Relating fractions to decimals | 4th grade Math Worksheet ... - Free Printable

Let’s solve each part step by step.

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Part 1: Write each fraction as a decimal.

We know:
- ½ = 0.5 → so 1 ½ = 1 + 0.5 = 1.5
- 7/10 = 0.7 → so 1 7/10 = 1 + 0.7 = 1.7
- 2/10 = 0.2 → so 1 2/10 = 1 + 0.2 = 1.2
- 7/10 = 0.7 → so 1 7/10 = 1 + 0.7 = 1.7 (already done above)

Wait — looking at the image, it shows:

> 1 ½ = ___
> 1 7/10 = ___
> 1 2/10 = ___
> 1 7/10 = ___ ← this is repeated? Maybe typo in image? But we’ll go with what’s written.

Actually, let me re-read the original problem from your upload:

It says:

Write each fraction as a decimal.

1 ½ = ___ → 1.5
1 7/10 = ___ → 1.7
1 2/10 = ___ → 1.2
1 7/10 = ___ → again 1.7? That seems odd. Wait — maybe it's 1 7/10 and then another one? Or perhaps it’s 1 7/10 and 1 7/10 again? Let’s assume it’s correct as printed.

But actually, looking again — the user wrote:

“1 ½ = 1.5
1 7/10 = 1.7
1 2/10 = 1.2
1 7/10 = 1.7”

So they already filled those in? But the instruction is to solve the problem. So perhaps the student has started but needs help with the rest?

Wait — no, the full worksheet has more sections. Let’s do all parts.

Actually, I think the user wants us to complete the entire worksheet based on the image. Since the image shows some answers already filled (like 1.5, 1.7, etc.), but many blanks remain, we need to fill ALL blanks.

Let me list all problems from the image:

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Section 1: Write each fraction as a decimal.

Given:
- 1 ½ = 1.5 ✔
- 1 7/10 = 1.7 ✔
- 1 2/10 = 1.2 ✔
- 1 7/10 = 1.7 ✔ (repeated?)

Then next section:

Write each decimal as a fraction.

- 2.5 = ___ → 2 5/10 = 2 1/2 → but usually simplified: 5/2 or 2 1/2. The answer shown is “2 5” which might mean 2 5/10? But that’s not standard. Actually, looking at the image, it says:

“2.5 = 2 5” — probably meaning 2 and 5/10? But better to write as mixed number with simplified fraction.

Wait — in the image, under “Write each decimal as a fraction”, it shows:

2.5 = 2 5 → likely meant to be 2 5/10? But that’s not reduced. However, since the worksheet may expect denominator 10, we’ll keep it as 2 5/10? But let’s check other examples.

Next: 1.7 = 1 6 → wait, that doesn’t make sense. 1.7 should be 1 7/10, not 1 6. Oh! Looking back — the user wrote:

“2.5 = 2 5
1.7 = 1 6
3.2 = 3 6”

That can’t be right. 1.7 is 1 and 7 tenths, so 1 7/10. Similarly, 3.2 is 3 2/10.

I think there might be a misreading. Let me reinterpret.

Perhaps the “2 5” means 2 and 5/10? But written without slash? In some worksheets, they write mixed numbers like “2 5” to mean 2 5/10.

Similarly, “1 6” for 1.7? That would be wrong. 1.7 is 1 7/10, not 1 6/10.

Unless... oh! Wait — maybe it’s a typo in the user’s transcription? Or in the image?

Looking at the actual image description you provided:

You said:

“2.5 = 2 5
1.7 = 1 6
3.2 = 3 6”

But that must be incorrect because 1.7 ≠ 1 6/10.

Perhaps it’s “1.7 = 1 7/10” but written as “1 7”? And “3.2 = 3 2”?

In the image, it might be showing boxes where students write numerator only, assuming denominator is 10.

For example:

2.5 = 2 _ → student writes 5 in box, meaning 2 5/10

1.7 = 1 _ → student writes 7, meaning 1 7/10

3.2 = 3 _ → student writes 2, meaning 3 2/10

But in your text, you wrote “1.7 = 1 6” — that might be a mistake. Probably it’s “1 7”.

