Question
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0. Higher Order Thinking Cindy is using division to write a fraction equivalent to \( \frac{30}{100 .} \) She tried to divide the numerator and denominator by 3 . She got stuck. What advice would you give her?

Ask by Davison Powers. in the United States
Jan 23,2025

Real Tutor Solution

Tutor-Verified Answer

Answer

To simplify \( \frac{30}{100} \), find the GCD of 30 and 100, which is 10. Divide both the numerator and denominator by 10 to get \( \frac{3}{10} \).

Solution

To help Cindy find a fraction equivalent to \( \frac{30}{100} \), we can guide her through the process of simplifying the fraction. 1. **Identify the Greatest Common Divisor (GCD)**: The first step in simplifying a fraction is to find the GCD of the numerator and the denominator. In this case, the numerator is 30 and the denominator is 100. 2. **Calculate the GCD**: The GCD of 30 and 100 can be found by listing the factors: - Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30 - Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100 - The common factors are 1, 2, 5, and 10. The greatest of these is 10. 3. **Divide by the GCD**: Now, we can simplify the fraction by dividing both the numerator and the denominator by their GCD (10): \[ \frac{30 \div 10}{100 \div 10} = \frac{3}{10} \] 4. **Conclusion**: The equivalent fraction to \( \frac{30}{100} \) is \( \frac{3}{10} \). So, the advice I would give Cindy is to find the GCD of the numerator and denominator, which is 10 in this case, and then divide both by that number to simplify the fraction correctly.

Reviewed and approved by the UpStudy tutoring team

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Mind Expander

Hey Cindy! It's great that you're using division to find an equivalent fraction! However, instead of dividing by 3, which doesn't evenly divide both 30 and 100, try using the greatest common divisor (GCD) of the numerator and denominator. In this case, both 30 and 100 can be simplified by dividing them by 10, giving you \( \frac{3}{10} \) instead. Also, remember that simplifying fractions is like playing a game where you're trying to find common factors! Next time, you might want to start by looking for the largest number that both your numerator and denominator share before diving into any divisions. Happy fraction hunting!

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