Step by step
The question
Question: 1 and 1/3 cups of water for 2/3 batch: how much is that per batch?
A unit rate says how much for 1 batch.
Per batch means: divide by the batchs.
1 Write the rate
Cups divided by batchs: 1 and 1/3 ÷ 2/3.
Careful!
Not the other way round.
That would be batchs per cup.
2 Divide
1 and 1/3 is a mixed number.
Each whole one is 3/3.
So we do 1 times 3, plus 1.
The bottom stays 3.
1 times 3 plus 1 is 4.
So it is 4/3.
Dividing by a fraction is the same as times its flip.
Keep the first number.
Change divide to times.
Turn the second fraction upside down.
So 2/3 becomes 3/2, and divide becomes times.
Before we multiply, we make the numbers smaller.
4 on top and 2 at the bottom both divide by 2.
3 on top and 3 at the bottom both divide by 3.
A top and a bottom divided by the same number: the answer stays the same.
So we multiply smaller numbers.
2 times 1 is 2.
So the unit rate is 2 cups of water per batch.
3 Check
Let's check: 2 cups of water per batch, for 2/3 batch.
2 times 2/3 is 4/3.
That is the cups of water we started with.
So the answer is right!
Let's look back.
First: write the rate.
Then: divide.
Last: check.