Textbooks often used ÷ to denote the divisor was the whole expression to the right of the symbol. For example, a textbook would have written:

But here’s my counter-point: a calculator is not going to say “it’s an ambiguous expression.” Just as courts rule about ambiguous legal sentences, calculators evaluate seemingly ambiguous numerical expressions. So if we take the expression as written, what would a calculator evaluate it as? as shown in the image to the right. Note that the denominator of a fraction cannot be 0, as it would make the fraction undefined. Fractions can undergo many different operations, some of which are mentioned below.The result is a (mixed) fraction reduced to it’s simplest form. Also a table with the result fraction converted in to decimals an percent is shown. This process can be used for any number of fractions. Just multiply the numerators and denominators of each fraction in the problem by the product of the denominators of all the other fractions (not including its own respective denominator) in the problem. EX: For years I’ve heard from people/math professors how this problem is a waste of time, and that no mathematician would talk about it. Now these same people are trying to tell everyone what the right answer is. I wish they would have researched the problem and its history carefully like I did. Please do share my videos with them–many times they realize their mistake. The in-line expression also omits the parentheses of the divisor. This is like how trigonometry books commonly write sin 2θ to mean sin (2θ) because the argument of the function is understood, and writing parentheses every time would be cumbersome.

Suppose it was 1917 and you saw 8÷2(4) in a textbook. What would you think the author was trying to write?

Curriculum

Since some people think the answer is 16, and others think it is 1, many people argue this problem is ambiguous: it is a poorly written expression with no single correct answer. the decimal would then be 0.05, and so on. Beyond this, converting fractions into decimals requires the operation of long division. The first multiple they all share is 12, so this is the least common multiple. To complete an addition (or subtraction) problem, multiply the numerators and denominators of each fraction in the problem by whatever value will make the denominators 12, then add the numerators. EX: Mind Your Puzzles is a collection of the three “Math Puzzles” books, volumes 1, 2, and 3. The puzzles topics include the mathematical subjects including geometry, probability, logic, and game theory. This gives the result of 1. This is not the correct answer that calculators will evaluate; rather it is what someone might have interpreted the expression according to older usage.