Question
Ben had 3/4 of a chocolate bar and gave 1/2 of what he had to his sister. Using the following model, determine the fraction of the whole chocolate bar Ben gave to his sister. The model shows 3 out of 4 shaded squares on the left and 3 out of 4 squares shaded on the right.
Answers
GPT-4o mini
To find the fraction of the whole chocolate bar that Ben gave to his sister, we start with the fraction of the chocolate bar that Ben had, which is \( \frac{3}{4} \).
Next, we need to determine how much of that \( \frac{3}{4} \) he gave to his sister. He gave away \( \frac{1}{2} \) of what he had.
To calculate the amount he gave away, we take \( \frac{1}{2} \) of \( \frac{3}{4} \):
\[
\text{Amount given to sister} = \frac{1}{2} \times \frac{3}{4}
\]
To multiply these fractions, we multiply the numerators and the denominators:
\[
\frac{1 \times 3}{2 \times 4} = \frac{3}{8}
\]
So, Ben gave \( \frac{3}{8} \) of the whole chocolate bar to his sister.
Thus, the fraction of the whole chocolate bar that Ben gave to his sister is \( \frac{3}{8} \).
Next, we need to determine how much of that \( \frac{3}{4} \) he gave to his sister. He gave away \( \frac{1}{2} \) of what he had.
To calculate the amount he gave away, we take \( \frac{1}{2} \) of \( \frac{3}{4} \):
\[
\text{Amount given to sister} = \frac{1}{2} \times \frac{3}{4}
\]
To multiply these fractions, we multiply the numerators and the denominators:
\[
\frac{1 \times 3}{2 \times 4} = \frac{3}{8}
\]
So, Ben gave \( \frac{3}{8} \) of the whole chocolate bar to his sister.
Thus, the fraction of the whole chocolate bar that Ben gave to his sister is \( \frac{3}{8} \).