Dividing Decimals: How and Why
We have looked at how we add, subtract, and multiply decimals. Now we’ll conclude with division: what we do, why we do it, and how we don’t really need to do it that way.
Arithmetic
Multiplying Decimals: How and Why
We’ve looked at how to add or subtract decimals. Now let’s move on to multiplication; we’ll look at three answers to the same sort of question.
Adding or Subtracting Decimals: How and Why
Recently a teacher (Hi, Edite!) asked for help teaching how to divide decimals; in particular, she wanted to be able to provide a deeper understanding of the process, giving a good reason for what we do. Here I want to start a long-delayed series on operations with decimals, doing exactly this for all four basic …
What is a Ratio, Really?
A recent question reminded me I hadn’t yet written about the complexity surrounding the definition of ratio (and related terms, like rate and fraction). Here are four questions about the words.
Casting Out Nines: Why It Works
Last week we looked at how to “cast out nines” to check arithmetic, and touched only briefly on its relationship with modular arithmetic and remainders. Here we’ll look at several explanations of why it works, aimed at different levels of students, with varying levels of success..
Casting Out Nines: What and How
This old technique for checking arithmetic is both easy and hard to describe: easy to explain in advanced terms, but hard to explain in elementary terms. We’ll try to do it all here, but a fuller explanation of the “why” will come next week.
Russian Peasant Multiplication: How and Why
In recently discussing Roman numerals, we ran across Egyptian multiplication. An improvement on that method is called the Russian peasant method, and deserves attention.
Arithmetic with Roman Numerals
Have you ever wondered how to add, subtract, multiply, and divide using Roman numerals? On one hand, we’ll give the simple answer that the Romans didn’t actually do what you think; on the other hand, we’ll consider what they actually did.
How Roman Numerals Work
Roman numerals are very different from the “Arabic” system we use; there is no “place value”. And yet, as we’ll see, the two systems have more in common than you might think.
Implied Multiplication 2: Is There a Standard?
This is part 2 of a series of extracts from discussions we have had on whether multiplication implied by juxtaposition is to be done before division (which I call IMF, for Implied Multiplication First). Some people write to us claiming that there is one official correct answer. Are they right?