Adding and Subtracting Fractions - Free Essay Example

Adding subtracting fractions 1. Where in life is this useful? a) Cooking: [pic] b) Measurements (construction, remodeling, etc): [pic] c) Time: [pic] d) Money: [pic] 2. Fractions with the same (â€Å"common†) denominators Example: (without converting back forth from mixed numbers): [pic] [pic] 3. Fractions with different denominators In order to add (or subtract) fractions with different denominators (as a reminder, that’s the bottom number), you’ll need to convert them to have the same denominators. This is one place where we get to use the â€Å"least common multiple† that we talked about a while ago. Let’s start with money, because we all do that conversion frequently, and without thinking about what we’re doing. If we add a quarter a nickel, we know off the top of our head that we have 30 cents, or 30/100 of a dollar. But what is the math that we’re doing? [pic] First, we need to convert to a common denominator. For money, ra ther than worrying about the lowest common denominator, we automatically convert to hundredths. We do that by multiplying by one in the form of a fraction: [pic]. We can do this because multiplying a number by 1 does not change its value. So, we now have: [pic]. All we’ve done is converted the quarter to 25 cents and the nickel to 5 cents. From this point, we can add them: [pic]. We don’t give much thought to all these steps that we go through, but as soon as it is phrased as â€Å"adding fractions†, it seems to get much harder! Now, let’s try a more abstract case. For no particular reason, we need to add 1/3 to 1/4. The LCM for 3 4 is 12 (if you get stuck finding the LCM, and don’t mind dealing with larger numbers, you can multiply the denominators and reduce your answer at the end). So: [pic]. With a little practice, you’ll be able to skip writing the second step the next to last step. Let’s work through one more example pro blem, where the lowest common denominator isn’t simply found my multiplying the numbers together: [pic]. The LCM of 3, 6 2 is 6, so we want to convert everything to sixths: [pic] [pic]. That can be reduced to [pic] or [pic]