Can I have some pre-algebra help?

Question

Okay, my daughter seems to be having an issue with 7th grade math. Algebra may just very well be a form of satan, I don't understand it...

But here's the problem:
-7a+3(a-c)+5c

Students are encouraged to use the distributive property, which I also don't know. So could you please explain this problem out step-by-step so she will have a shot at getting the other problems right?

Thanks!
-Kat

I've seen many answers so far. But where's the 2 coming from?!!?

Answer 1

the distributive property that is mentioned is directed toward 3(a-c). it just means to multiply 3 by both a and c so instead of 3(a-c) you get 3a-3c. this makes it easier to simplify.
-7a+3a-3c+5c
combine like terms
-4a+2c
and pull out any common terms, in this case 2,by dividing out a 2 from -4a and 2c (she might not have to do this)
so you end up with 2(-2a+c)
any questions feel free to ask

the 2 that gets pulled out of -4a+2c is the greatest number that both 2 and 4 share. here u are basically doing the opposite what you did with 3(a-c), instead of multiplying each term, a and c, by the number in front of the (), you pull out the number that was factored into it.
the steps are as follows:
1) find what the greatest number that both coefficients, numbers in front of the letters(variables),share. in this case it is 2 because 2 evenly divided both 2 and 4.
2)now that you have the greatest common factor, you simply divide the entire expression, -4a+2c, by 2 so you have
(-4a+2c)/2 or (-4a/2)+(2c/2).
3) simplify (-4a/2)+(2c/2) by just dividing. (-4a/2)= -2a and(2c/2)=c. then you just add them together, just like the original problem was doing, and you end up with (-2a+c)
4) now just put the number you factored out, in this case 2, in front of (-2a+c). you end up with 2(-2a+c)

hope that clarified things, if not feel free to ask away.

Answer 2

The distributive property applies to the part of the equation in parenthesis, and it states that you "distribute" the multiplier to all parts of the parenthesis term, so in this case:

3(a-c) = 3a - 3c

or in general
x(y+z) = xy +xz

this applies no matter how many terms are in the parenthesis, for instance

w(x+y+z)= wx + wy + wz

In terms of the equation you've written above, it needs to be equal to something in order to solve it, but if all you have to do is "simplify the expression", then use the distributive property as outlined above to re-write the expression as follows:

-7a + 3a -3c + 5c (normally there would be an = and some value after this)

now just take all the numbers in front of an "a" and add them together

-7 + 3 = -4, so you have -4a

now take all the numbers in front of a "c" and add them together

-3 + 5 = +2, so you have +2c

thus the expression simplifies to -4a + 2c.

Answer 3

I know you have a text book that defines and lays out what the distributive property is.

Here's how the prob goes:
-7a+3(a-c)+5c (mulitply a and -c in the parentheses with
+3, I think this is the part of the prob that
eals with the distributive property).
-7a+3a-3c+5c (then add or subtract like terms such as
the a's and the c's)
-4a+2c (this would be the simplest form of this
expression)

Answer 4

Its hard to explain but I'll do my best...I'm 8th grade Algebra 1, so heres what I know
Distributive:
You take the 3 next to the parenthesis and multiply to each number in the parenthesis, So it would be -7a+3a-3c+5c
Then you would combine like terms, so if you have two numbers being multiplyed by a, then you add them, so it would then be -4a+2c
Thats all I know how to do on this problem but I hope I helped a little bit
You could also have your daughter ask the teacher for additional help if she needs it

Answer 5

The first step it to, as you mentioned, use the distributive property. Multiply everything inside of the parentheses by 3. After you have done this, you are left with -7a+3a-3c+5c. From here you need to combine all like terms. -7a can be added to 3a. -3c can be added to 5c. You're now in the simplest form. -4a+2c

Answer 6

-7a + 3(a + -1c) + 5c
-7a + (a * 3 + -1c * 3) + 5c
-7a + (3a + -3c) + 5c

Combine like terms: -7a + 3a = -4a
-4a + -3c + 5c

Combine like terms: -3c + 5c = 2c
final answer:-4a + 2c

basically you have to work the 3 through both the a & c because that's the only number there is to distribute


check this page out if you need to have another one done, just put in the problem and hit simplify and they tell you the answer/check your work

http://www.algebrahelp.com/calculators/expression/oops/

Answer 7

1) Remove the brackets
2) Gather like terms
3) Solve the equation
-7a + 3(a - c) + 5c
-7a + 3a -3c + 5c
2c - 4a
2(c - 2a)
Can't solve it as it is an expression not an equation.

Answer 8

1. -7a+3(a-c)+5c (you first distribute the 3 into the parenthesis)
2. -7a+3a-3c+5c now combine the like terms, -7a and +3a =-4a and -3c and +5c = 2c
3. -4a+2c is your answer, you can't simplify it anymore

Answer 9

the adaptation between the two is Pre-Algebra is far less confusing, only getting you all started on Algebra. undemanding is extra complicated than Pre. Does that answer your question? wish so :) bye xoxox