Pop quiz – what’s one half divided by one quarter?
No, you’re not allowed to use a calculator, or or phone a friend…
Stuck? OK, it’s 2.
“What?” I hear you cry, “But that doesn’t make sense. We’ve divided something small by another small thing, that should make an even smaller thing, surely.”
And, of course, you’d be wrong. If you already knew the answer, or you’ve already seen this February’s Channel 4 documentary The Kids Don’t Count, then read on with a smug smile. If you were genuinely stuck by the question, let us demystify division for you.
First, division isn’t about making things smaller. Sure, that’s often what happens: when you divide 10 by 2 you get 5. But what does it mean to divide?
The division sentence A/B = C can be described in two ways:
- We’re taking A and splitting it into B groups of equal size
- We’re taking A and and finding out how many groups of size B it contains.
This sounds like splitting hairs, but the former is known as ‘partitioning’ division, the latter ‘quotative’ division. These aren’t terms that Maths-Whizzers need to know, but they can help show that division isn’t about making things smaller.
Let’s go back to our teaser. If you were stuck, then think of the question this way – “How many groups of one quarter are in one half?” You should know that there are two halves in a whole and four quarters in a whole, so there are two quarters in one half, which means the answer is 2!
Simple, no? Maybe not yet, but it will be.
What if we reverse the question: “What is one quarter divided by one half?”. Here the issue isn’t so straightforward. One half does not ‘fit’ completely into one quarter, but if we ask ourselves how much of that half can we squeeze into that quarter, we see the answer is one half. In other words, there’s half of a half in a quarter.
One quarter divided by one half equals one half!
Now we’re rolling!
You need a simple rule for dividing fractions, not simply an understanding of the principles. So remember this process below and forever look upon division of fractions with confidence.
Step 1. Turn the second fraction (the one you want to divide by) upside-down (this is now a reciprocal).
Step 2. Multiply the first fraction by that reciprocal
Step 3. Simplify the fraction (if required)
The Mathisfun page below goes into greater detail, explaining why this method works, so check it out to get all the info.
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