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How to Add Fractions
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Prime numbers are numbers that can only be divided by
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Hi, I'm Zoya Popova for About.com, and today I'm going to show you how to add fractions.When fractions have the same denominator, addition is easy. Just add up the nominators, and your denominator stays the same. So,1/5+2/5=(1+2)/5=3/5. But if you have to add fractions that have different denominators, such as 1/5+1/7, you first have to bring them to a common denominator. We take each of the fractions and multipy 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.When we perform these multiplications, you fractions now have common denominator, 35, so we can simply add the numerators:1/5+1/7=1/5*7/7+1/7*5/5=7/35+5/35=(7+5)/35=12/35.In this case, we acted intuitively. But for tougher cases, you should follow the step-by-step process of finding the least common denominator, or the LCD. Let's say the problem is 11/15+5/12. First, write down your denominators: 15 and 12.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 15. What prime numbers can it be divided into? Always start with the lowest prime number. So, “Is 18 divisible by 2?” No. Moving on. Is 15 divisible by 3? Yes. So 3 is our first prime factor of 15. When we divide 15 by 3, the result is 5. 5 is itself a prime number, and when we reach a prime number as a result of our division, that means we're done with our factorization. The prime factors for 15 are 3 and 5:15=3*5.For 12, the prime factorization is 12=2*2*3. Our next step is to write down our prime factorizations in a table, making sure that the prime factors shared by both of your numbers are written down in the same column:15: 3 511: 2 2 3 To figure out your LCD, multiply all of the prime factors listed in the table, making sure to include shared factors only once: 15: 3 511: 2 2 3 ------------------- 2 2 3 5LCD: 2*2*3*5 =60. When you know your least common denominator, all that's left to do is figure out is what numbers our fractions must be multiplied by to get the initial denominators to 60.
How many times 15 is 60?60/15=4,so our first fraction, 11/15, must be multiplied by 4/4. How many times 12 is 60?60/12=5,so our second fraction, 5/12, must be multiplied by 5/5. Our numerators are now 44 and 25, and, with a common denominator, we can now freely add them up:11/15+5/12=11/15*4/4+5/12*5/5=44/60+25/60=(44+25)/60=69/60.If we simplify this fraction, we will get to the final answer of 1 and 3/20.
This is how you add fractions, and more information please visit us on the web at About.com.
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