Use the number line to determine which fraction is larger: start fraction, 8, divided by, 9, end fraction 
9
8
​
  or start fraction, 4, divided by, 5, end fraction 
5
4
​
 .

You're going to plot start fraction, 8, divided by, 9, end fraction 
9
8
​
  and start fraction, 4, divided by, 5, end fraction 
5
4
​
  on the number line below. What's the smallest number of pieces you need to partition, or break, the segment from 0 to 1 into to plot both fractions on the number line?

To determine the smallest number of pieces to partition the segment from 0 to 1 in order to plot both fractions \( \frac{8}{9} \) and \( \frac{4}{5} \), we need to find a common denominator.

1. The fractions given are \( \frac{8}{9} \) and \( \frac{4}{5} \).
2. The denominators are 9 and 5.
3. To plot these fractions on the same number line, we need to find the least common denominator (LCD) of 9 and 5. 

The LCD of 9 and 5 is 45.

Now, we can rewrite the fractions with a denominator of 45:
- \( \frac{8}{9} = \frac{8 \times 5}{9 \times 5} = \frac{40}{45} \)
- \( \frac{4}{5} = \frac{4 \times 9}{5 \times 9} = \frac{36}{45} \)

### Conclusion:
The smallest number of pieces we need to partition the number line into is 45, as this allows us to plot both \( \frac{8}{9} \) and \( \frac{4}{5} \) as fractions of 45.

Would you like further details or have any questions?

Here are 5 related questions:
1. What is the least common denominator and how is it used in fraction comparison?
2. How do you plot fractions on a number line effectively?
3. Why is finding the least common denominator helpful when comparing fractions?
4. Can you compare fractions without finding a common denominator?
5. How would the number line change if we added more fractions?

**Tip:** When comparing fractions, the least common denominator helps make sure you're comparing "apples to apples" by converting the fractions to have the same denominator.

Use the number line to determine which fraction is larger: 8/9 or 4/5. You're going to plot 8/9 and 4/5 on the number line below. What's the smallest number of pieces you need to partition, or break, the segment from 0 to 1 into to plot both fractions on the number line?

Learn how to compare fractions 8/9 and 4/5 using the least common denominator to determine which is larger. This step-by-step solution involves partitioning the number line into 45 pieces to accurately plot both fractions. Suitable for students in Grades 4-6.

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