And once we understand this, it is relatively easy to see what a whole group (or serving) must be: In this case, we are saying that our total amount is only a fraction of the entire group or part, and we want to find out what size is the whole thing. Or, in the little sister’s first example:īut life gets more confusing when the number of parts is a fraction: This is easy to understand when we work with whole numbers: In partitive division, we imagine cutting our total amount into a given number of parts: Let’s look at two common mental models - partitive division and measurement division - to see how the sister could have divided her pie… Partitive Division: What Size Are the Groups? How can anyone answer a question that doesn’t make sense? Of course the big sister cannot divide a pie into one-quarter servings, because each piece, no matter what size, is by (unstated) definition a single serving. Like any ill-posed problem, this question stumps her big sister. “But,” she asks, “how do you cut a pie into one-quarter pieces?”
HOW TO TYPE FRACTIONS IN WORD 2017 HOW TO
She has (subconsciously) defined her “group” as one piece of pie - that is, as one serving - and easily sees how to divide the pie into 4 “groups” or pieces. In the comment question, the younger sister is only thinking of the first option: the total amount divided by the number of groups. Your answer will be the other number - the one you didn’t use.Īgain, children typically learn division by thinking about whole-number groups: You start from the end, the total amount or the final size, and divide by EITHER the scale factor or the original amount. “times the size of” = Ĭhildren typically learn to multiply whole numbers by thinking of groups: When you multiply using the mad scientist’s ray gun, you have:
How would you explain the above in a manner which makes sense?ĭivision is the inverse of multiplication, which means it is like doing multiplication backwards.
The young one isn’t convinced, and asks how on earth it is possible to divide something by a quarter - she reasons you can cut a pie into 4 pieces, but how do you cut a pie into one quarter pieces? The elder one was at a loss, and simply told her to “accept it” and move on. The elder girl replies without skipping a heartbeat: you simply invert the 1/4 to become 4/1 and hence 1/2 times 4 equals 2. Incidentally, this reminds me of a scene from a Japanese anime, where a young girl gets her elder sister to explain why 1/2 divided by 1/4 equals 2. A comment on my post Fraction Division - A Poem deserves a longer answer than I was able to type in the comment reply box.
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