Fractions on Number Line - Representation, Comparison, Examples - Free Printable

Let's solve each question step by step from the "Fractions on a Number Line" worksheet for 3rd grade.

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1) What fraction does A, B, and C represent?

We have a number line from 0 to 1, divided into 4 equal parts (since there are 3 marks between 0 and 1).

So, each segment represents:
$$
\frac{1}{4}
$$

Now:
- A is at the first mark: $ \frac{1}{4} $
- B is at the second mark: $ \frac{2}{4} = \frac{1}{2} $
- C is at the third mark: $ \frac{3}{4} $

✔ Answer:
- A = $ \frac{1}{4} $
- B = $ \frac{1}{2} $
- C = $ \frac{3}{4} $

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2) Identify M

Number line goes from 0 to 2, with 4 equal segments between 0 and 1, and same between 1 and 2.

So each segment is $ \frac{1}{4} $.

M is located between 0 and 1, at the third mark after 0.

So:
- 0 → $ \frac{0}{4} $
- First mark: $ \frac{1}{4} $
- Second: $ \frac{2}{4} $
- Third: $ \frac{3}{4} $

But wait — M is after 1. Let’s look again.

Wait — M is between 1 and 2, and it's the first mark after 1.

Since each segment is $ \frac{1}{4} $, then:

- After 1: $ 1 + \frac{1}{4} = \frac{5}{4} $

✔ Answer: M = $ \frac{5}{4} $ or $ 1\frac{1}{4} $

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3) Write the missing fractions

We have a number line from 0 to beyond 1, marked in fifths.

Given:
- $ \frac{2}{5} $
- $ \frac{3}{5} $
- $ \frac{4}{5} $

And two blanks:
- a. Before $ \frac{2}{5} $
- b. After $ \frac{4}{5} $

Each segment is $ \frac{1}{5} $, so:

- a. Before $ \frac{2}{5} $: $ \frac{1}{5} $
- b. After $ \frac{4}{5} $: $ \frac{5}{5} = 1 $

✔ Answer:
- a. $ \frac{1}{5} $
- b. $ 1 $

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4) Write the missing mixed fraction in the number line

Number line from 0 to 4, with thirds.

Marked values:
- $ 1\frac{1}{3} $, $ 1\frac{2}{3} $, $ 2\frac{1}{3} $, $ 3\frac{2}{3} $

We need to fill:
- a. Between $ 1\frac{2}{3} $ and $ 2\frac{1}{3} $ → that's 2
- b. Between $ 2\frac{1}{3} $ and $ 3\frac{2}{3} $ → that's $ 3 $
- c. Between $ 3\frac{2}{3} $ and 4 → that's $ 4 $, but we need the next one?

Wait — let's list all points:

- 0, $ \frac{1}{3} $, $ \frac{2}{3} $, $ 1 $, $ 1\frac{1}{3} $, $ 1\frac{2}{3} $, $ 2 $, $ 2\frac{1}{3} $, $ 2\frac{2}{3} $, $ 3 $, $ 3\frac{1}{3} $, $ 3\frac{2}{3} $, $ 4 $

Now, looking at the blanks:
- a. After $ 1\frac{2}{3} $: next is $ 2 $ → but $ 2 = 2\frac{0}{3} $, so this is $ 2 $
- b. After $ 2\frac{1}{3} $: next is $ 2\frac{2}{3} $
- c. After $ 3\frac{2}{3} $: next is $ 4 $

But the question says "mixed fraction", so:

- a. $ 2 $ → can be written as $ 2\frac{0}{3} $, but usually just $ 2 $
- b. $ 2\frac{2}{3} $
- c. $ 4 $

But perhaps they want mixed numbers:

Wait — maybe the blanks are:
- a. After $ 1\frac{2}{3} $ → $ 2 $
- b. After $ 2\frac{1}{3} $ → $ 2\frac{2}{3} $
- c. After $ 3\frac{2}{3} $ → $ 4 $

But $ 4 $ is not a mixed number — it's a whole number.

