Adding Fractions

The key aspect to remember when you are adding or subtracting fractions is to understand that you need to have the same size pieces before you can do any computations.  Finding a common denominator is creating equal size pieces.  Without breaking your pieces (denominators) into equal sizes you are unable to compute.  Notice that finding a common denominator is the same as finding common multiples.  See the videos from www.khanacadeny.org



When adding mixed numbers you do not have to convert to improper fractions.  (I notice many students doing this and it will work but it complicates your problem and leaves you open to more errors.)  Remember the commutative property allows you to reorganize your addends in any order.  You will see this in the video below.  Therefore you can add your whole numbers and your fractions separately.  Keep in mind you still need to have the same size pieces.




Part of your assessment will be to determine what operation to use when solving word problems.  Remember we developed many examples of word phrases that give you clues.  But it is not wise to rely on memorizing them to solve all word problems.  Some word problems will not fall into any of the categories we discussed; therefore, you need to make sense of the problem.  One strategy is to substitute the mixed numbers with easy whole numbers.  This will help you determine whether or not your approach is making sense.

Writing Equations Key

WRITING EQUATIONS KEY_001

Number Properties & Algebraic Expressions Key

NUMBER PROPERTIES _ ALGE_001

Number Properties & Aglebraic Expressions

Number Properties and Algebraic Expressions _Test Review Longer Version_

Combining Like Terms

Here are a few videos from Khan Academy. You will need to describe the number of terms, identify the coefficients, and name the like terms in a chart.  So you need to remember to add the opposite and complete any distribution BEFORE you complete the chart (see your pre-test)




This video may help you understand the importances of distribution.

One more...

Adding Integers

Remember in class we talked about "adding the opposite" whenever you see a subtraction sign.  We called it "add op."  For example, instead of solving the problem 32-78, we should look at it as 32 + (-78) or the problem 16 - (-32) as 16 + 32.  The reason why this works has to do with the direction you are going on a number line.  Subtracting (-2) means you are going to move two places to the right on the number line which is the same as adding positive 2.

The reason I suggest "add op" when you see subtraction because of two primary reasons.

1. When the work becomes more complicated with variables and various grouping symbols and you are expected to simpliy or solve, it becomes really easy to "lose the sign" meaning you have forgetten to include a negative sign as you are solving the problem.  "Add op" helps you to prevent this common error.
2. "Add op" allows you to make your problem/expression into all addition.  When you have all addition you can use the communitive and associative properties to group the work in ways that save time and allow you to do some mental math - essentially making the computation easier.

So you only have to worry about adding integers of the same sign or integers of opposite signs.  Adding integers of the same sign is simple if you think about positive and negative counters.  For example (-12) + (-13) can be viewed as 12 negative counters plus 13 negative counters, so when you add all the negative counters you will have 25 negative counters or (-25).  

So we can create a rule for adding integers of the same sign. RULE: Adding integers of the same sign will result in the sum with the sign of the addends. 3+4=7 OR (-3) + (-4) = (-7)

Adding integers with opposite signs becomes a little trickier.  Below are two videos that might help you understand. First is a video using a chip model.  The second video is from Khan Academy using a number line.

The second rule we can create then is RULE: When adding integers of opposite signs, subtract the absolute value of the addends (the numbers you are adding).  Give the difference the sign of the larger absolute value. I like to think of it as, "Do I have more negatives or more positives in my problem? If I have more negatives, my answer is negative.  If I have more positives, my answer is positive."

Answers to Review

If you were given a review packet in period 5/6.  The answers or given below. Answers to Packet beginning with Review 81