Adding and Subtracting FractionsDate: 10/25/1999 at 08:45:58 From: Kevin Balandin Subject: Fractions I am in grade 7 and (can you believe it?) I can't add or subtract fractions! Please help me out. Kevin Date: 10/25/1999 at 15:44:27 From: Doctor Rick Subject: Re: Fractions Hi, Kevin. Let's just go over some basics; if you have a problem with a particular part of this process, write again and we can work through it. Start with money. It doesn't make much sense to add quarters and dimes, does it? If I have 2 quarters and 3 dimes, then I have 5 coins, but this doesn't tell you anything about how much money I have. What you could do instead is to convert the quarters and dimes to cents: 2 quarters + 3 dimes = 2 * 25 cents + 3 * 10 cents = 50 cents + 30 cents = 80 cents Another way would be to convert the quarters and dimes into nickels. Each quarter becomes 5 nickels, and each dime becomes 2 nickels. So 2 quarters + 3 dimes = 2*5 nickels + 3*2 dimes = 10 nickels + 6 nickels = 16 nickels I can rewrite the problem as a sum of fractions, because a quarter is 1/4 dollar, a dime is 1/10 dollar, and a nickel is 1/20 dollar. 2 3 16 --- + --- = -- 4 10 20 Before you can add two fractions, you need to rewrite one or both fractions so they have the same denominator. This is the same thing as converting different coins into the same kind of coin. You have learned about equivalent fractions, right? If you multiply the numerator and denominator of a fraction by the same number, you get another name for the same fraction - an equivalent fraction. 3 3*2 6 --- = ---- = ---- 10 10*2 20 If you want to add, say, 3/10 and 5/6, you need to find a pair of fractions that are equivalent to these but that have the same denominator. Let's write out some equivalent fractions: 3/10 = 6/20 = 9/30 = 12/40 = 15/50 = ... 5/6 = 10/12 = 15/18 = 20/24 = 25/30 = ... You can see a pair of fractions that have the same denominator: 9/30 and 25/30. Let's add them: 3 5 9 25 34 ---- + --- = ---- + ---- = ---- 10 6 30 30 30 Now we can simplify the answer, by reducing it to lowest terms. Both 34 and 30 are divisible by 2, so a fraction equivalent to 34/30 is 17/15 (dividing the numerator and denominator by 2). Finally, because 17 is greater than 15, this is an improper fraction, so we can convert it into a mixed number: 17 15 2 2 -- = -- + -- = 1 -- 15 15 15 15 Subtraction works the same way. Here is an example: 5 3 25 9 16 8 --- - --- = -- - -- = -- = -- 6 10 30 30 30 15 You can find some further help with fractions in the links at the bottom of our Dr. Math FAQ on "Fractions, Decimals, Percentages": http://mathforum.org/dr.math/faq/faq.fractions.html In particular, you can find techniques for finding the smallest denominator that will work -- the Lowest Common Denominator (LCD), also called the Least Common Multiple (LCM). That's the trickiest part of adding fractions. You will find more help with this if you go to our Dr. Math Search page, http://mathforum.org/mathgrepform.html and search for LCD LCM selecting "At least one of your keywords". - Doctor Rick, The Math Forum http://mathforum.org/dr.math/ |
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