Written by Colin+ in basic maths skills.
As you might know (if you've spotted the big yellow bar above), I'm training for the Berlin Marathon in memory of my grandmother (you can support me - and the Alzheimer's Society - by sponsoring me here). One of the perks of marathon training is that I get to eat all sorts of puddings that wouldn't be good for me if I wasn't pounding out 40-odd miles a week.
But every so often, I pick up the ice cream tub and remember the days of carefully measuring out portions, and I noticed something: ice cream tubs are measured in grams. The recommended portion sizes, at least for this brand of ice cream, are measured in millilitres.
Which is a bit silly: the only way I know of to reliably measure millilitres is to melt the ice cream down, which kind of defeats the object. If only I could find a way to convert between mass and volume.
I scanned the packaging, in vain, for a measure of density. However, there's a handy table to help me: on the back of the tub, there are the nutritional values. A 125ml serving, it says, contains 2.4 grams of protein. It also gives details per 100g: 3.2g of protein. Aha! I could - if I needed to, figure out how much a portion weighs using proportion! It's time for the Table of Joy!
I know about grams of ice cream and grams of protein. I'm interested in "per 100g" and "per portion", so I can set my table up like this:
grams ice cream | grams protein | |
---|---|---|
per 100g | 100g | 3.2g |
per portion | ? | 2.4g |
My Table of Joy sum is "multiply diagonally and divide by the other number", or $2.4
\times 100 \div 3.2$.
You could, of course, reach for a calculator here, but I want to show you how to do it without. You can work out $2.4 \times 100$ by moving the dot two spaces to the right, filling in the gap with a 0, and saying "that's 240." But how do you divide that by 3.2?
I'd recommend moving both of the dots to the right to get $2400 \div 32$. And you know your 32 times table, right? Doesn't everyone? Oh. Well, ok, how about you spot that both numbers in the division sum are even and halve them both to get $1200 \div 16$. You can do the same again to get $600 \div 8$. Keep going: $300 \div 4 = 150 \div 2 = 75$.
So, a portion of ice cream works out to be - roughly - 75 grams. And my trusty kitchen scales will let me measure that (once I remember to take away the weight of the bowl, of course.)
MathbloggingAll
Basic maths skills: the ice cream portion http://t.co/0SegdQ5fGn
Joshua Zucker
I like your discovery here — and I wish American ice cream containers had such a thing! We generally only get per-serving nutrition information, and we do indeed get confusing serving sizes in terms of hard-to-measure quantities at times.
I would do the calculation here with “2.4/3.2 = 24/32 = 3/4” to make it easy and intuitive to see the result being 3/4 of 100, or 75.
Colin
Thanks! It’s always interesting to see what different people find intuitive (and in fact, your way is probably the way I did it mentally). Part of this is a sneaky campaign to get students working with fractions without realising it ðŸ˜‰
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