Step by step
The question
Question: 3/4 cup of sugar for 1/2 cake: how much is that per cake?
A unit rate says how much for 1 cake.
Per cake means: divide by the cakes.
1 Write the rate
Cups divided by cakes: 3/4 ÷ 1/2.
Careful!
Not the other way round.
That would be cakes per cup.
2 Divide
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 1/2 becomes 2, and divide becomes times.
Before we multiply, we make the numbers smaller.
2 on top and 4 at the bottom both divide by 2.
A top and a bottom divided by the same number: the answer stays the same.
So we multiply smaller numbers.
To multiply fractions, we do top times top, and bottom times bottom.
A whole number is a fraction over 1.
3 times 1 is 3.
2 times 1 is 2.
So the unit rate is 3/2 cups of sugar per cake.
3 Check
Let's check: 3/2 cups of sugar per cake, for 1/2 cake.
3/2 times 1/2 is 3/4.
That is the cups of sugar we started with.
So the answer is right!
Let's look back.
First: write the rate.
Then: divide.
Last: check.