Use Fraction Strips and Number Line - Math Worksheets - SplashLearn - Free Printable

Let’s solve this step by step.

We are given fraction strips and number lines from 0 to 1. The goal is to use the fraction strips to divide the number line into equal parts and label the fractions at each tick mark.

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First Number Line (with thirds):

The strip shows three pieces, each labeled 1/3. That means we divide the space between 0 and 1 into 3 equal parts.

So, starting at 0:

- First tick: 1/3
- Second tick: 2/3
- Third tick: 3/3 = 1 (already labeled)

✔ So labels on first number line:
At first dashed line → 1/3
At second dashed line → 2/3

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Second Number Line (with fourths):

The strip has four pieces, each 1/4. So we divide 0 to 1 into 4 equal parts.

Starting at 0:

- First tick: 1/4
- Second tick: 2/4 (which simplifies to 1/2, but since the strip uses 1/4 units, we can leave as 2/4 unless told to simplify — however, in most elementary contexts, they expect simplified form if possible. But looking at the pattern, they may want it in terms of the unit shown. Let’s check context.)

Wait — the problem says “label the fractions” using the fraction strips. Since the strip is made of 1/4 pieces, we should label each division as multiples of 1/4.

But often in these problems, they accept both, but let’s see what makes sense.

Actually, looking at the first example: with 1/3 strips, they would label 1/3 and 2/3 — not 3/3 because that’s already 1.

Similarly here:

- After 0: 1/4
- Then: 2/4 → which is same as 1/2, but since the strip is in fourths, maybe write 2/4? However, standard practice is to simplify unless instructed otherwise.

But wait — let’s think about consistency. In the first case, 2/3 is already simplified. In the third case, we’ll have fifths.

Actually, looking at common curriculum (like SplashLearn), when using fraction strips, they usually label the ticks as cumulative sums of the unit fraction, and simplify only if necessary or if asked.

But to be safe, let’s look at the structure:

For thirds: positions are 1/3, 2/3

For fourths: positions should be 1/4, 2/4, 3/4

But 2/4 reduces to 1/2 — should we write 1/2?

Hmm. Let me check a similar problem logic.

In many such worksheets, even if you’re using 1/4 strips, they still label 2/4 as 1/2 because it’s simpler and more meaningful.

But actually, no — in this specific type of exercise, since the strip is divided into 1/4 parts, and you’re placing marks based on those divisions, you label them as 1/4, 2/4, 3/4 — and sometimes they reduce later, but for labeling the number line according to the strip, you keep denominator consistent.

Wait — let’s think differently.

The instruction: “Use the fraction strips to divide the number lines into equal parts and label the fractions.”

That means: the number of segments equals the denominator, and each segment is 1/denominator.

So for 1/4 strip → 4 segments → labels at 1/4, 2/4, 3/4

But 2/4 is equivalent to 1/2 — so which one to write?

Looking at educational standards (e.g., Common Core), students are expected to recognize equivalence, but when partitioning with a specific unit, they often label with that unit until simplification is requested.

However, in the image provided (though I’m not describing it), typically in such diagrams, for fourths, they label 1/4, 2/4, 3/4 — and sometimes also note 1/2 above 2/4.

But since the problem doesn’t specify, and to match the pattern of the first one (where 2/3 is written, not reduced further), I think we should write:

For fourths: 1/4, 2/4, 3/4

But wait — 2/4 is not in simplest form. Maybe the worksheet expects simplified fractions?

Let me reconsider.

Actually, in the first example, 2/3 is already simplified. For fourths, 2/4 simplifies to 1/2 — and 1/2 is a key benchmark fraction. It’s very likely they want 1/2 there.

Moreover, in real teaching, when you divide into fourths, you point out that the middle is half.

I recall that in SplashLearn materials (as seen in the logo), they do simplify where appropriate.

To confirm: let’s imagine the number line for fourths:

0 ----|----|----|---- 1

Positions:

- First mark: 1/4

- Second mark: halfway → 1/2

- Third mark: 3/4

Yes, that makes sense pedagogically.

Similarly, for fifths: 1/5, 2/5, 3/5, 4/5 — none simplify except 5/5=1.

So for fourths, second mark should be 1/2.

But is that consistent with "using the fraction strip"? The strip is made of 1/4 pieces, so adding two gives 2/4, which equals 1/2.

I think it's acceptable to write 1/2.

However, to be precise, let’s see what the problem implies.

The problem says: “label the fractions” — plural — and doesn’t specify form.

Given that, and to avoid confusion, perhaps we should label them as multiples of the unit fraction used.

But I found a better way: look at the number of divisions.

For the first: 3 parts → labels at 1/3, 2/3

For the second: 4 parts → labels at 1/4, 2/4, 3/4 — but 2/4 can be written as 1/2.

In many textbooks, they write both: e.g., 2/4 (1/2)

But since this is a fill-in-the-blank style, probably single fraction per line.

I think the safest and most accurate approach is to label them as the sum of the unit fractions from the strip, and simplify only if it results in a whole number or obvious benchmark.

But 2/4 is obviously 1/2.

Let me decide:

After checking multiple sources mentally, I recall that in such exercises, for fourths, the labels are typically:

1/4, 1/2, 3/4

Because 2/4 is simplified to 1/2.

Similarly, if it were sixths, 2/6 becomes 1/3, etc.

So I'll go with simplified form where applicable.

Thus:

Second Number Line (fourths):

- First tick: 1/4

- Second tick: 2/4 = 1/2

- Third tick: 3/4

Third Number Line (fifths):

Strip has five 1/5 pieces → divide into 5 equal parts.

Labels:

- First: 1/5

- Second: 2/5

- Third: 3/5

- Fourth: 4/5

None of these simplify except 5/5=1.

So now, compiling all:

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Final labeling:

First number line (thirds):

Between 0 and 1, two dashed lines:

- Left dashed line: 1/3

- Right dashed line: 2/3

Second number line (fourths):

Three dashed lines:

- First: 1/4

- Second: 1/2 (since 2/4 = 1/2)

- Third: 3/4

Third number line (fifths):

Four dashed lines:

- First: 1/5

- Second: 2/5

- Third: 3/5

- Fourth: 4/5

This matches standard educational practice.

Now, to present the answer clearly.

Since the question is to "label the fractions", and there are multiple blanks implied (the dashed lines), we need to list the fractions for each number line in order from left to right.

So:

For the first number line (under 1/3 strips): labels are 1/3 and 2/3

For the second (under 1/4 strips): 1/4, 1/2, 3/4

For the third (under 1/5 strips): 1/5, 2/5, 3/5, 4/5

I think that's correct.

Just to double-check calculations:

- Thirds: 1/3 + 1/3 = 2/3; 2/3 + 1/3 = 1 → correct

- Fourths: 1/4, then 1/4+1/4=2/4=1/2, then 1/2+1/4=3/4, then 3/4+1/4=1 → correct

- Fifths: 1/5, 2/5, 3/5, 4/5, 5/5=1 → correct

All good.

Final Answer:

First number line: \frac{1}{3}, \frac{2}{3}

Second number line: \frac{1}{4}, \frac{1}{2}, \frac{3}{4}

Third number line: \frac{1}{5}, \frac{2}{5}, \frac{3}{5}, \frac{4}{5}