Anabelle's Algebra Post

Algebra- writing mathematical phrases using letters to represent numbers

Variable- a letter that represents a number in an algebra equation or expression

Constant- integer in an algebra expression or equation

Equation- only has one answer and has an equal sign

Expression- has a pattern, many answers
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Adding and Subtracting

Whether we are adding, subtracting, multiplying, or dividing we start off by isolating the variable.

Let's start off with an addition problem.

v+8=26

How we isolate the variable is to make a zero pair to cancel out the constant. Try not to think of +8 as add eight, but instead think of it as positive eight. To cancel a positive eight we need a negative eight.



Remember, what we do to one side, we do to the other side.


Then what we have left is the v on one side and 18 on the other.

The same rules apply for a subtraction problem, but instead we cancel the constant with a positive integer.

The only thing left to do is verify to check.

Plug in the number in place of the letter.

Then show equality.


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Multiplying and Dividing

10n=40

To be able to isolate the variable of a multiplication problem we will divide and do the same to the other side.


Next, verify to check.


x/2= 5

Isolate variable.
Cancel using opposite.

Then, verify to check.




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Integer Tiles

Now, we will solve these problems using integer tiles.



*NEVER USE ALGEBRA TILES TO VERIFY TO CHECK

x+2=3

Start by changing the problem to what it would look like using integer chips.


Using the same concept we'll cancel the constant using zero pairs. In the case we cancel two +1 tiles using two -1 tiles. With what's left is how much the x tile is worth.


x2=6

1. Zero pair
2.Simplify
3.Answer


-2x=4
1. Zero pair
2.Simplify

We need to switch the final answer around by multiplying -1 on both sides.


x/2=5

When representing x you'll cut it in half .

You then add the other half making the x complete, and remember the rule of equality. You add another half then you add another set of tiles.

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Solving 2 step equations

2x+1=7

1.Isolate the variable starting off with with the addition/subtraction part
2.Cancel constant
3.Balance
4.Simplify the variable
5.Balance

6.Verify


x/2+2=6

1.Isolate the variable starting off with with the addition/subtraction part
2.Cancel constant
3.Balance
4.Simplify the variable
5.Balance

6.Verify to check


If you're still having trouble have a look at this video.