Video

The five numbers that I use are just random numbers. I use these random numbers to help explain how the odds are calculated.

Thanks for working out the time stamps. I've added them to the video and given you credit. Thanks again

Thanks

My pleasure!

You're not doing multiplication first, you just have to leave the 4 in parenthesis because there is not a multiplication sign

The Distributive Property is a PROPERTY of Multiplication NOT Parentheses and not Parenthetical Implicit Multiplication. As such it has the same priority as Multiplication and Multiplication does not have priority over Division. The Distributive Property is congruent with the Order of Operations it doesn't supercede the Order of Operations... The Order of Operations work because of the Properties and Axioms of math not in spite of them... The Distributive Property when fully applied is an act of ELIMINATING the need for parentheses by drawing the TERMS inside the parentheses out not by drawing factors in... If you can't draw a factor in and get the same result as drawing the TERMS inside the parentheses out then you haven't applied the Distributive Property correctly... The Distributive Property does NOT change or cease to exist because of parenthetical implicit multiplication... The axiom a(b+c)= ab+ac however the variable "a" represents the TERM or TERM value outside the parentheses not just a numeral next to the parentheses. In this case a = 8÷2 OR 4. People just automatically assume that "a" is a single numeral... A variable can represent a single value, a set of operations that represent a TERM that represents a single value or a solution set... 8÷2(2+2)= 8÷2×2+8÷2×2 Distributive Property.. Parentheses removed... 8÷(2(2+2))= 8÷(2×2+2×2) Distributive Property. Inner parentheses REMOVED This can be further demonstrated using the vinculum.... 8 ------(2+2)= 8÷2(2+2)= 16 2 8 ------------ = 8÷(2(2+2))= 1 2(2+2) A vinculum (horizontal fraction bar) serves as a grouping symbol. Neither the obelus or solidus serve as grouping symbols. The vinculum groups operations within the denominator and when written in an inline infix notation extra parentheses are required to maintain the grouping of operations within the denominator.... ________ 2(2+2) = (2(2+2)) two grouping symbols each That over bar (vinculum) is a grouping symbol _______ _________ 2(2+2) = 2×2+2×2 = (2×2+2×2) (2(2+2))= (2×2+2×2) Note that when applying the Distributive Property one grouping symbol was REMOVED from each notation...

BODMAS/PEMDAS and any other acronym that is a memory tool for the Order of Operations 8÷2(2+2)= 8÷2(4)= 4(4)= 16 2(4) is not a bracketed priority and is exactly the same as 2×4 M not B or O in BODMAS. Brackets/Parentheses only group and give priority to operations (INSIDE) the symbol not outside .... There is no rule in math that says you have to open, clear, remove or take off parentheses. The rule is to evaluate operations (WITHIN) the symbol of INCLUSION as a priority and nothing more.... Commutative Property 8÷2(2+2)= 8(2+2)÷2= 8(4)÷2= 32÷2= 16 Distributive Property 8÷2(2+2)= 8÷2×2+8÷2×2= 4×2+4×2= 8+8= 16 Let me explain the Distributive Property... The Distributive Property is a PROPERTY of Multiplication NOT Parentheses and not Parenthetical Implicit Multiplication. As such it has the same priority as Multiplication and Multiplication does not have priority over Division. The Distributive Property is congruent with the Order of Operations it doesn't supercede the Order of Operations... The Order of Operations work because of the Properties and Axioms of math not in spite of them... The Distributive Property when fully applied is an act of ELIMINATING the need for parentheses by drawing the TERMS inside the parentheses out not by drawing factors in... If you can't draw a factor in and get the same result as drawing the TERMS inside the parentheses out then you haven't applied the Distributive Property correctly... The Distributive Property does NOT change or cease to exist because of parenthetical implicit multiplication... The axiom a(b+c)= ab+ac however the variable "a" represents the TERM or TERM value outside the parentheses not just a numeral next to the parentheses. In this case a = 8÷2 OR 4. People just automatically assume that "a" is a single numeral... A variable can represent a single value, a set of operations that represent a TERM that represents a single value or a solution set... 8÷2(2+2)= 4(2+2) no rules have been broken... 8÷2(2+2)= 8÷2×2+8÷2×2 Distributive Property. Operational inverse of division by the reciprocal 8÷2(2+2)= 8(1/2)(2+2)= 8(1/2)(4)=? Multiply in any order you want you still get 16 Proper use of grouping symbols 8 -----(2+2) = 8÷2(2+2)=16 2 8 -------- = 8÷(2(2+2))=1 2(2+2) Why?? The vinculum (horizontal fraction bar) serves as a grouping symbol. Neither the obelus or solidus serve as grouping symbols. The vinculum GROUPS operations within the denominator and when written in an inline infix notation extra parentheses are required to maintain the grouping of operations within the denominator...Remove the grouping power of the vinculum, replace it with the grouping power of parentheses... _______ 2(2+2) how many grouping symbols do you see grouping operations?? (2(2+2)) how many grouping symbols do you see grouping operations?? _________ 2×2+2×2 how many grouping symbols do you see grouping operations AND what was REMOVED?? (2×2+2×2) how many grouping symbols do you see grouping operations AND what was REMOVED?? Another argument people tend to use incorrectly is factoring.... 8 = 4+4 No parentheses required BUT 8÷(4+4) parentheses required 4+4 = 2(2+2) only one set of parentheses required. 8÷(4+4) we already have a set of parentheses and the factoring must take place within that first set of parentheses. You can NOT just dismiss the first set of parentheses out of hand in favor of the second set... The 2(2+2) must be placed within the first set of parentheses containing the (4+4) 8÷(4+4) = 8÷(2(2+2)) NOT 8÷2(2+2) Fyi... you can't factor a denominator without maintaining all operations of that factorization WITHIN a grouping symbol. You can factor out LIKE TERMS from an expanded expression... 8÷2×1+8÷2×2+8÷2×3^2-8÷2×4= 8÷2(1+2+3^2-4) as the LIKE TERM 8÷2 was factored out of the expanded expression... Let y= 1/2 or 0.5 8y(2+2)= ? 8y*2+8y*2= ? 8/y⁻¹*2+8/y⁻¹*2= ? If you answered 16 to all three of these algebraic expressions then it would be ILLOGICAL and INCONSISTENT as well as hypocritical to say that 8/y⁻¹(2+2) does not also equal 16. The rules of math have to remain logical and consistent across the board... THESE ARE THE FACTS....

Algebra says you can't have a parentheses without a multiplication happening immediately afterwards. The smallest tree you can make with a parentheses is 1x because all variables have a coefficient. * / \ 1 X Coefficients are either a quantity, or a variable. 6÷2 is neither. Both the coefficient and result of function X are leaf nodes, with equal priority going into the multiplication.

Thanks

Good luck tomorrow!

I read this comment and thought what does it mean?? Then I googled it and found this quote on the Prospecting Australia website...lol

@@howto...solvepuzzlesReally? I got it from the play “Rhodonite and Jeweliette”😂

Thanks 🤗