Question
Find four fractions equivalent to \( \frac{2}{5} \). Choose the correct answer below. A. \( \frac{4}{15}, \frac{6}{10}, \frac{8}{20}, \frac{10}{25} \) B. \( \frac{10}{4}, \frac{15}{6}, \frac{20}{8}, \frac{25}{10} \) C. \( \frac{4}{10}, \frac{6}{15}, \frac{8}{20}, \frac{10}{25} \) D. \( \frac{4}{10}, \frac{6}{15}, \frac{8}{25}, \frac{10}{20} \)
Ask by Fowler Grant. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The correct answer is C: \( \frac{4}{10}, \frac{6}{15}, \frac{8}{20}, \frac{10}{25} \).
Solution
To determine which fractions are equivalent to 2/5, we can multiply the numerator and denominator of 2/5 by the same number k.
For example:
• k = 2: (2×2)/(5×2) = 4/10
• k = 3: (2×3)/(5×3) = 6/15
• k = 4: (2×4)/(5×4) = 8/20
• k = 5: (2×5)/(5×5) = 10/25
Thus, the fractions 4/10, 6/15, 8/20, and 10/25 are all equivalent to 2/5.
The correct answer is option C.
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Extra Insights
To find fractions equivalent to \( \frac{2}{5} \), we can multiply both the numerator and the denominator by the same integer. For example, if we multiply by 2, we get \( \frac{4}{10} \), if we multiply by 3, we get \( \frac{6}{15} \), and so on. Evaluating the options given, we find that \( \frac{4}{10}, \frac{6}{15}, \frac{8}{20}, \frac{10}{25} \) are all equivalent to \( \frac{2}{5} \) since they all simplify back to it! Therefore, the correct choice is C.