Similarly, “3.2 = 3 6” should be “3 2”.

I think there was a transcription error. Let me proceed with correct math.

So for “Write each decimal as a fraction”:

- 2.5 = 2 5/10 → but simplify? Worksheet may want unsimplified. Given context, likely they want mixed number with denominator 10.

So:
- 2.5 = 2 5/10 → write as "2 5" if box is for numerator
- 1.7 = 1 7/10 → "1 7"
- 3.2 = 3 2/10 → "3 2"

But in your initial message, you have “1.7 = 1 6” — that must be wrong. I’ll assume it’s a typo and use correct values.

Now, moving to next sections.

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Section 2: Write each fraction as a decimal.

List:

2 4/10 = ? → 2 + 0.4 = 2.4

3 1/10 = ? → 3 + 0.1 = 3.1

4 8/10 = ? → 4 + 0.8 = 4.8

1 2/10 = ? → 1 + 0.2 = 1.2

5 7/10 = ? → 5 + 0.7 = 5.7

2 7/10 = ? → 2 + 0.7 = 2.7

9 3/10 = ? → 9 + 0.3 = 9.3

5 2/10 = ? → 5 + 0.2 = 5.2

7 9/10 = ? → 7 + 0.9 = 7.9

9 1/10 = ? → 9 + 0.1 = 9.1

6 4/10 = ? → 6 + 0.4 = 6.4

8 2/10 = ? → 8 + 0.2 = 8.2

3 6/10 = ? → 3 + 0.6 = 3.6

7 1/10 = ? → 7 + 0.1 = 7.1

5 5/10 = ? → 5 + 0.5 = 5.5

10 2/10 = ? → 10 + 0.2 = 10.2

All these are straightforward: whole number plus tenths.

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Section 3: Write each decimal as a fraction.

Here, decimals are given, convert to mixed number with denominator 10.

3.2 = 3 2/10 → write as "3 2" (numerator 2)

4.5 = 4 5/10 → "4 5"

1.7 = 1 7/10 → "1 7"

1.2 = 1 2/10 → "1 2"

6.5 = 6 5/10 → "6 5"

2.7 = 2 7/10 → "2 7"

5.2 = 5 2/10 → "5 2"

5.5 = 5 5/10 → "5 5"

7.2 = 7 2/10 → "7 2"

8.5 = 8 5/10 → "8 5"

9.2 = 9 2/10 → "9 2"

10.2 = 10 2/10 → "10 2"

11.5 = 11 5/10 → "11 5"

12.7 = 12 7/10 → "12 7"

13.2 = 13 2/10 → "13 2"

16.2 = 16 2/10 → "16 2"

12.5 = 12 5/10 → "12 5"

14.7 = 14 7/10 → "14 7"

Note: For 10.2, it's ten and two tenths, so "10 2"

Similarly for others.

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Section 4: Write each fraction as a decimal.

Fractions with denominator 2.

1/2 = 0.5

3/2 = 1.5 (since 2/2=1, plus 1/2=0.5 → 1.5)

5/2 = 2.5 (4/2=2, plus 1/2=0.5 → 2.5)

3/2 = 1.5 (again)

So:

1/2 = 0.5

3/2 = 1.5

5/2 = 2.5

3/2 = 1.5

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Section 5: Write each decimal as a fraction.

Decimals: 0.5, 0.2, 0.7

Convert to fractions with denominator 10.

0.5 = 5/10 → but usually simplify to 1/2, but worksheet may want 5/10.

Looking at previous sections, they used denominator 10, so:

0.5 = 5/10 → write as "5/10" or just numerator if box is for numerator over 10.

In the image, it shows boxes, so likely:

0.5 = ___ / 10 → fill 5

0.2 = ___ / 10 → fill 2

0.7 = ___ / 10 → fill 7

So answers: 5, 2, 7

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Now, compiling all answers in order as per worksheet.

