Use the number line to determine which fraction is larger: start fraction, 4, divided by, 9, end fraction94​ or start fraction, 3, divided by, 7, end fraction73​.




You're going to plot start fraction, 4, divided by, 9, end fraction94​ and start fraction, 3, divided by, 7, end fraction73​ 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 compare the fractions \( \frac{4}{9} \) and \( \frac{3}{7} \) on a number line, we first need to find a common denominator for both fractions so that they can be plotted accurately on the same scale. 

### Step 1: Find the Least Common Denominator (LCD)
The denominators of the two fractions are 9 and 7. The least common denominator (LCD) is the smallest number that both 9 and 7 divide into evenly. 

To find the LCD:
- The prime factorization of 9 is \( 3^2 \).
- The prime factorization of 7 is \( 7^1 \).
- The LCD is the product of all prime factors, raised to their highest powers: \( 3^2 \times 7 = 63 \).

Thus, the LCD of 9 and 7 is 63.

### Step 2: Convert the Fractions
Now that we know the LCD is 63, we convert both fractions to have this denominator:
- \( \frac{4}{9} = \frac{4 \times 7}{9 \times 7} = \frac{28}{63} \)
- \( \frac{3}{7} = \frac{3 \times 9}{7 \times 9} = \frac{27}{63} \)

### Step 3: Determine the Number of Pieces
To plot both fractions on the number line, we need to partition the segment from 0 to 1 into 63 equal pieces. This is because 63 is the smallest denominator that allows us to place both \( \frac{28}{63} \) and \( \frac{27}{63} \) on the number line.

### Conclusion:
The smallest number of pieces needed to partition the number line from 0 to 1 in order to plot both fractions is **63**.

Would you like further details or clarifications?

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Here are 5 related questions:
1. How do you compare two fractions without finding a common denominator?
2. Can the number line method be used to compare improper fractions?
3. How would the method change if the denominators were larger numbers?
4. What are other ways to visually compare fractions besides using a number line?
5. How can decimals help in comparing fractions like \( \frac{4}{9} \) and \( \frac{3}{7} \)?

**Tip:** When comparing fractions, simplifying them as much as possible before finding a common denominator can save time and effort.

Use the number line to determine which fraction is larger: start fraction, 4, divided by, 9, end fraction 4/9 or start fraction, 3, divided by, 7, end fraction 3/7. You're going to plot start fraction, 4, divided by, 9, end fraction 4/9 and start fraction, 3, divided by, 7, end fraction 3/7 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 4/9 and 3/7 by finding the least common denominator (63) and plotting them on a number line. Discover step-by-step methods to partition the number line into 63 equal pieces to visualize and compare both fractions. Suitable for students in Grades 5-7.

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