Converting rates! Need math help...(Before my brain explodes!)

[Whitney in KY]

I am trying to help dd with her math. She is converting rates. I am drawing a blank on this one...

The direction says to convert each rate to an equivalent rate.
0.45 kilograms per pound to grams per pound.

I understand how to do this using common sense, but I can't figure out how to write it using conversion factors...Am I making this too hard?

Thanks,
Whitney

[Claire]

1,000 grams in a kilogram. To convert kilograms to grams, you need to multiply by 1,000.

0.45 kilogram per pound x 1,000 = 4,500 grams per pound

I think? (math is not my forte!)

[Laura Corin]

I checked Calvin's (British) text book, which is largely metric. It introduces imperial units (more or less as a curiosity) but converting from metric to imperial and back is an end-of-chapter activity - optional.

Personally, I think you need rule-of-thumb conversion ability (a kilo is roughly two pounds, a metre is a little longer than a yard) but anything else you can look up when the time comes. What's much more important is explaining how metric relates internally: how many grams in a kilo, mililitres in a litre. etc.

Not much help, I'm afraid. Feel free to ignore my rant.

Laura

[Herding Cats in NC]

I think the best way to teach this is by using dimensional analysis. It's the easiest way to do conversions and make sure that you have them correct. Plus, when your dd goes on to Chemistry or Physics it'll be very helpful. You want to set up your problem written as a fraction:
0.45 kg
lb

As Claire said, 1000 g = 1 kg. So (sorry, you'll have to ignore the white dots; it's the only way I could get the format close):
0.45 kg x 1000 g = 450 g/lb
lb............1 kg
Cancel out your kgs, and you're left with g/lb. Since that's what you're trying to find, you know you've got it set up correctly.

Now, if you had to change 25 kg per hour to g per minute, you do this:
25 kg x 1000 g x 1 hr = 416.67 g/min
hr........ 1 kg ... 60 min.

I hope this makes sense. It may seem confusing, but it really is super easy once you get used to it. I always tell my son that dimensional analysis is a beautiful thing. He mostly rolls his eyes at that :rolleyes:.

[Whitney in KY]

That is exactly the way I needed to see it.
Whitney

[Carol in Cal.]

I think the best way to teach this is by using dimensional analysis. It's the easiest way to do conversions and make sure that you have them correct. Plus, when your dd goes on to Chemistry or Physics it'll be very helpful. You want to set up your problem written as a fraction:
0.45 kg
lb



Yes, this is what I do with DD as well. It's by far the best way to check your work, and as quoted is used a lot in chemistry and physics. In chemistry, the conversions are multiple and just go on and on, so this is a crucial skill to get straight now. I would say that DD doesn't 'get it' yet, and there is much eye rolling when I insist on walking her through it, but I know that it will pay off down the road.