Adding and Subtracting Fractions
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 (“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 “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, rather 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 “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
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 (“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 “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, rather 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 “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