A fairly common question arises when students learn to multiply or divide fractions and decimals: They discover that multiplication, which always used to make numbers larger (2, multiplied by 3, becomes 6), now can make them smaller (2, multiplied by 1/2, becomes 1). How can that be? Here we’ll look at a few answers we’ve …
(A new question of the week) Let’s look at a quick question from mid-September, that had a number of different answers. In some ways, this is an easy question; but we’ll take it a little further, so keep reading to the end.
I’ll finish this series on place value and writing numbers, with a question that’s not quite as simple as you might think: why we use commas and decimal points as we do. Americans may be surprised at some of the answers – and some of the questions.
Last time we looked at how to convert a number between decimal and word form. Now we’ll move into some tricky cases such as where to use “and” or a hyphen, to eliminate ambiguity.
We’ve been looking at the place value concept, and writing number in expanded form(s); but how about the word form of decimals? This can be confusing at several points. We’ll start with reading a number and writing its word form, and then do the reverse.
A concept regularly taught along with place value is “expanded form”, a way to write a number that displays each place separately. As we’ll see, there is considerable variation in terminology here, so parents may have to check what form a teacher wants, rather than look it up and expect a single answer!
(An archive question of the week) Last time we ended with questions about writing (or ignoring) zeros at the end of a decimal. I didn’t have room for one more question, so I’ll put it here.
Last time we looked at the concept of place value as children first learn it, with whole numbers. Here, we’ll expand that to look at decimals.
We’ll be looking at various aspects of place value, starting here with the basic concepts. As soon as you learn to write numbers beyond 10, you have to start understanding this concept; so we have to begin at a concrete level and move gradually to something more abstract.
We have often received questions about things called “Order of Operations problems”, or some similar name. Generally, what that means is simply that they are puzzles to give lots of practice evaluating expressions using the order of operations. I have collected a few quite different puzzles in this broad category.