The problem with this is that the division symbol is not an accurate representation of the intended meaning. Division is usually written in fractions which has an implied set of parenthesis, and is the same priority as multiplication. This is because dividing by a number is the same as multiplying by the inverse, same as subtracting is adding the negative of a number.
8/2(2+2) could be rewritten as 8Γ1/2Γ(2+2) or (8Γ(2+2))/2 which both resolve into 16.
You left out the way it can be rewritten which most mathematicians would actually use, which is 8/(2(2+2)), which resolves to 1.
Division is usually written in fractions
Division and fractions aren't the same thing.
fractions which has an implied set of parenthesis
Fractions are explicitly Terms. Terms are separated by operators (such as division) and joined by grouping symbols (such as a fraction bar), so 1Γ·2 is 2 terms, but Β½ is 1 term.
8/2(2+2) could be rewritten as 8Γ1/2Γ(2+2)
No, it can't. 2(2+2) is 1 term, in the denominator. When you added the multiply you broke it into 2 terms, and sent the (2+2) into the numerator, thus leading to a different answer. 8/2(2+2)=1.
The problem with this is that the division symbol is not an accurate representation of the intended meaning. Division is usually written in fractions which has an implied set of parenthesis, and is the same priority as multiplication. This is because dividing by a number is the same as multiplying by the inverse, same as subtracting is adding the negative of a number.
8/2(2+2) could be rewritten as 8Γ1/2Γ(2+2) or (8Γ(2+2))/2 which both resolve into 16.
You left out the way it can be rewritten which most mathematicians would actually use, which is 8/(2(2+2)), which resolves to 1.
Division and fractions aren't the same thing.
Fractions are explicitly Terms. Terms are separated by operators (such as division) and joined by grouping symbols (such as a fraction bar), so 1Γ·2 is 2 terms, but Β½ is 1 term.
No, it can't. 2(2+2) is 1 term, in the denominator. When you added the multiply you broke it into 2 terms, and sent the (2+2) into the numerator, thus leading to a different answer. 8/2(2+2)=1.