Okay. Let's get down to business with these GCF things.
Here are the answers from yesterday's assignment (pg. 193, 17 - 24). I know they were very difficult so please don't worry if you got them wrong. I wanted to let you try them first though after reading the textbook:
17. 5
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18.
7
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19. 25
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20. 3
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21.
7c
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22. 3y2
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23. 6c3
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24. 2mn
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Before we can really tackle finding the GCF for those complicated variable expressions, we need to master the "hard" way of finding a GCF.
As we learned yesterday, we can find the GCF of two numbers two different ways. First, by listing the factors, and identifying the biggest one they have in common.
Example:
Find the GCF of 30 and 18.
If we list the factors of 30, we get: 1, 2, 3, 5, 6, 10, 15, and 30.
If we list the factors of 18, we get: 1, 2, 3, 6, 9, and 18.
When we compare the two lists, we see that the greatest common factor shared by both of them is 6.
This method is easiest with relatively small numbers.
Let's look at the other way.
To find the GCF of two numbers by using prime factorization, first do factor trees for the two numbers.
30 18
2 x 15 2 x 9
2 x 3 x 5 2 x 3 x 3
The prime factorizations for both numbers are, as usual, @ the bottom of the tree.
Now here's where it gets tricky. After this step, identify all of the common factors @ the bottom of the trees. The thing is, each common (or "shared") factor has to have a match!
We see that both sides have one 2. So we can select 2 as a common factor. Only one side has a 5, so we cannot use the 5 as a common factor. Both sides have one 3, so we can select 3 as a common factor. Now, look on the side for 18. We have an extra 3 hanging around at the bottom. The thing is, that 3 doesn't have a match on the other side. No twin, no bff, no match. So the extra 3 is not a "common" factor.
Follow me so far? We've identified the common factors at the bottom of each tree to be 2 and 3. Now we multiply those common factors together: 2 x 3. We get 6. Now we know that 6 is the GCF of 30 and 18.
Let's stop here and practice the method of finding the GCF using prime factorization without worrying about polynomials, variables, exponents, etc. We're going to break it down step-by-step.
Try the following 5 problems individually using the prime factorization method. Find the GCF:
1) 16, 60
2) 36, 81
3) 15, 30
4) 32, 64
5) 10, 13 ---> This is a tricky one! Can anyone figure it out? :)
Feel better Ms. Johnson!
ReplyDeleteum mrs johnson, for number 19 you had 25. but i got five. maybe i did something wrong or maybe it was just a typo??? get well soon!!!
ReplyDeletefor number 22 I got 9y. I believe that 3y to the 2nd power is another way of saying 9y because 3*3=9 and I plugged in the variable which makes it 9y. Im not sure if I did it wrong or if I put it in another way. -Madi I
ReplyDeleteI also did the same thing for number 23.
ReplyDelete#23-I got 27c
Thank you Shelby! Jessica - for #19, if we list all the factors of 25, we have: 1, 5, and 25. (Remember, a number is always its own factor, because we can multiply by 1 to get the same thing. That's why 25 is a factor for 25.) If we list the factors for 100, we have: 1, 2, 4, 5, 10, 20, 25, 50, and 100. The great number that these two lists have in common is 25, so 25 is the GCF for 25 and 100. Does that help?
ReplyDelete@ Madi - we are actually going to revisit those questions after we pause for a bit to learn how to find the GCF using prime factorization. Then we'll look at how to do the prime factorization for polynomials (those expressions with variables) - and THEN we will travel back to visit 22 and 23 to talk about how to tackle those problems. They're quite tricky.
ReplyDelete@Ms.Johnson-I'm sorry you are feeling bad. You are in everyone's prayers. I can't wait to see you!!!
ReplyDelete