35/-105 in standard form (rational numbers

To express \(\frac{35}{-105}\) in standard form, follow these steps:

1. Simplify the fraction by finding the greatest common divisor (GCD) of the numerator (35) and the denominator (-105).
2. Use the GCD to reduce the fraction to its simplest form.

### Step-by-Step Solution

1. **Find the GCD:**
   - The factors of 35 are: 1, 5, 7, 35.
   - The factors of 105 are: 1, 3, 5, 7, 15, 21, 35, 105.
   - The common factors are: 1, 5, 7, 35.
   - The greatest common divisor (GCD) is 35.

2. **Simplify the fraction:**
   \[
   \frac{35}{-105} = \frac{35 \div 35}{-105 \div 35} = \frac{1}{-3}
   \]

3. **Express in standard form:**
   - The standard form for rational numbers typically has a positive denominator.
   - To achieve this, multiply both the numerator and the denominator by -1:
   \[
   \frac{1}{-3} = -\frac{1}{3}
   \]

Thus, \(\frac{35}{-105}\) in standard form is \(-\frac{1}{3}\).

Would you like any additional details or have any questions? Here are some related questions you might want to explore:

1. How do you find the GCD of two numbers?
2. How do you simplify a fraction?
3. What is the standard form of a rational number?
4. How do you handle negative signs in fractions?
5. How do you convert a fraction to a decimal?

**Tip:** When simplifying fractions, always ensure the denominator is positive for the standard form.

Learn how to convert \(\frac{35}{-105}\) to standard form with a detailed step-by-step solution. This problem covers key concepts including fractions, negative numbers, and achieving standard form in rational numbers. Suitable for students in Grades 6-8.

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