Algebra I #2.10d, Theorems and Proofs

An explanation of how to use theorems to prove or justify a statement (whether algebraically or geometrically ) with three examples of completed proof tables.
#2.10d

Grade 8 Math #11.2c, Chain of Reasoning for a deduction

The previous video
Algebra I #2.10c, Properties of Equality

Algebra I #2.10a, Axioms and Fields

Algebra I #2.10b,
Field Axioms for rational numbers & the Closure Property

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[huskythegreat]

You're an amazing teacher. My teachers were terrible at explaining this concept.

[yugi]

I'm starting a major in math and this is hella helpful! Thanks so much!

[petepalmere]

Excellent presentation. I apologize for bringing this up but you may have seen the video that went viral because of the ambiguous expression 6÷2(1+2) where there are basically two camps: one using PEMDAS and a left-to-right order of operations to solve it to 9 as they see the 2 outside the group as the denominator and divide it into 6 first as division comes first according to that camp so it becomes 3x3=9; the other camp simplifies 2(1+2) to 2(3)=6 and, of course, 6÷6=1. It is interesting that if we use the commutative property we could just as well change 2(1+2) to (1+2)2 in which case the PEMDAS people would have to resolve this to 4 since they would have to divide 6 by (1+2) or 6÷3=2 then times 2=4. what say you and can we prove that the answer is 1 to the expression?

[frodo]

But we need to prove the distributive property, and you used the distributive property to prove itself right? albeit in a different letter order.. I'm not sure what I can use and what I can't use yet, so I'm confused most of the time. Could you explain this point please :)

[chase]

Is that the only way to do it, or are there multiple ways?

[raideneyyy]

Prove that if b=ac+d then b/a= c+d/a. how about this?