Printable math worksheet for students to practice identifying missing fractions on a number line.

Explanation:
We are given five number lines, each marked from 0 to 1, with some fractions labeled and some empty boxes. Our job is to fill in the missing fractions.

Let’s go line by line.

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Line 1: Denominator is 10 (since labels are in tenths: 2/10, 5/10, 7/10, 9/10).
The marks are evenly spaced — there are 10 equal parts between 0 and 1. So each tick is 1/10 apart.

Mark positions (from left to right, starting at 0):
- Tick 0: 0
- Tick 1: □
- Tick 2: 2/10
- Tick 3: □
- Tick 4: □
- Tick 5: 5/10
- Tick 6: □
- Tick 7: 7/10
- Tick 8: □
- Tick 9: 9/10
- Tick 10: 1

So:
- Tick 1 = 1/10
- Tick 3 = 3/10
- Tick 4 = 4/10
- Tick 6 = 6/10
- Tick 8 = 8/10

✔ Missing: 1/10, 3/10, 4/10, 6/10, 8/10

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Line 2: Denominator is 8 (labels: 1/8, 5/8, 6/8, 7/8). So each tick is 1/8.

Tick positions:
- 0
- □
- 1/8
- □
- □
- 5/8
- 6/8
- 7/8
- 1

Let’s count ticks: from 0 to 1 in eighths → 8 equal parts → ticks at 0/8, 1/8, 2/8, ..., 8/8.

So:
- After 0 is tick 1 → 1/8 (already labeled)
Wait — actually, the first box is *before* 1/8, so that must be tick 1? Let's map carefully.

The number line shows:
- Arrow, then box, then mark labeled 1/8, then box, box, then 5/8, then 6/8, 7/8, then 1.

Let’s count total tick marks (including 0 and 1): There are 9 vertical marks (as in line 1), meaning 8 equal intervals → denominator 8.

So positions:
1. 0
2. □ → this is 1/8? But 1/8 is labeled at the *next* tick. Wait — look again:

In the image layout (text description), it says:
`← 0 [box] 1/8 [box] [box] 5/8 6/8 7/8 1 →`

That means:
- Tick 0: 0
- Tick 1: □
- Tick 2: 1/8
- Tick 3: □
- Tick 4: □
- Tick 5: 5/8
- Tick 6: 6/8
- Tick 7: 7/8
- Tick 8: 1

So if tick 2 = 1/8, then each step is 1/8, so:
- Tick 1 = 1/8 × 1 = 1/8? No — that would make tick 2 = 2/8. Contradiction.

Ah! The label “1/8” is placed *at* its correct position. So the tick where “1/8” is written is at position 1/8 → that’s the 1st tick after 0.

Therefore:
- Tick 0: 0
- Tick 1: 1/8 (labeled)
- Tick 2: □
- Tick 3: □
- Tick 4: □
- Tick 5: 5/8 (labeled)
- Tick 6: 6/8 (labeled)
- Tick 7: 7/8 (labeled)
- Tick 8: 1

But the image shows a box *before* 1/8, so maybe the first box is at tick 1, and 1/8 is at tick 2? That would mean spacing is not 1/8 — but denominators suggest uniform spacing.

Let me reinterpret using consistent spacing:

Since the labeled fractions are multiples of 1/8, and 0 to 1 is divided into 8 equal parts, the tick marks are at:
0/8, 1/8, 2/8, 3/8, 4/8, 5/8, 6/8, 7/8, 8/8.

Now match to what’s shown:

Line 2:
`← 0 [box] 1/8 [box] [box] 5/8 6/8 7/8 1 →`

That’s 9 vertical marks → positions 0 through 8.

So:
- Mark 0: 0
- Mark 1: □
- Mark 2: 1/8
- Mark 3: □
- Mark 4: □
- Mark 5: 5/8
- Mark 6: 6/8
- Mark 7: 7/8
- Mark 8: 1

If mark 2 = 1/8, then each step = 1/8 ÷ 2 = 1/16? That contradicts other labels.

Better idea: The labels are placed *on* the tick marks — so “1/8” sits exactly on its tick. Therefore, the tick with “1/8” is at position 1/8 → that’s the first tick after 0. So there should be no box before it.

But the worksheet clearly draws a box before 1/8. So likely, the first box is at 1/8, and the label “1/8” is just indicating the value — but the box is where we write it.

