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.

Question

UpStudy AI · Accepted Answer

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.**
The quotient will be less than the unit fraction.

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.

Upstudy AI Solution

Answer

Solution

Extra Insights

Related Questions

Latest Arithmetic Questions