Can You Solve This?

[00:00:00]This is a super viral problem, which has shook the internet.

[00:00:04]Evaluate the following expression. What do you think?

[00:00:08]Is the answer 1, 9, or something else?

[00:00:12]Many people make a common mistake when entering this expression into a calculator.

[00:00:18]Since calculators cannot display stacked fractions easily, people often rewrite the expression as 9 - 3 / 1 / 3 + 1.

[00:00:29]However, this notation is dangerous because it no longer clearly shows that 1/3 is supposed to be treated as a single fraction.

[00:00:38]Once the grouping is lost, the calculator may interpret the expression differently from what was originally intended. The calculator sees it as 3 / 1 / 3.

[00:00:51]Since all the operations are divisions, it evaluates them from left to right.

[00:00:56]First, it calculates 3 / 1, which gives 3.

[00:01:00]Then it divides that result by 3, giving 1.

[00:01:05]The expression would then become 9 - 1 + 1, which equals 9.

[00:01:11]This is why some calculators or people incorrectly arrive at the answer 9. The correct way to enter the expression is to make sure that 1/3 remains grouped together. In other words, the expression should be interpreted as 9 - 3 / open bracket 1 / by 3 close bracket + 1.

[00:01:33]Once the fraction is properly grouped, the meaning of the original expression is preserved. Now we can evaluate it according to the standard order of operations called PEMDAS or BODMAS.

[00:01:47]First come parentheses or brackets, then exponents, then multiplication and division, and finally addition and subtraction.

[00:01:58]Another important detail is that multiplication and division have equal priority, and addition and subtraction also have equal priority.

[00:02:07]Whenever operations have the same priority, we evaluate them from left to right.

[00:02:13]Looking at our expression, there are no brackets to simplify and no exponents to evaluate.

[00:02:21]The first operation that must be performed is the division.

[00:02:25]We need to calculate 3 / 1/3.

[00:02:28]Many students find this step confusing, but dividing by a fraction is the same as multiplying by its reciprocal.

[00:02:36]The reciprocal of 1/3 is 3.

[00:02:39]Therefore, 3 / 1/3 becomes 3 * 3.

[00:02:45]Multiplying these numbers gives 9. So, the original expression now simplifies to 9 - 9 + 1.

[00:02:54]9 - 9 = 0.

[00:02:57]So, the expression becomes 0 + 1.

[00:03:00]Therefore, the value of the entire expression is 1. This is the correct answer. That is why parentheses and proper notations are so important in mathematics. Like, share and subscribe.

[00:03:13]So good.

[00:03:21]>> [music]