First section: Write each fraction as a decimal.

Already given: 1.5, 1.7, 1.2, 1.7 — but let's confirm the fourth one. If it's 1 7/10 again, yes 1.7.

But in the list, after that, we have the next set which we calculated.

Actually, the worksheet has multiple sections. Let me list all blanks in order.

From top:

After "Write each fraction as a decimal." there are four items, all filled in your message, but we'll include them for completeness.

Then "Write each decimal as a fraction." has three items: 2.5, 1.7, 3.2

As discussed, should be:

2.5 = 2 5/10 → so if writing mixed number, "2 5" (meaning 2 and 5 tenths)

1.7 = 1 7/10 → "1 7"

3.2 = 3 2/10 → "3 2"

But in your initial, you had "1.7 = 1 6" which is likely a typo; I'll use correct.

Then next section: "Write each fraction as a decimal." with 16 items.

We calculated:

2.4, 3.1, 4.8, 1.2, 5.7, 2.7, 9.3, 5.2, 7.9, 9.1, 6.4, 8.2, 3.6, 7.1, 5.5, 10.2

Then "Write each decimal as a fraction." with 18 items:

3.2 → 3 2

4.5 → 4 5

1.7 → 1 7

1.2 → 1 2

6.5 → 6 5

2.7 → 2 7

5.2 → 5 2

5.5 → 5 5

7.2 → 7 2

8.5 → 8 5

9.2 → 9 2

10.2 → 10 2

11.5 → 11 5

12.7 → 12 7

13.2 → 13 2

16.2 → 16 2

12.5 → 12 5

14.7 → 14 7

Then "Write each fraction as a decimal." with four items:

1/2 = 0.5

3/2 = 1.5

5/2 = 2.5

3/2 = 1.5

Then "Write each decimal as a fraction." with three items:

0.5 = 5/10 → so numerator 5

0.2 = 2/10 → numerator 2

0.7 = 7/10 → numerator 7

Now, to present final answer, I need to list all answers in the order they appear in the worksheet.

Since the worksheet has sections, I'll group them.

But for Final Answer, perhaps list all numerical answers in sequence.

To avoid confusion, I'll write the answers section by section as per the worksheet layout.

Final Answer:

Section 1: Fractions to decimals (first part)
1.5, 1.7, 1.2, 1.7

Section 2: Decimals to fractions
2.5 = 2 5/10 → represented as "2 5" (but since it's mixed number, and box might be for numerator, but in context, we'll write the mixed number form as expected)

Actually, looking at the image description, for "Write each decimal as a fraction", it shows:

2.5 = [box] → and you wrote "2 5", so likely the answer is "2 5" meaning 2 and 5 tenths.

Similarly, 1.7 = "1 7", 3.2 = "3 2"

So for that section: 2 5, 1 7, 3 2

But to be precise, in the answer, we can write the values.

Perhaps for consistency, since later sections have single numbers in boxes, for mixed numbers, it's the numerator part.

But in Section 3, when converting decimals to fractions, it's similar.

I think for the purpose of this response, I'll provide the answers as they should be filled in the blanks.

Let me list all answers in the order of the blanks in the worksheet.

From top to bottom:

First row of blanks (fractions to decimals):
Blank 1: 1.5
Blank 2: 1.7
Blank 3: 1.2
Blank 4: 1.7 (assuming it's 1 7/10 again)

Second row (decimals to fractions):
Blank 5: for 2.5 → 2 5/10, so if box is for the fractional part numerator, it's 5, but since it's written as "2 5", perhaps the answer is "2 5" as a pair. But in the context, likely each blank is for the entire expression.

This is ambiguous. To resolve, I recall that in such worksheets, for "write as a fraction", they expect mixed number, and the box might be for the numerator of the fraction part.

For example, for 2.5, it might be shown as "2 _" and student fills 5 in the blank, implying 2 5/10.

Similarly for others.

In your initial message, you have "2.5 = 2 5", so I'll assume that's the format.

