A baker decorates 424242 cupcakes in 303030 minutes. She decorates cupcakes at a constant rate. How many cupcakes can the baker decorate per minute?

Hey. Let me help you on this one.

In this problem, we have a constant rate of baker decorating cupcakes, and it gives us both values - cupcakes, and minutes.

In order for us to solve this question, we will need to simplify this ratio in order to make denominator, which is going to be 303030 minutes, equal to one. This can be done by property of division.

I will also be attaching an image that might help you with your studies. I recommend looking over it if you have trouble simplifying ratios. 

Alright, let's set up a ratio for this problem. It should be cupcakes over minutes, since this is the rate of change and our main focus here is the time. We are also doing this because amount of minutes is less than the amount of cupcakes, meaning that simplification will be much easier and actually make more sense.

[tex] \frac{424242}{303030} [/tex]

So, now that we have this ratio, all we have to do is simplify it. We need to have 3030303 simplified into one; however, all we do with denominator has to be done with the numerator - the number above. 

In order for us to transform 303030 into one, we will need to divide it by 303030. This division will simplify the denominator, but we must not forget about numerator as well.

[tex]424242/303030=42/30=1.4[/tex]

Awesome. Now, we have the fixed ratio of 1.4 over 1, or simply 1.4 cupcakes per minute.

Answer: Baker will decorate 1.4 cupcakes per minute if the constant rate is kept.