Solve for x. (type an integer or a simplified fraction. use a comma to separate answers as needed.)

Ursula can make two batches (2) of brownies with fraction 1 over 2 cup of butter.

Step-by-step explanation:

A fraction of 1 over 2 is .

A fraction of 1 over 4 is .

Ursula has cup of butter available to make brownies, and we know that she uses cup of butter to make a batch of brownies.

We are obviously dealing here with fractions, and we have to remember:

Therefore, is larger than .

How many batches of brownies can Ursula make with fraction 1 over 2 cup of butter?

Because Ursula uses cup of butter to make a batch of brownies, and she has cup of butter, then she needs to know how many times does fit into (we already know that is larger than ), or

÷ which is , or, equivalently:

.

That is, there are two into . So, if Ursula can make one batch of brownies with cup of butter, then she can make two batches of brownies with two cup of butter.

We can see that two is , which gives us the total of butter available or .

Then, the answer is that Ursula can make two batches of brownies with the cup of butter available.

There is a sketch as an attachment of the total of butter that Ursula has to make brownies (see below) labeled Making a Batch of Brownies.

We can divide the cup of butter into four equal parts. Each part is equivalent to of the total of butter available. In other words, we divided the cup of butter into four equal parts.

We also know that Ursula has cup of butter available, and we can appreciate from the sketch that she only has two or two quarters of butter, which is equivalent to or a half of a cup of butter, because .

So, she can make two batches of brownies with the available butter because she uses cup of butter to make each one, which confirms the result obtained in the Part A.