Question

For Aliyah’s graduation party, her mom made her a chocolate cake. Her siblings ate 1/4
of the cake, and her friends ate 2/3
of the cake. How much of the cake was left?

Desmos Scientific Calculator

(1 point)
Responses

3/4
3 fourths

1/2
1 half

1 12
1 over 12

5/6

plz give me a correct answer

Answer 1

are you sure

Answer 2

To find out how much of the cake is left, we first need to determine how much cake was consumed by Aliyah's siblings and friends.

1. Aliyah's siblings ate \( \frac{1}{4} \) of the cake.
2. Her friends ate \( \frac{2}{3} \) of the cake.

To find the total amount of cake eaten, we need to add these fractions:

\[
\text{Total eaten} = \frac{1}{4} + \frac{2}{3}
\]

To add these fractions, we need to find a common denominator. The least common denominator (LCD) of 4 and 3 is 12.

Now, we can convert each fraction:

\[
\frac{1}{4} = \frac{3}{12} \quad (\text{multiply the numerator and denominator by 3})
\]
\[
\frac{2}{3} = \frac{8}{12} \quad (\text{multiply the numerator and denominator by 4})
\]

Now we can add the converted fractions:

\[
\frac{3}{12} + \frac{8}{12} = \frac{11}{12}
\]

So, \( \frac{11}{12} \) of the cake has been eaten.

To find out how much of the cake is left, we subtract the amount eaten from the whole cake (which is \( 1 = \frac{12}{12} \)):

\[
\text{Cake left} = 1 - \frac{11}{12} = \frac{12}{12} - \frac{11}{12} = \frac{1}{12}
\]

Therefore, the amount of cake left is **\( \frac{1}{12} \)**.

Answer 3

Yes, the calculations can be summarized as follows:

1. **Calculate the amount consumed by Aliyah's siblings and friends:**
- Siblings ate: \( \frac{1}{4} \)
- Friends ate: \( \frac{2}{3} \)

2. **Add the two fractions:**
- Find a common denominator (the least common denominator for 4 and 3 is 12):
- Convert \( \frac{1}{4} \) to \( \frac{3}{12} \)
- Convert \( \frac{2}{3} \) to \( \frac{8}{12} \)

So now we have:
\[
\frac{1}{4} + \frac{2}{3} = \frac{3}{12} + \frac{8}{12} = \frac{11}{12}
\]

3. **Calculate the amount of cake left:**
- Start with the whole cake, which can be represented as \( 1 \) or \( \frac{12}{12} \).
- Subtract the amount eaten:
\[
\text{Cake left} = 1 - \frac{11}{12} = \frac{12}{12} - \frac{11}{12} = \frac{1}{12}
\]

So, the correct answer is indeed **\( \frac{1}{12} \)** of the cake is left.