What is a Fraction, Really?

(An archive question of the week) One of the things I have learned as a Math Doctor is that it can be dangerous looking up a definition online. Sources vary — not because they are wrong, but because definitions depend on context, so you can easily find what appear to be contradictions because they refer …

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Dividing Fractions: How and Why

Fractions have always given students trouble, and we have had many questions about working with them. Even looking only at division of fractions, I have had to restrict my attention to a few sample answers. These show the reasons for the standard method, presented in a variety of ways, together with some alternative methods.

Challenging Rate Questions

(New question of the week) A conversation last week went through a number of interesting questions, starting with a couple on percentages, and moving into some that I would call rate questions. I will extract these, which I think will be useful for others. (The rest could, too, but there was just too much there …

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Mathematical Thinking Solves an Operation Puzzle (Or Not)

(Archive problem of the week) Having just written about sequence puzzles, which sometimes can be solved mathematically, and sometimes are just psychological tests, I want to show a different kind of puzzle that I ran across while searching for those. At first, it looks like mere guess-and-check; then we find it can be solved easily …

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How to Convert a Fraction to a Decimal – and Why

(Archive Question of the Week) Fractions are a frequent source of questions from elementary students. I plan to devote several posts to various aspects of this, from using a common denominator to add fractions, to flipping and multiplying to divide fractions, to converting between improper fractions and mixed numbers. Here, I want to look at …

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Rounding: Contextual Issues

Previously, I discussed how to round a number to the nearest whole number [or tenth, ten, etc.]. I focused there on what to do when you are simply told to do it — what “round to nearest” means, and how that determines whether you round a particular number up or down. I also pointed out …

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Kids Ask About Even and Odd Numbers

(Archive Question of the Week) Although high school and up probably constitute the majority of our questions, I always enjoy answering younger children. For today’s look at the archives, I thought I’d look at two such questions, both from 1999, and very memorable. The first is almost certainly the youngest “patient” we’ve ever had, and …

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What Operation Was She Doing?

(Archive question of the week) For Wednesdays, I plan to find a single interesting question from the past and discuss it. One of the things I’ve enjoyed about Ask Dr. Math is getting questions I’d never have thought of on my own, but which lead to some fascinating ideas. Here is an old favorite from …

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