after solving for the term in the parentheses, the 2(3) should be thought of as 2x3 then work from left to right with the multiplication/division per PEMDAS. Thx for watching, G
@@mymathchalkboard firstly this problem would never exist in the real world and the problem could be written 6/2(1+2) and get the proper answer which is 1.
Explicit multiplication and number(…..) , ie. implicit multiplication are different. a(b)=(ab). But a cross (b) cannot be written as (ab). AI explained. Don’t mislead the theory please.
6 : 2x3 DEBE SER IGUAL QUE 6 : 3x2 = 6 : 6 = 1 Si 6 : 2x3 = 3x3 = 9, SIENDO 2x3 = 3x2, ES ABSURDO que 6 : 3x2 sea igual a 2x2 = 4 Y no hace falta poner paréntesis, ya los factores 2 y 3, están "amarrados" por el signo de la multiplicación.
6÷2(1+2) = 6÷2(3) = 6÷(2*3)= 6÷6 = 1 When changing from implicit to explicit multiplication, always enclose the factors involved, i.e., 2 and (3), in (). Distributive rule. Alternatively, 6÷2(1+2) = 6÷2(3) = 3÷(3) = 1 Division by a product, 2(3) = Division by both its factors, i.e., 2 and (3). Answer a) 1.
Distibutive property is not an operation. Order of operations is the topic. If the expression were 6÷(2(1+2)), then 1 is correct but it's not expressed that way. Enclosing all factors means (2(1+2)) That isn't the given expression.
@@Joe_Narbaiz The only operation we have to worry about is division. This is a simple and unambiguous problem of division, a÷b, where a = 6 and b = 2(1+2). Amazed that people can't handle division by a product, or even recognize that 2(1+2) is a product and that the multiplication of the two factors has already taken place. That's why the problem is written as 6÷2(1+2) and not as 6÷2x(1+2). BTW, we add () and enter 6÷2(1+2) as 6÷(2(1+2)) when using some calculators and math engines, because the instructions tell us to do so: "Special care is needed when interpreting the meaning of a solidus in in-line math because of the notational ambiguity in expressions such as a/bc. Whereas in many textbooks, "a/bc" is intended to denote a/(bc), taken literally or evaluated in a symbolic mathematics languages such as the Wolfram Language, it means (a/b)×c. For clarity, parentheses should therefore always be used when delineating compound denominators."
@@dgkcpa1 You are misinterpreting the function of an obelus (÷) or solidus (/) as being equivalent to that of a vinculum or horizontal fraction bar (---). "For clarity, parentheses should therefore always be used when delineating compound denominators" Isn't that what I said? 🤔😉
@@Joe_Narbaiz The obelus(÷) , solidus (/) and vinculum (---) are functionally equivalent - they denote division and are used to separate the numerator, or dividend, from the denominator, or divisor. In normal usage, we do not need an extra set of () to denote the divisor, when we use an obelus(÷) , solidus (/) or vinculum (---) . However, as noted above, not all calculators or math engines view a/bc as a/(bc), even though it is recognized as such in many textbooks. Not a problem. The calculator is our tool, not vice versa. It is not a mind reader, and will not do our thinking for us. It is up to us to tell the calculator or math engine how to handle any given problem. Accordingly, if we want the calculator to treat a/bc as a/(bc), instead of as (a/b)×c (its default), we simply enclose the product bc (the devisor) in (), as the instructions advise us, and enter 6÷2(1+2) as 6÷(2(1+2)).
@dgkcpa1 So you agree that 6÷2(1+2) is ambiguous in nature and parentheses are necessary to determine the intention. Again, the distributive property is not an operation. It is a math concept using the operations of multiplication and addition and/or subtraction. The purpose of parentheses is to determine precedence. So only that which is contained WITHIN a set of parentheses is evaluated. 6÷2(3) defaults to 6÷2*3 as you said Multiplication and division share equal precedence and therefore are evaluated from left to right in the order of occurrence withon the expression. Regarding the division symbols: The obelus and solidus require parentheses to determine the denominator. The vinculum does not.. Clear denominator. Can you say grouping properties? That is why I said they are not the same. 6÷2(1+2)...implied or implicit multiplication 6÷(2(1+2))...juxtaposition. 6÷2*(1+2)...expressed or explicit multiplication
B is right answer ❤❤❤❤
B
1
Wrong
9
6÷2=3
(1+2)=3
3(3)=9
Go back to school!
@@JoepKortekaas-l4q Why?
6÷2(1+2)
6÷2(3)
6÷2*3
3*3=9
It is not 6÷(2(1+2))
6÷(2(3))
6÷(2*3)
6÷6=1
I'd have done 2(3+1) = 8 initially. This equation is ambiguous as we're now supposed to treat 2 ( explicitly as 2x ( and then follow pemdas.
after solving for the term in the parentheses, the 2(3) should be thought of as 2x3 then work from left to right with the multiplication/division per PEMDAS. Thx for watching, G
Excellent explanation ❤. Thank you sir
This explanation is totally wrong!
9
6 : 6 = 1
Yeah, but that is not the problem.
6:2 (1+ 2 ) = 6:2 (3) = 3 (3) = 9
I did this in my head it's 9 6÷2(1+2) using pemdas the equations turns into 3(3) which is 9
Your head seems to be wrong!
