Let’s carefully compare the two fractions shown on the number lines:
- Top line:
1/4 is highlighted.
- Bottom line:
2/6 is highlighted.
We need to figure out which fraction is larger — or if they are equal.
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Step 1: Understand what each fraction means
-
1/4 means 1 part out of 4 equal parts between 0 and 1.
-
2/6 means 2 parts out of 6 equal parts between 0 and 1.
But comparing them directly is hard because the denominators (bottom numbers) are different. So let’s make them easier to compare.
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Step 2: Simplify 2/6
2/6 can be simplified by dividing both top and bottom by 2:
→ 2 ÷ 2 = 1
→ 6 ÷ 2 = 3
So,
2/6 = 1/3
Now we’re comparing
1/4 and
1/3
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Step 3: Compare 1/4 and 1/3
Think about pizza slices:
- If you cut a pizza into 4 pieces, each piece is bigger than if you cut it into 6 pieces? Wait — no! Actually, more pieces mean smaller pieces.
Wait — let’s think again:
If you have 1 whole thing:
- Divided into 4 → each piece is 1/4
- Divided into 3 → each piece is 1/3
Which is bigger? A third or a quarter?
Imagine sharing a candy bar:
- With 3 friends → you get 1/3
- With 4 friends → you get 1/4
You’d rather share with fewer people — so 1/3 > 1/4
✔ So,
1/3 is bigger than 1/4
And since 2/6 = 1/3, then
2/6 > 1/4
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Step 4: Double-check using common denominator
Let’s convert both fractions to have the same denominator to be sure.
Find least common denominator of 4 and 6 → that’s 12.
Convert:
- 1/4 = ?/12 → multiply numerator and denominator by 3 →
3/12
- 2/6 = ?/12 → first simplify to 1/3, then 1/3 = 4/12 → OR directly: 2/6 × 2/2 =
4/12
So:
- 1/4 = 3/12
- 2/6 = 4/12
Clearly,
4/12 > 3/12, so
2/6 > 1/4
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Final Check: Look at the number lines visually (even though we don’t describe the image)
On the top line, 1/4 is one mark after 0 (since marks are at 0, 1/4, 2/4, 3/4, 1).
On the bottom line, 2/6 is two marks after 0 (marks at 0, 1/6, 2/6, 3/6, etc.).
Even without seeing the image, mathematically we’ve proven 2/6 is farther from 0 than 1/4.
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Final Answer:
2/6 is greater than 1/4
Parent Tip: Review the logic above to help your child master the concept of comparing fractions on a number line.
