Fraction problem with mental math

Someone asked me,
How many times does 3/4 fit into 15 6/8?

Here are two ways to solve this:

1) These numbers look awkward, but if I changed them to easier ones, for example
"How many times does 2 fit into 834", then we'd all soon realize that we need to use DIVISION.

So the original problem is solved by fraction division:

15 6/8 ÷ 3/4

Are you ready? Remember how to divide fractions?

2) But wait a minute! These numbers aren't so difficult after all... because 6/8 equals 3/4. Let's use this thinking cap of ours - mental math.

3/4 goes into 1 1/2 two times. Doubling that, we find 3/4 goes into 3 four times. And so to 15... fives times that: 3/4 goes into 15 4 × 5 or 20 times!

And, of course 3/4 goes into 6/8 exactly one time.

So all total 3/4 goes into 15 6/8 exactly 21 times. No leftovers. And that was easy!

On another note, Denise in Illinois has made up a mnemonic poem for kids to remember better the "invert and multiply" rule.

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