@JoepKortekaas-l4q the my calculator must be wrong 💀
Ambiguous.
why?
@@mymathchalkboard firstly this problem would never exist in the real world and the problem could be written 6/2(1+2) and get the proper answer which is 1.
@ this is just an order of operation problem. Following PEMDAS will result in 9 as the answer. Thanks for watching.
@@mymathchalkboard so what is the value of 2(1+2)?
@ Answer this: Do you believe the P (in PEMDAS) includes “2(1+2)” or just “(1+2)”?
Explicit multiplication and number(…..) , ie. implicit multiplication are different. a(b)=(ab). But a cross (b) cannot be written as (ab). AI explained. Don’t mislead the theory please.
Option A Bodmas rule first small bracket
2 (3) = 6
2(1+2) =
(2*1+2*2)
( 2 + 4) = 6
6 : 6 = 1
after solving for the term in the parentheses, work from left to right with the multiplication/division. 6÷2x3 = 3x3 = 9. thx for watching.
Jes 6 : 6 = 1 🙂
6 : 2x3 DEBE SER IGUAL QUE 6 : 3x2 = 6 : 6 = 1 Si 6 : 2x3 = 3x3 = 9, SIENDO 2x3 = 3x2,
ES ABSURDO que 6 : 3x2 sea igual a 2x2 = 4 Y no hace falta poner paréntesis, ya los factores
2 y 3, están "amarrados" por el signo de la multiplicación.
this is just an order of operation problem. Following PEMDAS will result in 9 as the answer. Thanks for watching.
Absolutely wrong, the right answer is 1! And you know what? Mr. Casio and Mr. Canon agree with me!
Wolfram Alpha‘s Mathematica, Google, Bing and Calculators on MacOS or Windows give 9.
6
- * ( 1 +2 ) = 9.
2
6÷2(1+2) = 6÷2(3) = 6÷(2*3)= 6÷6 = 1 When changing from implicit to explicit multiplication, always enclose the factors involved, i.e., 2 and (3), in (). Distributive rule.
Alternatively, 6÷2(1+2) = 6÷2(3) = 3÷(3) = 1 Division by a product, 2(3) = Division by both its factors, i.e., 2 and (3).
Answer a) 1.
Distibutive property is not an operation. Order of operations is the topic.
If the expression were 6÷(2(1+2)), then 1 is correct but it's not expressed that way.
Enclosing all factors means (2(1+2))
That isn't the given expression.
@@Joe_Narbaiz The only operation we have to worry about is division. This is a simple and unambiguous problem of division, a÷b, where a = 6 and b = 2(1+2).
Amazed that people can't handle division by a product, or even recognize that 2(1+2) is a product and that the multiplication of the two factors has already taken place.
That's why the problem is written as 6÷2(1+2) and not as 6÷2x(1+2).
BTW, we add () and enter 6÷2(1+2) as 6÷(2(1+2)) when using some calculators and math engines, because the instructions tell us to do so:
"Special care is needed when interpreting the meaning of a solidus in in-line math because of the notational ambiguity in expressions such as a/bc. Whereas in many textbooks, "a/bc" is intended to denote a/(bc), taken literally or evaluated in a symbolic mathematics languages such as the Wolfram Language, it means (a/b)×c. For clarity, parentheses should therefore always be used when delineating compound denominators."
@@dgkcpa1 You are misinterpreting the function of an obelus (÷) or solidus (/) as being equivalent to that of a vinculum or horizontal fraction bar (---).
"For clarity, parentheses should therefore always be used when delineating compound denominators"
Isn't that what I said?
🤔😉
@@Joe_Narbaiz The obelus(÷) , solidus (/) and vinculum (---) are functionally equivalent - they denote division and are used to separate the numerator, or dividend, from the denominator, or divisor. In normal usage, we do not need an extra set of () to denote the divisor, when we use an obelus(÷) , solidus (/) or vinculum (---) .
However, as noted above, not all calculators or math engines view a/bc as a/(bc), even though it is recognized as such in many textbooks.
Not a problem. The calculator is our tool, not vice versa. It is not a mind reader, and will not do our thinking for us. It is up to us to tell the calculator or math engine how to handle any given problem.
Accordingly, if we want the calculator to treat a/bc as a/(bc), instead of as (a/b)×c (its default), we simply enclose the product bc (the devisor) in (), as the instructions advise us, and enter 6÷2(1+2) as 6÷(2(1+2)).
@dgkcpa1 So you agree that 6÷2(1+2) is ambiguous in nature and parentheses are necessary to determine the intention.
Again, the distributive property is not an operation. It is a math concept using the operations of multiplication and addition and/or subtraction. The purpose of parentheses is to determine precedence. So only that which is contained WITHIN a set of parentheses is evaluated.
6÷2(3) defaults to 6÷2*3 as you said
Multiplication and division share equal precedence and therefore are evaluated from left to right in the order of occurrence withon the expression.
Regarding the division symbols:
The obelus and solidus require parentheses to determine the denominator.
The vinculum does not..
Clear denominator.
Can you say grouping properties?
That is why I said they are not the same.
6÷2(1+2)...implied or implicit multiplication
6÷(2(1+2))...juxtaposition.
6÷2*(1+2)...expressed or explicit multiplication
9
thanks for watching
6 :2 ( 1 + 2 ) = 6:2 (3) = 3(3) = 9
9
9