Division, explained:
Dividing by fractions is often hard to picture, frequently due to the verbiage used to establish division in elementary school. If we have 6 objects, and we divide by 3, we are often told to divide them into three groups" or "divide them into groups of three." Though not wrong, this verbiage makes it unclear what we are doing when we divide by fractions. Think of "divide 6 by 3" as "these 6 objects represent 3 groups; how many are in a single group?" instead. We still naturally arrive at 2 objects per group. However, when dividing by fractions, "6 divided by 1/2" then becomes "these 6 objects represent half a group," and grasping that there are 12 items in a single complete group becomes much easier, and far more natural.
So simple. I wish I'd heard this in 6th grade.
Whoa, that’s neat. I will show it to Ellen, who is having trouble teaching fractions to her GED class.
Wha? When dividing by fractions I was always told to flip them over and then multiply by the resulting fraction (if it’s still a fraction). Thus 6 divided by 1/2 = 6 x 2/1, or 12.
Or 6 divided by 2/3 = (6 x 2)/3 = 9.
That seems simpler than “these 6 objects represent two-thirds of a group,” okay, soo then…what do I do?
the mechanics of the arithmetic is the same either way.
but conceptually, i like “…of a group” a bit better. it’s much easier for me to visualize the rough answer. a little number line pops into my head, the left 2/3 is colored green, the right 1/3 is red, and there’s a 6 under the green. it’s easy to see that there should be a ‘3’ under the red part.
the “divide into groups” method is much harder for me to visualize. i see a line segment 6 units long but there are tick marks every 2/3. i could count the tick marks, i guess. but then i’m adding fractions, which gets ugly.
and, i suspect there’s a quantum-mechanical reason the author wrote this. it’s from a “Q.M. without math” series, and i’m guessing this way of thinking about / is going to be useful when they start talking about spin and charge…
spin and charge
I thought that was what politicians did.
Also rhinoceroses.