Pregunta
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5. When you divide a unit fraction by a whole number, which statement is true? A. The quotient will be greater than the whole number. B. The quotient will be greater than the unit fraction. C. The quotient will be less than the unit fraction. D. The quotient will be equal to the unit fraction.

Ask by Hall Gordon. in the United States
Mar 13,2025

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The quotient will be less than the unit fraction.

Solución

To solve this problem, let's first define what a unit fraction and a whole number are. - A **unit fraction** is a fraction where the numerator is 1 and the denominator is a positive integer. For example, \( \frac{1}{2}, \frac{1}{3}, \frac{1}{4} \), etc. - A **whole number** is any non-negative integer (0, 1, 2, 3, ...). Now, let's analyze what happens when we divide a unit fraction by a whole number. 1. **Dividing a unit fraction by a whole number**: - Let's take a unit fraction \( \frac{1}{n} \) (where \( n \) is a positive integer) and divide it by a whole number \( m \) (where \( m \) is a positive integer). - The operation can be expressed as: \[ \frac{1}{n} \div m = \frac{1}{n} \times \frac{1}{m} = \frac{1}{n \cdot m} \] 2. **Analyzing the quotient**: - The result \( \frac{1}{n \cdot m} \) is still a fraction where the numerator is 1 and the denominator is the product of two positive integers \( n \) and \( m \). - Since \( n \) and \( m \) are both greater than or equal to 1, \( n \cdot m \) will also be greater than \( n \) and \( m \). Therefore, \( \frac{1}{n \cdot m} \) will be less than \( \frac{1}{n} \). 3. **Conclusion**: - The quotient \( \frac{1}{n \cdot m} \) is less than the original unit fraction \( \frac{1}{n} \). Based on this analysis, the correct statement is: **C. The quotient will be less than the unit fraction.**

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Extra Insights

When you divide a unit fraction (like 1/3) by a whole number (like 2), you essentially distribute that fraction into smaller parts. For example, dividing 1/3 by 2 gives you 1/6, which is indeed less than the original fraction. This shows that when splitting up the unit fraction, you’re making it smaller, leading us to the correct answer: C. The quotient will be less than the unit fraction. This concept is not just a mathematical exercise—it can be applied in real-life scenarios, such as splitting a pizza! If you have 1/4 of a pizza (the unit fraction) and you want to share it with 2 friends, each person would get 1/8 of the pizza (resulting in a smaller portion). So, the math helps us in making fair divisions in our lives!

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