Question

How to order fractions with common denominators and the ones with common numerators

Answer 1

To order fractions with common denominators and those with common numerators, follow these steps:

### Fractions with Common Denominators
When the fractions have the same denominator, you can compare them just by looking at the numerators.

1. **Identify the Denominator**: Ensure all fractions have the same denominator.
2. **Compare the Numerators**: The fraction with the larger numerator is the larger fraction.

**Example**: Compare \( \frac{3}{7} \) and \( \frac{5}{7} \).

- Since both fractions have the same denominator (7), compare the numerators:
- 3 vs. 5
- Therefore, \( \frac{5}{7} > \frac{3}{7} \).

### Fractions with Common Numerators
When the fractions have the same numerator, you can compare them using the denominators.

1. **Identify the Numerator**: Ensure all fractions have the same numerator.
2. **Compare the Denominators**: The fraction with the smaller denominator is the larger fraction.

**Example**: Compare \( \frac{4}{5} \) and \( \frac{4}{8} \).

- Since both fractions have the same numerator (4), compare the denominators:
- 5 vs. 8
- Therefore, \( \frac{4}{5} > \frac{4}{8} \) because 5 is smaller than 8.

### Summary
- **Common Denominator**: Compare numerators directly; larger numerator = larger fraction.
- **Common Numerator**: Compare denominators; smaller denominator = larger fraction.

Using these methods will help you order fractions quickly and accurately!