Alternatively, maybe the blank c is between $ 3\frac{2}{3} $ and 4, so it should be $ 3\frac{3}{3} = 4 $? But that’s already the endpoint.

Wait — the labels are:
- a. After $ 1\frac{2}{3} $ → $ 2 $
- b. After $ 2\frac{1}{3} $ → $ 2\frac{2}{3} $
- c. After $ 3\frac{2}{3} $ → $ 4 $

But $ 4 $ is not a mixed fraction. However, $ 4 = 3\frac{3}{3} $, but that’s unusual.

Alternatively, perhaps the blanks are:
- a. $ 2 $ → $ 2\frac{0}{3} $, but typically just $ 2 $
- b. $ 2\frac{2}{3} $
- c. $ 3\frac{3}{3} = 4 $, but again, not standard

Wait — actually, the number line shows:
- $ 1\frac{1}{3} $, $ 1\frac{2}{3} $, then blank a, then $ 2\frac{1}{3} $, blank b, $ 3 $, blank c, $ 3\frac{2}{3} $

Wait — no, the image says:

> 0 → $ 1\frac{1}{3} $ → $ 1\frac{2}{3} $ → [a] → $ 2\frac{1}{3} $ → [b] → 3 → [c] → $ 3\frac{2}{3} $ → 4

Wait — but that doesn’t make sense because $ 1\frac{2}{3} $ to $ 2\frac{1}{3} $ is a jump of $ \frac{2}{3} $, which skips one mark.

Actually, the number line is divided into thirds, so:

- 0, $ \frac{1}{3} $, $ \frac{2}{3} $, 1, $ 1\frac{1}{3} $, $ 1\frac{2}{3} $, 2, $ 2\frac{1}{3} $, $ 2\frac{2}{3} $, 3, $ 3\frac{1}{3} $, $ 3\frac{2}{3} $, 4

So:
- After $ 1\frac{2}{3} $: 2
- After $ 2\frac{1}{3} $: $ 2\frac{2}{3} $
- After 3: $ 3\frac{1}{3} $
- Then $ 3\frac{2}{3} $

But the blanks are:
- a. After $ 1\frac{2}{3} $ → 2
- b. After $ 2\frac{1}{3} $ → $ 2\frac{2}{3} $
- c. After 3 → $ 3\frac{1}{3} $

Yes! So:
- a. $ 2 $
- b. $ 2\frac{2}{3} $
- c. $ 3\frac{1}{3} $

✔ Answer:
- a. $ 2 $
- b. $ 2\frac{2}{3} $
- c. $ 3\frac{1}{3} $

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5) Identify the following on the number line.

We have:
- A: $ \frac{7}{10} $
- B: $ \frac{1}{10} $
- C: $ \frac{3}{10} $

Number line from 0 to 1, divided into 10 equal parts (tenths).

So:
- Each tick = $ \frac{1}{10} $
- $ \frac{1}{10} $ = 1st tick → B
- $ \frac{3}{10} $ = 3rd tick → C
- $ \frac{7}{10} $ = 7th tick → A

So we need to label the positions:
- A at 7th tick
- B at 1st tick
- C at 3rd tick

✔ Answer: On the number line:
- Mark $ \frac{1}{10} $ → B
- Mark $ \frac{3}{10} $ → C
- Mark $ \frac{7}{10} $ → A

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✔ Final Answers Summary:

1)
- A = $ \frac{1}{4} $
- B = $ \frac{1}{2} $
- C = $ \frac{3}{4} $

2)
- M = $ \frac{5}{4} $ or $ 1\frac{1}{4} $

3)
- a. $ \frac{1}{5} $
- b. $ 1 $

4)
- a. $ 2 $
- b. $ 2\frac{2}{3} $
- c. $ 3\frac{1}{3} $

5)
On the number line:
- $ \frac{1}{10} $ → B
- $ \frac{3}{10} $ → C
- $ \frac{7}{10} $ → A

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