What is the correct answer of [6/2(2+1)], 1 or 9?
Originally answered for “What is the correct answer of [6÷2(2+1)], 1 or 9?”
It is a typical divisive question, there is not a single true answer, it depends on your previos knowledge and your belief.
Many people use BOMDAS, if they follow the B - O - M - D - A - S rule mechanically (ignoring that D-M and A-S are interchangeable), the result is 1.
More advanced people, who use BOMDAS are taking M-D and A-S interchangeability (sometimes referred as PEMA) will come to 9 as a result, because within equal precedence operators the evaluation order is left-to-right. Google and some other calculators are also using this method. But that’s not the full picture.
Some people notice, that ÷ is an old sign for division, and it had higher precedence than * or /. That’s true, but as of today, its precedence is the same as * or /.
If you write “2(1+2)”, it is different from “2*(1+2)”, because it omits the multiplication sign. It suggests that these factors “stick together”, this operation has higher precedence than others within the same precedence level. It’s called juxtaposition. Using this observation the result is still 1. Many scientific calculators are also using this rule.
Finally, mathematicians etc. who are working with formulas generally treat the division as if it was fraction, therefore they put the “2(2+1)” part into the denominator, automatically. For mathematicians, the formula is inconsistent, but the contradiction can be resolved, and the result is 1.
Bottom line: Since there’s a heated debate about the result, let’s accept those opinion who are expert of this field. The practice of the mathematicians say that this formula should be interpreted as “6 / (2 * (2 + 1))”, so the result is 1.
Disclaimer: my degree is programmer-mathematician, I learned math in uncountable hours at uni.
Originally answered for “What is the correct answer of [6÷2(2+1)], 1 or 9?”
It is a typical divisive question, there is not a single true answer, it depends on your previos knowledge and your belief.
Many people use BOMDAS, if they follow the B - O - M - D - A - S rule mechanically (ignoring that D-M and A-S are interchangeable), the result is 1.
More advanced people, who use BOMDAS are taking M-D and A-S interchangeability (sometimes referred as PEMA) will come to 9 as a result, because within equal precedence operators the evaluation order is left-to-right. Google and some other calculators are also using this method. But that’s not the full picture.
Some people notice, that ÷ is an old sign for division, and it had higher precedence than * or /. That’s true, but as of today, its precedence is the same as * or /.
If you write “2(1+2)”, it is different from “2*(1+2)”, because it omits the multiplication sign. It suggests that these factors “stick together”, this operation has higher precedence than others within the same precedence level. It’s called juxtaposition. Using this observation the result is still 1. Many scientific calculators are also using this rule.
Finally, mathematicians etc. who are working with formulas generally treat the division as if it was fraction, therefore they put the “2(2+1)” part into the denominator, automatically. For mathematicians, the formula is inconsistent, but the contradiction can be resolved, and the result is 1.
Bottom line: Since there’s a heated debate about the result, let’s accept those opinion who are expert of this field. The practice of the mathematicians say that this formula should be interpreted as “6 / (2 * (2 + 1))”, so the result is 1.
Disclaimer: my degree is programmer-mathematician, I learned math in uncountable hours at uni.
2023-01-15 21:37:41
Там же почитайте комментарии математиков 😁
2023-01-15 19:03:27
Пробежался, половина пишет что запись неточная.
2023-01-15 19:08:36