Wait — looking at line 1:
`0 [box] 2/10 [box] [box] 5/10 [box] 7/10 [box] 9/10 1`

That matches:
Tick 0: 0
Tick 1: □ → should be 1/10
Tick 2: 2/10 (labeled)
Tick 3: □ → 3/10
Tick 4: □ → 4/10
Tick 5: 5/10
Tick 6: □ → 6/10
Tick 7: 7/10
Tick 8: □ → 8/10
Tick 9: 9/10
Tick 10: 1

Yes! So there are 11 ticks for 10 intervals → denominator = 10.

Similarly, line 2 has:
0, box, 1/8, box, box, 5/8, 6/8, 7/8, 1 → that’s 9 ticks → 8 intervals, so denominator = 8.

So positions:
- Tick 0: 0
- Tick 1: □
- Tick 2: 1/8
- Tick 3: □
- Tick 4: □
- Tick 5: 5/8
- Tick 6: 6/8
- Tick 7: 7/8
- Tick 8: 1

Since tick 2 = 1/8, then each interval = (1/8)/2 = 1/16? No — that can’t be, because tick 5 = 5/8, and from tick 0 to tick 5 is 5 intervals, so 5 × step = 5/8 → step = 1/8. So tick numbers correspond directly to numerator.

Thus: tick *n* = n/8.

Then:
- tick 0 = 0/8 = 0
- tick 1 = 1/8
- tick 2 = 2/8
- tick 3 = 3/8
- tick 4 = 4/8
- tick 5 = 5/8
- tick 6 = 6/8
- tick 7 = 7/8
- tick 8 = 8/8 = 1

But the worksheet writes “1/8” at tick 2? That would be wrong.

Conclusion: The labels are placed at the correct tick, and the boxes are at other ticks. So in line 2:
- The first box is at tick 1 → 1/8
- Then label “1/8” is probably a typo in our reading — actually, looking back, the user’s text says:
`← 0 [box] 1/8 [box] [box] 5/8 6/8 7/8 1 →`

This matches:
tick 0: 0
tick 1: box → value = 1/8
tick 2: label “1/8” — but that would duplicate. So more likely, the label “1/8” is *on* the box’s position — meaning that box should be filled with 1/8. But it's already written, so maybe the box is elsewhere.

Given standard worksheets of this type, the pattern is: equally spaced ticks, labeled fractions tell you the denominator, and missing boxes are at unlabeled ticks.

Let me count ticks per line:

Line 1: marks at 0, (box), 2/10, (box), (box), 5/10, (box), 7/10, (box), 9/10, 1 → 11 ticks → 10 intervals, so step = 1/10. Labeled at numerators 2,5,7,9 → so boxes at numerators 1,3,4,6,8 → values: 1/10, 3/10, 4/10, 6/10, 8/10.

Line 2: 0, (box), 1/8, (box), (box), 5/8, 6/8, 7/8, 1 → 9 ticks → 8 intervals → step = 1/8. Labeled at 1,5,6,7 → so boxes at numerators: 2,3,4 → values: 2/8, 3/8, 4/8.

Yes! Because:
- tick 0: 0
- tick 1: box → 1/8? But 1/8 is labeled at next tick — wait, if tick 2 is labeled 1/8, then tick 1 = 1/16 — impossible.

I think the correct interpretation (standard for such worksheets) is: the labeled fractions sit *on* their tick, and the boxes are at other ticks. The count of intervals equals the denominator.

In line 2: fractions shown are 1/8, 5/8, 6/8, 7/8 — all over 8, and 0 and 1 present. So denominator = 8 → 8 equal parts → 9 tick marks.

The tick marks are at:
0, 1/8, 2/8, 3/8, 4/8, 5/8, 6/8, 7/8, 1.

Now, which of these are labeled? 1/8, 5/8, 6/8, 7/8 are labeled. So missing are: 2/8, 3/8, 4/8.

How many boxes? In the line: after 0, there’s a box, then 1/8, then box, box, then 5/8... So boxes at positions: 2/8, 3/8, 4/8. Yes — 3 boxes, matches.

So line 2 missing: 2/8, 3/8, 4/8

(We can simplify later, but worksheet keeps as eighths, so leave as is.)

