Ways of Adding FractionsDate: 03/19/99 at 23:53:21 From: demarie Subject: Fractions If you need to calculate 1/3 + 1/6, what do you do since the denominators are different? Do you add the denominators? Date: 03/20/99 at 09:24:13 From: Doctor Derrel Subject: Re: Fractions Remember that a fraction is composed of three things: The first is the whole thing, also called the unit or the one. It might be the distance from 0 to 1 on the number line. It might be a whole square. It might be the kind of one cup measurement you use in cooking. The second is how many equal pieces the whole thing is divided into. The number of equal pieces is the denominator. If you have a measuring cup that you would use for flour, it holds one cup exactly. (This is the type of measuring cup that you fill so the flour is heaped up, and then you scrape off the stuff that is above the cup.) Some of these cups are divided into four equal parts by lines that are drawn on the inside or outside. Cups like these are divided into fourths, so the denominator is 4. You might get one from your kitchen and see how many parts it is divided into. The third thing is how many of those equal pieces you are interested in. That is the numerator. If you are interested in three of the four parts in the cup, you would be interested in 3/4 of the cup. Now, it is possible for the numerator to be larger than the denominator. This happens when you are interested in more pieces than are in the whole thing. For example, a pancake recipe might call for 3/2 cups of flour. (But the cookbook would probably write it as 1 1/2 cups; 3/2 is what is called an "improper fraction," while 1 1/2 cups is what is called a "mixed number.") So, does it make sense to add the denominator? Let me suggest something to you. Go into your kitchen and get all of the measuring cups you can find that have fractions marked on them, like 1/3 or 1/4 or 1/2. Next, write a fraction equation, like 1/4 + 1/2. Solve that by putting a quarter cup (1/4) of water in a one-cup measure and then pouring it in a glass, and then getting a half cup (1/2) of water and pouring that in the same glass. Finally, pour the water in the glass back into the measuring cup to see what you get. Now make a table on paper and write down several equations and the answers you get. Some of these might be kind of hard, so work on this with a friend. Put these equations in a table in this order and figure out how much the answer is. Then, look for patterns. 1/4 cup of water plus 1/4 cup of water = ?/? cup of water 1/4 cup of water plus 2/4 cup of water = ?/? cup of water 1/4 cup of water plus 3/4 cup of water = ?/? cup of water 1/4 cup of water plus 4/4 cup of water = ?/? cup of water 1/4 cup of water plus 1/3 cup of water = ?/? cup of water 1/4 cup of water plus 2/3 cup of water = ?/? cup of water 1/4 cup of water plus 3/3 cup of water = ?/? cup of water 1/4 cup of water plus 1/2 cup of water = ?/? cup of water 1/4 cup of water plus 2/2 cup of water = ?/? cup of water 1/3 cup of water plus 1/3 cup of water = ?/? cup of water 1/3 cup of water plus 2/3 cup of water = ?/? cup of water 1/3 cup of water plus 3/3 cup of water = ?/? cup of water 1/3 cup of water plus 1/2 cup of water = ?/? cup of water 1/3 cup of water plus 2/2 cup of water = ?/? cup of water If you do not want to play with water, take strips of paper all the same length and fold separate strips into 2 parts, 3 parts, 4 parts, 5 parts, 6 parts, 8 parts, 9 parts, 10 parts, or 12 parts. Make the parts as equal as you can. You should have 9 strips, each representing one type of fraction. Draw lines in the folds so that it is easy to see each of the equal pieces that makes up the whole fraction strip. Write on each strip what it is: for example, halves, thirds, fourths, fifths, sixths, eighths, nineths, tenths, or twelfths. Then, try adding various fractions by lining the strips up side by side. For example, 1/4 + 1/2 would look like: +---------+---------+---------+---------+ ||||||||||| 1/4 | | | +---------+---------+---------+---------+ +-------------------+-------------------+ ||||||||||||||||||||| 1/2 | +-------------------+-------------------+ You can see from the fraction strips that 1/4 + 1/2 is 3/4. So, rather than trying to figure out how to add the fractions just by looking at the numbers, use your fraction strips or draw little pictures to help you. - Doctor Derrel, The Math Forum http://mathforum.org/dr.math/ |
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