- (5 min) Mental Math
- Take 50% of 40, multiply by 2 [40]
- What is 5/8 - 1/2? [1/8]
- Take 1/3 of 900 and add 45 [345]
- Take 100% of 80 and divide by 4 [20]
- What is 150% of 60? [90]
- Take 1/2 of 1/2 of 100 [25]

- (5 min) Rules for simplifying

In algebra, we treat variables just like we treat units of anything else. We can add and subtract variables (letters) having the same power (exponent).If we have: 2 apples and 3 bananas and we add: 3 apples and 5 bananas ---------------------- Then we have: 5 apples and 8 bananas It works with letters: 2 a + 3 b 3 a + 5 b ----------- 5 a + 8 b

Can you see that this is the same as: 2a + 3b + 3a + 5b = 5a + 8b ?

You cannot add or subtract different letters from each other, anymore than you can add to or subtract apples from bananas.3 apples + 4 bananas 5 apples + 6 cherries --------------------------------- 8 apples + 4 bananas + 6 cherries with letters: 3 a + 4 b 5 a + 6 c ---------------- 8 a + 4 b + 6 c

We also write it like this: 3a + 4b + 5a + 6c = 8a + 4b + 6c

Now suppose we have two variables, T and O which are multiplied together. TO is different from T and different from O and cannot be combined with either. Pretend T stands for tangerine and O stands for orange and TO stands for the fruit you get when you crossbreed a tangerine with an orange: the tangelo. We cannot combine tangelos with tangerines or with oranges. When we add them to a bowl of fruit, they are still tangelos.2 tangerines + 2 oranges + 2 tangelos 2 T + 2 O + 2 TO + 3 tangerines + 4 oranges + 5 tangelos + 3 T + 4 O + 5 TO ------------------------------------- ---------------- 5 tangerines + 6 oranges + 7 tangelos 5 T + 6 O + 7 TO

There's one more thing you need to know. If a variable is raised to a power by multiplying by itself, then it becomes a different animal and cannot be added to or subtracted from the ordinary variable.

X + X^{2}+ X^{3}+ 2X + 3X^{2}+ 4X^{3}= 3X + 4X^{2}+ 5X^{3}

Find the X's and add them up. Next find the X^{2}and add them up. Finally, add the X^{3}s. Think of X as a line segment, X^{2}as a two-dimensional square and X^{3}as a three dimensional cube (which they are). You can probably agree that you can't add lines and squares and you can't add squares and cubes--it just won't work! The problem above basically says:

1 line + 1 square + 1 cube + 2 lines + 3 squares + 4 cubes

= 3 lines + 4 squares + 5 cubes

- (Remainder of class) In-class exercise

- Hand out homework as students successfully complete the in-class exercise.