How to order fractions in ascending order if they are unlike

To order fractions in ascending order when they have different denominators (unlike fractions), follow these steps:

### 1. **Find the Least Common Denominator (LCD):**
   - Identify the denominators of all the fractions.
   - Find the least common multiple (LCM) of these denominators. This LCM is your Least Common Denominator (LCD).

### 2. **Convert Each Fraction:**
   - Convert each fraction to an equivalent fraction with the LCD as the new denominator. 
   - To do this, multiply both the numerator and the denominator of each fraction by the same number that converts the denominator to the LCD.

### 3. **Compare the Numerators:**
   - Now that all fractions have the same denominator, simply compare the numerators.
   - The fraction with the smallest numerator is the smallest fraction, and the one with the largest numerator is the largest.

### 4. **Order the Fractions:**
   - Arrange the fractions based on their numerators in ascending order.

### Example:
Let's say you have the fractions: \( \frac{3}{4} \), \( \frac{2}{5} \), and \( \frac{5}{6} \).

1. **Find the LCD:**
   - The denominators are 4, 5, and 6.
   - The LCM of 4, 5, and 6 is 60, so the LCD is 60.

2. **Convert each fraction:**
   - \( \frac{3}{4} = \frac{3 \times 15}{4 \times 15} = \frac{45}{60} \)
   - \( \frac{2}{5} = \frac{2 \times 12}{5 \times 12} = \frac{24}{60} \)
   - \( \frac{5}{6} = \frac{5 \times 10}{6 \times 10} = \frac{50}{60} \)

3. **Compare the numerators:**
   - \( \frac{24}{60} \), \( \frac{45}{60} \), \( \frac{50}{60} \)

4. **Order the fractions:**
   - The order is \( \frac{2}{5} \), \( \frac{3}{4} \), \( \frac{5}{6} \).

So, in ascending order: \( \frac{2}{5} < \frac{3}{4} < \frac{5}{6} \).

Would you like more details or have any questions?

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Here are 5 related questions:

1. How do you find the Least Common Denominator (LCD) for a set of fractions?
2. Can you order these fractions in ascending order: \( \frac{1}{3} \), \( \frac{4}{9} \), \( \frac{2}{5} \)?
3. How do you compare fractions that have the same denominator?
4. What is an alternative method to compare fractions without finding the LCD?
5. How do you order a set of improper fractions?

**Tip:** When working with fractions, it’s often easier to simplify them before finding the LCD.

Learn how to order fractions in ascending order when they have different denominators. Follow a step-by-step guide including finding the Least Common Denominator (LCD), converting fractions, and comparing numerators. Suitable for students in Grades 5-8.

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