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Line 3: Labels: 3/4, and 0, 1. Only two labels besides ends. Number of ticks? From diagram: 0, box, box, 3/4, 1 → that’s 5 ticks → 4 intervals → denominator 4.

So ticks at: 0/4, 1/4, 2/4, 3/4, 4/4.

Labeled: 3/4 and 0,1. Boxes at 1/4 and 2/4.

Missing: 1/4, 2/4

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Line 4: Only one box, centered. 0 and 1 at ends. Likely 2 intervals → midpoint = 1/2.

Yes, one box at halfway → 1/2

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Line 5: Denominator 10 again (labels: 1/10, 3/10, 6/10, 8/10). Ticks: 0, 1/10, box, 3/10, box, box, 6/10, box, 8/10, box, 1 → let’s count:

0, 1/10, [box], 3/10, [box], [box], 6/10, [box], 8/10, [box], 1 → 11 ticks → 10 intervals.

So numerators: 0,1,2,3,4,5,6,7,8,9,10.

Labeled at 1,3,6,8.

Boxes at numerators: 2,4,5,7,9.

Values: 2/10, 4/10, 5/10, 7/10, 9/10

Wait — 9/10 is labeled in line 1, but here 9/10 is a box? In line 5, the last box is before 1, after 8/10, so yes — 9/10 is missing here.

Double-check line 5 description:
`0 1/10 [box] 3/10 [box] [box] 6/10 [box] 8/10 [box] 1`

So positions:
1. 0
2. 1/10
3. □ → 2/10
4. 3/10
5. □ → 4/10
6. □ → 5/10
7. 6/10
8. □ → 7/10
9. 8/10
10. □ → 9/10
11. 1

Yes — missing: 2/10, 4/10, 5/10, 7/10, 9/10

Now compile all missing fractions in order of lines:

Line 1: 1/10, 3/10, 4/10, 6/10, 8/10
Line 2: 2/8, 3/8, 4/8
Line 3: 1/4, 2/4
Line 4: 1/2
Line 5: 2/10, 4/10, 5/10, 7/10, 9/10

But the question says “Find missing fractions on a number line” — likely expects each box filled. Since the worksheet has specific boxes, we list all missing values in order they appear (top to bottom, left to right).

Let’s list per line, left to right:

Line 1: 5 boxes → 1/10, 3/10, 4/10, 6/10, 8/10
Line 2: 3 boxes → 2/8, 3/8, 4/8
Line 3: 2 boxes → 1/4, 2/4
Line 4: 1 box → 1/2
Line 5: 5 boxes → 2/10, 4/10, 5/10, 7/10, 9/10

We can simplify where obvious, but the worksheet uses unsimplified forms (like 2/8, 2/4), so keep as is.

However, in many curricula, they prefer simplified, but since 2/8 appears alongside 6/8 etc, likely keep denominator consistent.

But let’s verify line 2: 2/8 = 1/4, but since others are eighths, keep 2/8.

Same for 2/4 = 1/2, but line 3 has 3/4, so probably keep 2/4.

Now, final answer should be all missing fractions in order.

But the problem likely expects us to fill each box — and since it's a worksheet, the answer is the list of fractions for the boxes.

Given the format, and that the user only wants the final answer, I will provide the missing fractions in order, as they appear top to bottom, left to right:

Line 1 boxes: 1/10, 3/10, 4/10, 6/10, 8/10
Line 2: 2/8, 3/8, 4/8
Line 3: 1/4, 2/4
Line 4: 1/2
Line 5: 2/10, 4/10, 5/10, 7/10, 9/10

To confirm, let’s ensure no duplicates or errors:

- Line 1: between 0 and 1 in tenths, missing numerators 1,3,4,6,8 → correct.
- Line 2: eighths, labeled at 1,5,6,7 → missing 2,3,4 → 2/8,3/8,4/8 → correct.
- Line 3: quarters, labeled at 3/4 → missing 1/4, 2/4 → correct.
- Line 4: half → 1/2 → correct.
- Line 5: tenths, labeled at 1,3,6,8 → missing 2,4,5,7,9 → correct.

All good.

Final Answer:
1/10, 3/10, 4/10, 6/10, 8/10, 2/8, 3/8, 4/8, 1/4, 2/4, 1/2, 2/10, 4/10, 5/10, 7/10, 9/10