Question
Eduardo owned 6/7 of a family business and sold 1/5 of the business to his son. Can you find out what portion of the business Eduardo still owns?
Answers
GPT-4o mini
To find out what portion of the business Eduardo still owns after selling \( \frac{1}{5} \) of it to his son, we can follow these steps:
1. **Determine the portion sold**: Eduardo owned \( \frac{6}{7} \) of the business. He sold \( \frac{1}{5} \) of this portion to his son. To find out how much of the total business he sold, we calculate:
\[
\text{Portion sold} = \frac{1}{5} \times \frac{6}{7} = \frac{6}{35}
\]
2. **Calculate the remaining portion**: Next, we subtract the portion sold from what Eduardo originally owned:
\[
\text{Remaining portion} = \frac{6}{7} - \frac{6}{35}
\]
To perform this subtraction, we need a common denominator. The least common multiple of 7 and 35 is 35. We can convert \( \frac{6}{7} \) to a fraction with a denominator of 35:
\[
\frac{6}{7} = \frac{6 \times 5}{7 \times 5} = \frac{30}{35}
\]
Now we can perform the subtraction:
\[
\frac{30}{35} - \frac{6}{35} = \frac{30 - 6}{35} = \frac{24}{35}
\]
Therefore, the portion of the business that Eduardo still owns is \( \frac{24}{35} \).
1. **Determine the portion sold**: Eduardo owned \( \frac{6}{7} \) of the business. He sold \( \frac{1}{5} \) of this portion to his son. To find out how much of the total business he sold, we calculate:
\[
\text{Portion sold} = \frac{1}{5} \times \frac{6}{7} = \frac{6}{35}
\]
2. **Calculate the remaining portion**: Next, we subtract the portion sold from what Eduardo originally owned:
\[
\text{Remaining portion} = \frac{6}{7} - \frac{6}{35}
\]
To perform this subtraction, we need a common denominator. The least common multiple of 7 and 35 is 35. We can convert \( \frac{6}{7} \) to a fraction with a denominator of 35:
\[
\frac{6}{7} = \frac{6 \times 5}{7 \times 5} = \frac{30}{35}
\]
Now we can perform the subtraction:
\[
\frac{30}{35} - \frac{6}{35} = \frac{30 - 6}{35} = \frac{24}{35}
\]
Therefore, the portion of the business that Eduardo still owns is \( \frac{24}{35} \).