Hi Sharon,

This question bothers me also but my reaction is "Why would anyone in their right mind write such a ridiculous expression?" Mathematics is a form of human expression and mathematicians and users of mathematics try very hard to make their expressions clear and precise. This why the rules of precedence (BEDMAS) are important, so that everyone understands that $4 + 3 \times 5$ is $19$ not $35.$ The expression you sent is created to be confusing not to be clear. Using the rules of precedence the value is 12 but the expression itself is not anything anyone would write except to try to confuse you.

In my opinion when teaching students about the rules of precedence we should be asking students to create non ambiguous expressions themselves. Here is an example of what I mean.

Write a mathematical expression to perform the following task.

Add 3 and 7 and multiply the result by 2. Add 4 to the result and then divide the resulting number by 6.

Evaluate the expression. What did you get?
Give your expression to a classmate and ask him or her to evaluate it. Did your classmate get the same result as you did? If not, where is the confusion?

Harley