 18=2*3*3.For 14, using the same process, we find that 14=2*7.The next step is to write down your prime factorizations in a table, making sure that the prime factors shared by both of your numbers are written down in the same column:18: 2 3 314: 2 7To figure out your LCD, multiply all of the prime factors listed in the table, making sure to include shared factors only once: 18: 2 3 314: 2 7--------------- 2 3 3 7For us, the LCD is 2*3*3*7 =126. When you know your least common denominator, all that's left to do is figure out what numbers the tops and bottoms of your fractions must be multiplied by to get the initial denominators to 126.
How many times 18 is 126?126/18=7So our first fraction, 7/18, must be multiplied by 7/7. How many times 14 is 126?126/14=9So our second fraction, 3/14, must be multiplied by 9/9. We subtract the resulting numerators, 49 and 27, and keep the denominator the same:7/18-3/14=7/18*7/7-3/14*9/9=49/126-27/126=(49-27)/126=22/126=11/63.
This is how you subtract fractions. For more information please visit us on the web at About.com.
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