Explanation:
We are given five number lines (each from 0 to 3), and for each, we need to place two mixed numbers or fractions at the correct positions.
Let’s convert each fraction/mixed number to a decimal or think in fifths, since all denominators are 5. That makes it easier to locate them on the number line.
Recall:
- $ \frac{1}{5} = 0.2 $
- $ \frac{2}{5} = 0.4 $
- $ \frac{3}{5} = 0.6 $
- $ \frac{4}{5} = 0.8 $
A mixed number like $ 2\frac{2}{5} $ means $ 2 + \frac{2}{5} = 2.4 $
Similarly:
- $ 2\frac{3}{5} = 2.6 $
- $ 1\frac{3}{5} = 1.6 $
- $ 2\frac{1}{5} = 2.2 $
- $ 1\frac{2}{5} = 1.4 $
Now go one by one:
1. Points: $ \frac{3}{5} $ and $ 2\frac{2}{5} $
- $ \frac{3}{5} = 0.6 $ → between 0 and 1, 3/5 of the way from 0 to 1
- $ 2\frac{2}{5} = 2.4 $ → between 2 and 3, 2/5 of the way from 2 to 3
So: first point at 0.6, second at 2.4
2. Points: $ 2\frac{3}{5} $ and $ \frac{4}{5} $
- $ 2\frac{3}{5} = 2.6 $
- $ \frac{4}{5} = 0.8 $
So: first point at 2.6, second at 0.8
3. Points: $ 1\frac{3}{5} $ and $ 2\frac{1}{5} $
- $ 1\frac{3}{5} = 1.6 $
- $ 2\frac{1}{5} = 2.2 $
So: first at 1.6, second at 2.2
4. Points: $ \frac{3}{5} $ and $ 2\frac{4}{5} $
- $ \frac{3}{5} = 0.6 $
- $ 2\frac{4}{5} = 2.8 $
So: first at 0.6, second at 2.8
5. Points: $ \frac{2}{5} $ and $ 1\frac{2}{5} $
- $ \frac{2}{5} = 0.4 $
- $ 1\frac{2}{5} = 1.4 $
So: first at 0.4, second at 1.4
To confirm: Each number line is divided into whole units (0–1, 1–2, 2–3). Since denominator is 5, each unit can be imagined as split into 5 equal parts — so 0.2 per tick.
Let’s double-check each:
1. 0.6 and 2.4
✔
2. 0.8 and 2.6
✔
3. 1.6 and 2.2
✔
4. 0.6 and 2.8
✔
5. 0.4 and 1.4
✔
All correct.
Final Answer:
1. $ \frac{3}{5} $ at 0.6, $ 2\frac{2}{5} $ at 2.4
2. $ 2\frac{3}{5} $ at 2.6, $ \frac{4}{5} $ at 0.8
3. $ 1\frac{3}{5} $ at 1.6, $ 2\frac{1}{5} $ at 2.2
4. $ \frac{3}{5} $ at 0.6, $ 2\frac{4}{5} $ at 2.8
5. $ \frac{2}{5} $ at 0.4, $ 1\frac{2}{5} $ at 1.4
Parent Tip: Review the logic above to help your child master the concept of comparing fractions on a number line worksheet.