4.6+Adding+and+Subtracting+Like+Fractions

Section 4.6 - Adding and Subtracting Like Fractions
"Like fractions" are fractions that have exactly the same denominator.

Remember that in order to add or subtract terms they must be "like terms". You can't add or subtract "unlike" terms. The same applies to fractions. In order to add or subtract fractions, they must be "like fractions." (Although that doesn't matter for multiplying or dividing.)

Think of a tray of brownies. Mmmmmm. Suppose there were 40 brownies on a tray and you took 3 of them. Ten minutes later you were back and took 2 more. It's easy to figure out how many you took altogether. 3 + 2 = 5. But if the question were asked slightly differently the same logic should be used. What fraction of the brownies did you take? Well, if a whole tray of brownies is cut into 40 pieces, the total number of brownies would be represented as 40/40. So, the math showing what you took would be represented:



There are two things going on here that are important to understand. If you kind of ignore the denominators, you can see the same math problem -- 3 + 2 = 5. The denominator of 40 doesn't change when you add (or subtract) fractions. The denominator must be the same to add or subtract fractions, and it is the same when you are done.** In multiplication you multiply both the numerators and denominators, but in addition and subtraction, you only mess with the numerators. **

The second thing, however, is that fractions might need to be reduced after adding or subtracting, so in a way that does change the denominator, or appears to.


 * Adding and Subtracting Like Fractions with Variables**

This seems a bit more complicated, but it follows those same rules: Make sure the denominators are the same, then just add or subtract the numerators. The catch here is that you can't add unlike terms, so the answer is not as "clean" as you might otherwise expect. One other important thing to notice. If you only look at the constant in the numerator, you can see that 5 is a factor of both 5 and 15. Normally you might reduce the fraction then to 1/3. However, because you can't "divide out" the same factor from all terms in the numerator (5 and 3m), you can't reduce it at all.




 * Chapter Four Practice Problems**

**Where to from here?**
4.1 Greatest Common Factor 4.2 What is a Fraction? 4.3 Equivalent Fractions 4.4 Multiplying Fractions 4.5 Dividing Fractions 4.6 Adding and Subtracting Like Fractions 4.7 Adding and Subtracting Unlike Fractions 4.8 Fraction Coefficients 4.9 Solving for X with Fractions Chapter Four Review Chapter Four Homework