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Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion


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May 21st, 2018, 10:18 AM   #1
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Not understanding simple factorization

I'm not understanding how this simple factorization works...I know how to solve it, but it is making no sense to me.

3p+3
--------
3

I know the answer is p+1, but I don't understand how factoring 3p+3 works.

My instructions say to rewrite as 3p + 1(3), then factor out the common term: 3(p+1). Why does this work when it's addition? Why wouldn't it be 6p+1? I'm probably missing something really simple but it makes no sense to me and I don't like to move forward with math unless I understand why it works that way.

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May 21st, 2018, 10:48 AM   #2
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If you have 3 eggs and 6 slices of bread and wish to share this food equally between three people, you would give 1 egg and 2 slices of bread to each of those people.
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May 21st, 2018, 10:49 AM   #3
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note the numerator has two terms with a common factor of $3$ ...

$3p+3 = \color{red}{3}(p) + \color{red}{3}(1) = \color{red}{3}(p+1)$

... it's just the reverse of the distributive property of multiplication over addition
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May 21st, 2018, 01:11 PM   #4
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Quote:
Originally Posted by dreamcatcher View Post
3p+3
-------
3
Well, to "see it", assign a value to p; let's have p=7:
unfactored:
(3p + 3) / 3 = (3*7 + 3) / 3 = (21 + 3) / 3 = 24 / 3 = 8
factored:
3*(p + 1) / 3 = p + 1 = 7 + 1 = 8
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May 22nd, 2018, 01:30 AM   #5
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Math Focus: Physics, mathematical modelling, numerical and computational solutions
Multiplication tells us that we need to add up a number by itself a number of times equal to the other number. So, for example, if we have

$\displaystyle 3 \times 4 $

then the solution is to add 3 4s, like so

$\displaystyle 3 \times 4 = 4 + 4 + 4 = 12$

We also know that

$\displaystyle 4 = 1 + 3$

So, if we replace 4 in our original problem with 1 + 3, we get

$\displaystyle 3 \times (1 + 3)$

and we need to evaluate this. Using the definition of multiplication, we expect

$\displaystyle 3 \times (1 + 3) = 1 + 3 + 1 + 3 + 1 + 3$

We can also add up the items in any order, so let's swap some of them around to get all the similar numbers together in a group:

$\displaystyle 3 \times (1 + 3) = 1 + 1 + 1 + 3 + 3 + 3$

Finally, we have 3 1s and 3 3s, so we can use the definition of multiplication to say that this is

$\displaystyle 3 \times (1 + 3) = 3 \times 1 + 3 \times 3$

There's a pattern
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