
Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion 
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May 21st, 2018, 10:18 AM  #1 
Newbie Joined: May 2018 From: USA Posts: 1 Thanks: 0  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. Thank you! 
May 21st, 2018, 10:48 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 19,302 Thanks: 1688 
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.

May 21st, 2018, 10:49 AM  #3 
Math Team Joined: Jul 2011 From: Texas Posts: 2,761 Thanks: 1416 
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 
May 21st, 2018, 01:11 PM  #4 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 12,930 Thanks: 884  
May 22nd, 2018, 01:30 AM  #5 
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,125 Thanks: 714 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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