SIXTH GRADE

Today's homework is simplifying fractions using prime factorization. This is useful when the numbers are really big or you aren't sure what the GCF of the numerator and denominator are. First, do the prime factorization of each by doing the factor tree. Then write like a fraction. Here is an example:

72  2 x 2 x 2 x 3 x 3           3
96  2 x 2 x 2 x 2 x 2 x 3     4

The prime factorization of 72 is 2 x 2 x 2 x 3 x 3 so I put that on top. The prime factorization of 96 is 2 x 2 x 2 x 2 x 2 x 3 so I put that on bottom. Now you would cross off any numbers that are on top and bottom. There are three sets of 2 on top and bottom so 3 2's are crossed off on top and on bottom. Then there is a 3 on top and a 3 on bottom. Cross these off. What you have left is one 3 on top and two 2's on bottom. The top number is 3 and the bottom number is 4 since 2 x 2 = 4.

SEVENTH GRADE

The homework today is combining like terms. Remember to first find the terms that have the same variable. Then combine the numbers in front of the variables by using your integer rules.

Here is an example:

-3x + 2y - 5y + 9x

I have colored the like terms in the same colors. So, the two red terms both have x. The coefficients (the numbers in front of the variables) are -3 and +9. So, you think, "what is -3 + 9"? Using integer rules, the answer is +6 because the signs are different so you subtract. So far, we have 6x.

The two terms in blue both have a y. The coefficients are +2 and -5 so you think "what is +2 - 5"? Since the 5 has a minus sign in front, you can change it to addition and change the 5 to a negative. Like this: +2 + - 5. Now the signs are different so you subtract and get -3. So the y term is -3y

Your final answer would be 6x - 3y or 6x + -3y. Either way is correct.

SEVENTH GRADE PRE-ALGEBRA

Today's assignment is the markup and discount worksheet. You are doing the first 6 in the markup section and the first 6 in the discount section. Remember, first you multiply the amount by the percent written as a decimal. Round any amounts to the nearest cent. Then, to find the selling price when it's a markup, add that amount to the original amount. To find the sale price when it's a discount, subtract that amount from the original amount.

EIGHTH GRADE PRE-ALGEBRA

Today's assignment is the Labyrinth worksheet with finding slope from two points. Don't forget that the y's go on top and the x's go on bottom! Also, don't forget to reduce!

ALGEBRA I

Solving systems of equations by substitution. I can't do a video tonight because I'm losing my voice. Remember, the first thing you have to do is make sure that you have a variable isolated in one of your equations. If you don't, you will have take one of the equations and isolate one of the variables by moving everything to the other side. Once you have that, you can substitute what that variable equals into the other equation. Here is an example:

y = 6x − 11
−2x − 3y = −7

The first equation is already solved for y, so I'm going to substitute 6x - 11 in for y in the second equation.

y = 6x − 11
−2x − 3y = −7

-2x - 3(6x-11) = -7

Now I will solve this for x. First I have to distribute the -3 to the parentheses.

-2x - 18x + 33 = -7    Now, I need to combine like terms on the left side.

-20x + 33 = -7    Now I need to move the 33 to the right side by subtracting.

-20x = -40  Now divide both sides by -20

x = 2

Now that I know what x equals, I can plug this value into either original equation. I will use the first one because the y is already by itself on the left side.

y = 6*2 - 11   (The * means times)

y = 12 - 11

y = 1

So your ordered pair is (2, 1)

Here is another example:

y = −5x − 17
y = -x - 1

This one has the y isolated in both equations. It's actually deceptively simple. I'll substitute what y equals in the first equation for where y is in the second equation. I've highlighted above to show this.

It would look like this:

-5x - 17 = -x -1    Now we can solve for x. First, I'll move the -5x to the right side by adding 5x to                                   both sides.

-17 = 4x -1          Now, move the -1 to the left by adding 1.

-16 = 4x          Divide both sides by 4.

-4 = x

Now that we know what x equals, we can plug this in either equation. It doesn't matter which since the y is already by itself in both. I'll do the second one because the numbers look friendlier.

y = - -4 - 1   That becomes a double negative, so it changes to 4 - 1

y = 3

Your ordered pair is (-4, 3)

Here is one more example:

−3x + 3y = 4
−x + y = 3

First, I need to isolate one of the variables. Both variables have a coefficient in the first equation, but in the second, neither one does. I'm going to solve for y since the x is a negative. I just need to add x to both sides. The second equation becomes:

y = x + 3

Now I'll substitute x + 3 in for y in the first equation. I've highlighted it above and below in the first equation:

-3x +3y = 4

-3x + 3(x+3) = 4  Now I'll simplify by using distributive property.

-3x + 3x + 9 = 4   Now I need to combine like terms. -3x + 3x cancels out to zero.

9 = 4         I'm left with a false statement! 9 does not equal 4.

The answer her is NO SOLUTION.

I hope this is helpful!

See you tomorrow,

Mrs. Swickey