Let's solve this step-by-step. The task is to
represent each given fraction on a number line by marking it with an "X". Each number line goes from 0 to 1, and we need to divide the segment from 0 to 1 into equal parts based on the denominator of the fraction.
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🔍 General Rule:
To represent a fraction $ \frac{a}{b} $ on a number line:
1. Divide the segment from 0 to 1 into
b equal parts.
2. Count
a parts from 0.
3. Mark that point with an
"X".
Let’s go through each one:
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a. $ \frac{2}{5} $
- Denominator = 5 → divide the number line into
5 equal parts.
- Numerator = 2 → count
2 parts from 0.
- Mark the second tick after 0 with an
"X".
✔ So, place
X at the
2nd tick mark.
---
b. $ \frac{3}{7} $
- Denominator = 7 → divide the number line into
7 equal parts.
- Numerator = 3 → count
3 parts from 0.
- Mark the third tick with an
"X".
✔ Place
X at the
3rd tick mark.
---
c. $ \frac{5}{9} $
- Denominator = 9 → divide the number line into
9 equal parts.
- Numerator = 5 → count
5 parts from 0.
- Mark the fifth tick with an
"X".
✔ Place
X at the
5th tick mark.
---
d. $ \frac{2}{6} $
- Denominator = 6 → divide the number line into
6 equal parts.
- Numerator = 2 → count
2 parts from 0.
- Mark the second tick with an
"X".
✔ Place
X at the
2nd tick mark.
> Note: $ \frac{2}{6} $ can be simplified to $ \frac{1}{3} $, but we still use the original denominator for marking (since the number line has 6 divisions).
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e. $ \frac{4}{7} $
- Denominator = 7 → divide into
7 equal parts.
- Numerator = 4 → count
4 parts from 0.
- Mark the fourth tick with an
"X".
✔ Place
X at the
4th tick mark.
---
f. $ \frac{1}{9} $
- Denominator = 9 → divide into
9 equal parts.
- Numerator = 1 → count
1 part from 0.
- Mark the first tick after 0 with an
"X".
✔ Place
X at the
1st tick mark.
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✔ Summary of Where to Place "X":
| Fraction | Number of Divisions | Position of X |
|--------|---------------------|---------------|
| a. $ \frac{2}{5} $ | 5 | 2nd tick |
| b. $ \frac{3}{7} $ | 7 | 3rd tick |
| c. $ \frac{5}{9} $ | 9 | 5th tick |
| d. $ \frac{2}{6} $ | 6 | 2nd tick |
| e. $ \frac{4}{7} $ | 7 | 4th tick |
| f. $ \frac{1}{9} $ | 9 | 1st tick |
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📌 How to Draw It:
For each number line:
1. Count the total number of segments between 0 and 1 (equal to the denominator).
2. Count forward the number of segments equal to the numerator.
3. Put an
"X" at that point.
> Example: For $ \frac{2}{5} $, you split the line into 5 parts, then go 2 steps from 0 → put X there.
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✔ Final Answer:
You should draw an
"X" at:
- a. 2nd tick (out of 5)
- b. 3rd tick (out of 7)
- c. 5th tick (out of 9)
- d. 2nd tick (out of 6)
- e. 4th tick (out of 7)
- f. 1st tick (out of 9)
This visually represents each fraction correctly on the number line.
Parent Tip: Review the logic above to help your child master the concept of fractions on number lines worksheet.
