Fractions on a Number Line Worksheets - 15 Worksheets Library - Free Printable

Let’s solve each problem step by step.

We are looking at number lines from 0 to 2. Each number line is divided into equal parts, and we need to find the fraction that matches where the object is placed.

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Problem 1:
The number line goes from 0 to 2. Between 0 and 1, there are 8 small marks (so 9 total points including 0 and 1). That means each mark is 1/8.
The cloud is on the 7th mark after 1 → so it’s at 1 + 7/8 = 15/8? Wait — let’s count again carefully.

Actually, from 0 to 1: how many spaces? Let’s count the gaps between ticks.

Looking at Problem 1: From 0 to 1, there are 8 equal segments → so each segment is 1/8.

The cloud is located at the 7th tick after 1 → which is 1 + 7/8 = 15/8? But wait — maybe it’s easier to think in terms of total eighths from 0.

From 0 to the cloud: 1 whole (which is 8/8) plus 7 more eighths → 8/8 + 7/8 = 15/8.

But let’s check if that’s correct by counting all ticks from 0:

Tick 0: 0
Tick 1: 1/8
Tick 2: 2/8
...
Tick 8: 8/8 = 1
Tick 9: 9/8
Tick 10: 10/8
Tick 11: 11/8
Tick 12: 12/8
Tick 13: 13/8
Tick 14: 14/8
Tick 15: 15/8 ← this is where the cloud is? Wait, no — let’s look again.

Actually, in the image for #1, from 0 to 1 there are 8 intervals → so 9 ticks including 0 and 1. The cloud is on the 7th tick AFTER 1 → so that’s tick #15 overall? No — better to count from 0.

Wait — perhaps I’m overcomplicating. Let me recount visually:

In #1: Between 0 and 1, there are 8 small lines → meaning 8 equal parts → denominator is 8.

The cloud is 7 parts past 1 → so 1 and 7/8 → which is 15/8.

But let’s verify with other problems to see if denominators change.

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Problem 2:
Number line from 0 to 2. Between 0 and 1, there are 4 segments → so each is 1/4.

The butterfly is on the 3rd tick after 1 → so 1 + 3/4 = 7/4.

Counting from 0: 0, 1/4, 2/4, 3/4, 1 (4/4), 5/4, 6/4, 7/4 → yes, 7th tick from 0? Wait — ticks:

Tick 0: 0
Tick 1: 1/4
Tick 2: 2/4
Tick 3: 3/4
Tick 4: 4/4 = 1
Tick 5: 5/4
Tick 6: 6/4
Tick 7: 7/4 ← butterfly is here → so 7/4.

Correct.

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Problem 3:
Between 0 and 1: 4 segments → each is 1/4.

The pencil is on the 2nd tick after 0 → so 2/4 → which simplifies to 1/2.

But let’s confirm: Tick 0: 0, Tick 1: 1/4, Tick 2: 2/4 → yes.

So answer is 2/4 or 1/2. Since the worksheet doesn’t specify simplified form, either is fine, but usually we simplify. However, looking at the context, they might expect unsimplified since the number line shows fourths. Let’s keep as 2/4 for now, but note that 1/2 is equivalent.

Wait — actually, in school worksheets, sometimes they want the fraction based on the divisions shown. Since it’s divided into fourths, 2/4 is acceptable. But let’s see what makes sense.

Actually, let’s check the position: halfway between 0 and 1 → definitely 1/2. So probably best to write 1/2.

But to be safe, let’s see the pattern.

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Problem 4:
Between 0 and 1: 12 segments? Let’s count.

From 0 to 1: how many small lines? Looking at #4: from 0 to 1, there are 12 intervals → so each is 1/12.

The book is on the 5th tick after 1 → so 1 + 5/12 = 17/12.

Counting from 0: 12/12 (at 1) + 5/12 = 17/12.

Yes.

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Problem 5:
Between 0 and 1: 3 segments → each is 1/3.

The umbrella is on the 2nd tick after 1 → so 1 + 2/3 = 5/3.

