Answer:

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 \ frac{1}{2}.

A fraction of 1 over 4 is \ frac{1}{4}.

Ursula has \ frac{1}{2} cup of butter available to make brownies, and we know that she uses \ frac{1}{4} cup of butter to make a batch of brownies.

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

  • How to divide two fractions.
  • If we compare two fractions with the same numerator, the fraction with the smaller denominator is the largest one.

Therefore, \ frac{1}{2} is larger than \ frac{1}{4}.

Part A

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

Because Ursula uses frac{1}{4} cup of butter to make a batch of brownies, and she has frac{1}{2} cup of butter, then she needs to know how many times does frac{1}{4} fit into frac{1}{2} (we already know that \ frac{1}{2} is larger than \ frac{1}{4}), or

frac{1}{2} √∑ frac{1}{4} which is frac{frac{1}{2}}{frac{1}{4}}, or, equivalently:

\ frac{1}{2} * frac{4}{1} = frac{4}{2} = 2.

That is, there are two frac{1}{4} into \ frac{1}{2}. So, if Ursula can make one batch of brownies with frac{1}{4} cup of butter, then she can make two batches of brownies with two frac{1}{4} cup of butter.

We can see that two frac{1}{4} is \ 2 * frac{1}{4} = frac{2}{4} = frac{1}{2}, which gives us the total of butter available or \ frac{1}{4} + frac{1}{4} = frac{1+1}{4} = frac{2}{4} = frac{1}{2}.

Then, the answer is that Ursula can make two batches of brownies with the frac{1}{2} cup of butter available.

Part B

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 \ frac{1}{4} 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 frac{1}{2} cup of butter available, and we can appreciate from the sketch that she only has two \ frac{1}{4} or two quarters of butter, which is equivalent to \ frac{2}{4} = frac{1}{2} or a half of a cup of butter, because frac{1}{4} + frac{1}{4} = frac{2}{4} = frac{1}{2}.

So, she can make two batches of brownies with the available butter because she uses frac{1}{4} cup of butter to make each one, which confirms the result obtained in the Part A.