Indicater: D6. Justify that two forms of an algebraic expression are equivalent, and recognize when an expression is simplified.

Are you having trouble with algebraic expressions? Don't know when they are simplified or equivalent? Here's where to find out!
Well, first you need to know the order of operations...(parenthesis, exponets, multiplication, or division, addition or subtraction).
Once you know how to start the problem with the order of operations, then you will be able to work out the problem.

Simplified Expressions
To know when a algebraic expression is simplified follow these instructions.
Look at the following problem: 2x + 3y - 2 + 3x + 6y + 7.
Did you know that this is the problem simplified? 12 + 5x + 9y.
Look at the bolded numbers in this: 2x + 3y - 2 + 3x + 6y + 7.
Do you see how they have the X on the end of them? That means that number has to get mulitpied by a number. But since you don't know what the mulitplier is, then you can just add other numbers that have the same X on the back.
So, you have this: 2x + 3y - 2 + 3x + 6y + 7. 2x + 3x equals 5x. The problem would be like this: 3y - 2 + 5x+ 6y + 7. Do you see the bolded 5x?

3y - 2 + 5x + 6y + 7. Again, since 3y and 6y have the same mulitplier, they can be added together. Like so: 3y + 6y equals 9y. The problem would then be 2 + 5x + 9y + 7. Do you see the bolded 9y?

7 and 5 can be added together. 7 + 5 = 12. The problem would then be 12 + 5x + 9y, which is then simplified.

Watch the video below if you need more help:

Equivalent Expressions:
expressions that have the same value but are presented in a different format using the properties of numbers.
external image scale.jpgBoth sides have to be equal.
ax + bx
Look at the expression above. You can't find out what it equals because you don't know what the values of A and B are. The only way you can put the expression into another format is: (a + b) x. Do you see how the x in the first expression is behind the A and the B? You can just add the A and B together because X is going to be the same value. (a + b), you then mulitply the letter: (a+b)x. It means you have to add the A and B together first, then multiply those two by the X.

Lets look at a number expression 5+9x. Obviously, you have to add the 5 and 9 together, which will be 14. The expression would be 14x. Any other information you would need, would be to know what the X equals.

Using Equivalent Expressions in real life:
You will need to know how expressions are equivalent when you are using money. You will need to know how to simplify money and other things like that.

Resoures: Type in "Simplified expressions" or Equivalent Expressions" on either,,, or