Counting from 0: 0, 1/3, 2/3, 1 (3/3), 4/3, 5/3 → yes, 5th tick from 0? Ticks:

Tick 0: 0
Tick 1: 1/3
Tick 2: 2/3
Tick 3: 3/3 = 1
Tick 4: 4/3
Tick 5: 5/3 ← umbrella is here.

Perfect.

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Now let’s go back and double-check each one with careful counting.

Recheck Problem 1:

Number line #1: From 0 to 1, how many equal parts? Count the spaces between ticks.

There are 8 spaces between 0 and 1 → so denominator 8.

Cloud is located at the 7th space after 1 → so position = 1 + 7/8 = 15/8.

Is 15/8 correct? Yes.

But let’s count total ticks from 0:

- Tick 0: 0
- Tick 1: 1/8
- ...
- Tick 8: 8/8 = 1
- Tick 9: 9/8
- Tick 10: 10/8
- Tick 11: 11/8
- Tick 12: 12/8
- Tick 13: 13/8
- Tick 14: 14/8
- Tick 15: 15/8 → cloud is on tick 15? In the image, it looks like it's on the 7th mark after 1, which would be tick 8+7=15 → yes.

So 15/8.

But 15/8 is an improper fraction. Is that okay? Yes, because the number line goes to 2, and 15/8 is less than 2 (since 16/8=2).

Okay.

Problem 2:

0 to 1: 4 spaces → denominator 4.

Butterfly is 3 spaces after 1 → 1 + 3/4 = 7/4.

Ticks: 0,1,2,3,4(=1),5,6,7 → 7th tick is 7/4 → correct.

Problem 3:

0 to 1: 4 spaces → denominator 4.

Pencil is on 2nd tick after 0 → so 2/4.

But 2/4 = 1/2. Should we simplify? In most elementary contexts, they accept both, but often prefer simplified. However, since the number line is marked in fourths, writing 2/4 shows you counted correctly. But let’s see the instruction: “write the fraction” — doesn’t specify simplified. To be safe, I’ll write 2/4, but note that 1/2 is also correct. Actually, looking at common practice, they might expect 1/2. Hmm.

Wait — in the image, the pencil is exactly halfway, so 1/2 is natural. But the divisions are fourths, so 2/4 is precise. I think either is acceptable, but let’s choose 1/2 as it’s simpler.

Actually, let’s check online or standard practice — in such worksheets, if the point is on a reduced fraction, they usually expect the simplified form. For example, if it’s halfway, they say 1/2 even if divided into fourths. So I’ll go with 1/2.

But to match the division, perhaps 2/4. I’m conflicted.

Let me think differently: in problem 4, if it was on 6/12, they’d probably want 1/2, but here it’s 2/4. Since 2/4 reduces to 1/2, and it’s a common fraction, I’ll use 1/2.

But let’s see the answer format — the box is empty, so any correct fraction is fine. I’ll put 1/2 for clarity.

Problem 4:

0 to 1: 12 spaces → denominator 12.

Book is 5 spaces after 1 → 1 + 5/12 = 17/12.

Correct.

Problem 5:

0 to 1: 3 spaces → denominator 3.

Umbrella is 2 spaces after 1 → 1 + 2/3 = 5/3.

Correct.

Now, let’s list them:

1. 15/8
2. 7/4
3. 1/2 (or 2/4) — I’ll go with 1/2
4. 17/12
5. 5/3

But let’s confirm problem 3 once more. If the number line has marks at 0, 1/4, 2/4, 3/4, 1, etc., and the pencil is on the second mark, that’s 2/4. Writing 2/4 is technically more accurate to the diagram, but 1/2 is equivalent. In many curricula, they teach to simplify, so I think 1/2 is better.

To resolve this, let’s assume the worksheet expects the fraction in simplest form unless otherwise specified. So for #3, 1/2.

Final answers:

1. 15/8
2. 7/4
3. 1/2
4. 17/12
5. 5/3

I think that’s correct.

Final Answer:
1. \frac{15}{8}
2. \frac{7}{4}
3. \frac{1}{2}
4. \frac{17}{12}
5. \frac{5}{3}