I forget how I can get the answer by converting all at once

## Farmer Joe says "I'll trade with you 3 horses for 20 pigs, 4 frogs for 1 duck, 3 cows for 8 pigs and 35 ducks for 4 horses." how many frogs for 1 cow?

# 1 Answer

Hi, Mathalina.

Rewriting each of these conversions as fractions will help you see the process better.

3 horses
4 frogs 3 cows
35 ducks

20 pigs 1 duck 8 pigs 4 horses

They are asking for the number of frogs, given 1 horse. Start by writing 1 horse over 1 (as a fraction). Then find a fraction in the list above that has either a horse, frog, or duck in its expression. Keep in mind, you want to have frogs at the end of the problem. Also, it's okay to write the fractions "upside down."

1 horse
35 ducks 4 frogs

1 4 horses 1 duck

Now multiply these fractions together:

1 horse •
35 ducks • 4 frogs

1 4 horses 1 duck

Do you see that horse cancels with horses and ducks cancels with duck?

This leaves us with:

1 • 35 • 4 frogs

1 4 1

When we multiply these (yes, you may cancel the 4's), we get 35 frogs.

In chemistry, this is called the "factor-label method." I suppose it works for farm animals too. ;-)