Question

Jose is baking a cake. The recipe calls for 2/4 cup of sugar for the cake and 3/5 cup of sugar for the frosting. How many cups of sugar will he need in all?(1 point)
Responses

2 2/20
2 2/20

159
15 ninths

1110
11 tenth
Question 3
True or False: When adding or subtracting fractions, you must always have a common denominator.(1 point)
Responses

True
True

False
False

Answer 1

To determine the total amount of sugar needed for both the cake and the frosting, we will add the two fractions:

1. Sugar for the cake: \( \frac{2}{4} \)
2. Sugar for the frosting: \( \frac{3}{5} \)

First, simplify \( \frac{2}{4} = \frac{1}{2} \).

To add the fractions \( \frac{1}{2} \) and \( \frac{3}{5} \), we need a common denominator. The least common multiple of 2 and 5 is 10.

Convert \( \frac{1}{2} \) to have a denominator of 10:
\[
\frac{1}{2} = \frac{5}{10}
\]

Convert \( \frac{3}{5} \) to have a denominator of 10:
\[
\frac{3}{5} = \frac{6}{10}
\]

Now add the fractions:
\[
\frac{5}{10} + \frac{6}{10} = \frac{11}{10}
\]

Converting \( \frac{11}{10} \) into a mixed number gives:
\[
1 \frac{1}{10}
\]

So, in total, Jose needs \( 1 \frac{1}{10} \) cups of sugar.

---

For the second question:

True or False: When adding or subtracting fractions, you must always have a common denominator.

The answer is **True**. When adding or subtracting fractions, it is necessary to have a common denominator to combine them correctly.

---

To summarize:
1. Total sugar required: \( 1 \frac{1}{10} \) cups of sugar.
2. For the common denominator question: **True**.