Question

I'm working on conversions and can't ever figure out when I need to multiply and when I need to divide.

For example - 50L = ? gal

I know 3.79 L = 1 gal but do I divide or multiple to get the correct answer?

Or, 2 mi = ? m

I know 1 m = 3.28 ft and 5280 ft = 1 mile, but I don't know in what order to use those, or how to figure out HOW to use them.

Is there an easy rule of them to know if you use multiplication or division?

Thank you.

Answer 1

watch the units. They cancel out just like numbers.

3.79L = 1gal, so
3.79L/1gal = 1
1gal/3.79L = 1

you can always multiply by 1 without changing anything, so use the fraction which cancel the undesired units.

50L * 1gal/3.79L = 50/3.79 gal

see? The L units canceled out, leaving just gals.

Answer 2

easy rule: keep your units in the equation:
50L*( ) so you want L to divide out, so you multiply
50L*(1gal/3.79L)= 50/3.79 gallons

2 mile( ) you need miles to divide out, so you 2miles(5280ft/mile) and that give you feet. But you want more, you want meters
2*5280ft( ) ft has to divide out, so
2*5280ft(1m/3.28ft) and then you have it.