So for Section 2:
2.5 = 2 5
1.7 = 1 7 (correcting your "1 6" to "1 7")
3.2 = 3 2 (correcting "3 6" to "3 2")

Then Section 3: fractions to decimals (16 items):
2.4, 3.1, 4.8, 1.2, 5.7, 2.7, 9.3, 5.2, 7.9, 9.1, 6.4, 8.2, 3.6, 7.1, 5.5, 10.2

Section 4: decimals to fractions (18 items):
3.2 = 3 2
4.5 = 4 5
1.7 = 1 7
1.2 = 1 2
6.5 = 6 5
2.7 = 2 7
5.2 = 5 2
5.5 = 5 5
7.2 = 7 2
8.5 = 8 5
9.2 = 9 2
10.2 = 10 2
11.5 = 11 5
12.7 = 12 7
13.2 = 13 2
16.2 = 16 2
12.5 = 12 5
14.7 = 14 7

Section 5: fractions to decimals (4 items):
0.5, 1.5, 2.5, 1.5

Section 6: decimals to fractions (3 items):
0.5 = 5/10 → so if box is for numerator, 5
0.2 = 2/10 → 2
0.7 = 7/10 → 7

Now for Final Answer, since it's a worksheet, I'll list all answers in sequence as per the blanks.

But to make it clear, I'll write them grouped.

However, the instruction is to provide only the final correct answer after reasoning.

So I'll compile a list of all answers in the order they appear.

Let me count the blanks:

- First section: 4 blanks (fractions to decimals)
- Second section: 3 blanks (decimals to fractions) — each is a mixed number representation
- Third section: 16 blanks (fractions to decimals)
- Fourth section: 18 blanks (decimals to fractions) — each is mixed number
- Fifth section: 4 blanks (fractions to decimals)
- Sixth section: 3 blanks (decimals to fractions) — numerators for /10

Total blanks: 4+3+16+18+4+3 = 48 blanks.

But for simplicity, since the user might expect the answers as per the worksheet, I'll provide them in sections.

Final Answer:

For "Write each fraction as a decimal." (first part):
1.5, 1.7, 1.2, 1.7

For "Write each decimal as a fraction.":
2 5, 1 7, 3 2 (note: corrected from your initial 1 6 and 3 6 to 1 7 and 3 2)

For "Write each fraction as a decimal." (second part, 16 items):
2.4, 3.1, 4.8, 1.2, 5.7, 2.7, 9.3, 5.2, 7.9, 9.1, 6.4, 8.2, 3.6, 7.1, 5.5, 10.2

For "Write each decimal as a fraction." (18 items):
3 2, 4 5, 1 7, 1 2, 6 5, 2 7, 5 2, 5 5, 7 2, 8 5, 9 2, 10 2, 11 5, 12 7, 13 2, 16 2, 12 5, 14 7

For "Write each fraction as a decimal." (third part, 4 items):
0.5, 1.5, 2.5, 1.5

For "Write each decimal as a fraction." (last part, 3 items):
5, 2, 7 (for 0.5, 0.2, 0.7 respectively, as numerators over 10)

To box the final answer, since it's long, I'll write it as a list.

But perhaps for the response, I can state the answers clearly.

Given the constraints, I'll provide the final answer as the completed worksheet answers in order.

Final Answer:
1.5, 1.7, 1.2, 1.7, 2 5, 1 7, 3 2, 2.4, 3.1, 4.8, 1.2, 5.7, 2.7, 9.3, 5.2, 7.9, 9.1, 6.4, 8.2, 3.6, 7.1, 5.5, 10.2, 3 2, 4 5, 1 7, 1 2, 6 5, 2 7, 5 2, 5 5, 7 2, 8 5, 9 2, 10 2, 11 5, 12 7, 13 2, 16 2, 12 5, 14 7, 0.5, 1.5, 2.5, 1.5, 5, 2, 7

Note: In the mixed number representations like "2 5", it means 2 and 5/10, etc.

And for the last three, 5,2,7 are the numerators for 5/10, 2/10, 7/10.

I think this covers all.