Question
7. In the pet show, \( \frac{3}{8} \) of the pets are dogs. Of the dogs, \( \frac{2}{3} \) have long hair. What fraction of the pets are dogs with long hair?
Ask by Fernandez Grant. in the United States
Mar 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The fraction of pets that are dogs with long hair is \( \frac{1}{4} \).
Solution
1. The fraction of pets that are dogs is given as \( \frac{3}{8} \).
2. Among the dogs, the fraction with long hair is \( \frac{2}{3} \).
3. To find the fraction of all pets that are dogs with long hair, multiply the two fractions:
\[
\frac{3}{8} \times \frac{2}{3} = \frac{3 \times 2}{8 \times 3} = \frac{6}{24}
\]
4. Simplify the fraction:
\[
\frac{6}{24} = \frac{1}{4}
\]
Thus, the fraction of pets that are dogs with long hair is \( \frac{1}{4} \).
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Mind Expander
To find the fraction of the pets that are dogs with long hair, we start by calculating how many pets are dogs. Since \( \frac{3}{8} \) of the pets are dogs, we take this fraction and then find \( \frac{2}{3} \) of the dogs that have long hair. First, calculate the fraction of pets that are dogs with long hair: \[ \text{Fraction of pets that are dogs with long hair} = \frac{3}{8} \times \frac{2}{3} \] When we multiply these fractions: \[ = \frac{3 \times 2}{8 \times 3} = \frac{6}{24} = \frac{1}{4} \] So, \( \frac{1}{4} \) of the pets are dogs with long hair.
