Grade 6 Fraction Worksheet: Convert Mixed Numbers to Decimals

To convert a mixed number to a decimal, we keep the whole number part as it is and convert only the fraction part into a decimal. Then we add them together.

Here’s how to do each one step by step:

---

1. 4 18/25

Fraction: 18 ÷ 25 = 0.72
Whole number: 4
→ 4 + 0.72 = 4.72

---

2. 1 2/3

Fraction: 2 ÷ 3 = 0.666... (repeating) → usually written as 0.6̅ or rounded to 0.67 if needed, but since this is exact conversion, we’ll use repeating decimal notation or leave as fraction? Wait — let’s check instructions: “Convert to decimals” — so we should write decimal form. For 2/3, it’s 0.666..., which is often written as 0.6̅. But in grade 6, sometimes they expect rounding or exact decimal if possible. However, 2/3 does not terminate. Let’s see other problems — some have denominators that divide evenly into powers of 10.

Actually, looking at problem 2: 1 2/3 — 2÷3=0.666… So answer is 1.666... or 1.6̅

But let’s check all first — maybe we can write as exact decimal where possible, and for repeating, use bar or round? The worksheet doesn’t specify, but since it’s grade 6, likely expects exact decimal if terminates, otherwise perhaps rounded to two places? But no instruction.

Wait — look at problem 4: 8 86/100 — that’s easy: 8.86

Problem 6: 7 42/50 — 42/50 = 84/100 = 0.84 → 7.84

So probably, for non-terminating, we should write the repeating decimal with bar, or maybe the problem expects us to recognize when it repeats.

But let’s proceed carefully.

Actually, re-examining: In many grade 6 worksheets, if the fraction doesn’t convert to a terminating decimal, they might still expect the decimal representation with ellipsis or bar. But to be safe, I’ll compute exactly.

Let me list all:

---

1. 4 18/25

18 ÷ 25 = 0.72 → 4.72

---

2. 1 2/3

2 ÷ 3 = 0.666... → 1.666... or 1.6̅

In many school contexts, they write it as 1.67 if rounding to hundredths, but since others are exact, perhaps we should note it's repeating. But let’s see what the standard is.

Actually, looking ahead: Problem 9: 7 13/30 — 13/30 = 0.4333... also repeating.

Problem 10: 4 1/2 = 4.5 — exact.

I think for consistency, we should write the exact decimal, using bar notation for repeating decimals if allowed, or just write the full repeating pattern? But since it’s a worksheet, likely expects numerical value.

Perhaps the teacher expects students to know that 2/3 = 0.666... and write 1.666... or 1.6̅.

But to match format, let’s assume we write the decimal as calculated.

Alternatively, maybe convert all fractions to have denominator 100 or 1000 if possible, but not always possible.

Another approach: multiply numerator and denominator to make denominator power of 10.

For 2/3: cannot make denominator power of 10, so it repeats.

I think for accuracy, I'll write the repeating decimal with bar where applicable.

But since the user didn't specify, and it's grade 6, perhaps they expect rounded to two decimal places? But no indication.

Looking at problem 15: 6 3/8 — 3/8=0.375, exact.

Problem 16: 2 2/3 — same as #2.

I recall that in such worksheets, for repeating decimals, they often accept the fractional form converted to decimal with bar or just write the first few digits. But to be precise, I'll calculate each exactly.

Let me do all calculations:

---

1. 4 18/25

18 ÷ 25 = 0.72 → 4.72

---

2. 1 2/3

2 ÷ 3 = 0.666... → 1.666... (or 1.6̅)

---

3. 10 1/2

1/2 = 0.5 → 10.5

---

4. 8 86/100

86/100 = 0.86 → 8.86

---

5. 10 1/4

1/4 = 0.25 → 10.25

---

6. 7 42/50

42/50 = ? Divide numerator and denominator by 2: 21/25

21 ÷ 25 = 0.84 → 7.84

(Or 42/50 = 84/100 = 0.84)

---

7. 8 4/5

4/5 = 0.8 → 8.8

---

8. 2 6/10

6/10 = 0.6 → 2.6

---

9. 7 13/30

13 ÷ 30 = ?

30 * 0.4 = 12, remainder 1 → 0.4 + 1/30

1/30 = 0.0333... so 0.4333... → 7.4333... or 7.43̅

More precisely: 13 ÷ 30 = 130 ÷ 300 = but better: 13/30 = 130/300 = wait, direct division:

30 into 130 (for tenths): 4 times (120), remainder 10 → bring down 0 → 100, 30*3=90, remainder 10 → so 0.4333... yes.

So 7.4333... or 7.43̅

---

10. 4 1/2

1/2 = 0.5 → 4.5

---

11. 4 21/25

21 ÷ 25 = 0.84 → 4.84

---

12. 9 3/8

3 ÷ 8 = 0.375 → 9.375

---

13. 1 41/50

41 ÷ 50 = 0.82 → 1.82

(Because 41/50 = 82/100 = 0.82)

---

14. 6 5/10

5/10 = 0.5 → 6.5

---

15. 6 3/8

3 ÷ 8 = 0.375 → 6.375

---

16. 2 2/3

Same as #2: 2/3 = 0.666... → 2.666... or 2.6̅

---

Now, for the repeating decimals, in many educational contexts at grade 6, they might expect the student to write the decimal as is, recognizing the repeat. Since the worksheet doesn't specify rounding, I'll present the exact decimal values, using bar notation for repeating parts where appropriate.

However, upon second thought, looking at common practice in such worksheets, for problems like 2/3, they often write it as 0.67 if rounding to nearest hundredth, but that would be approximate. Given that other answers are exact, and 2/3 is a common fraction, I think it's better to indicate the repeating nature.

But to match the expected output, perhaps the system wants the decimal representation as calculated without rounding.

I recall that in some curricula, they teach that 1/3 = 0.333..., so 2/3 = 0.666..., and they write it as such.

For consistency, I'll write all answers as decimals, and for repeating, I'll use the bar notation if possible, but since this is text, I'll write "0.666..." or specify.

But the final answer should be clean.

Perhaps the worksheet expects all answers as terminating decimals or rounded, but that doesn't make sense for 2/3.

Another idea: maybe convert all fractions to have denominator 100 by finding equivalent fractions.

For example:

2/3 = ? /100 — not integer, so not possible.

So, I think we have to accept repeating decimals.

Let me check online or standard practice — but since I can't, I'll proceed with exact values.

For the purpose of this response, I'll write the decimal as computed, and for repeating, I'll use the ellipsis or bar.

But in the final answer, to keep it simple, perhaps list them as:

1. 4.72

2. 1.666... (but better to use bar)

Since this is text, I'll write "1.6 repeating" but that's not standard.

I think for accuracy, I'll calculate each and present the decimal form, and for repeating, note it.

But let's see the user's request: "Solve the problem accurately." and "provide only the final correct answer"

So for the final answer section, I need to list all 16 answers.

Perhaps in such cases, for 2/3, they expect 0.67, but that's rounded.

Let's look at problem 9: 13/30 — 13÷30=0.4333..., which is 0.43 if rounded to hundredths, but again, not specified.

I recall that in K5 Learning worksheets, for converting mixed numbers to decimals, they include both terminating and repeating, and for repeating, they might expect the student to recognize and write the repeating decimal.

Upon checking my knowledge, in grade 6, students learn that some fractions result in repeating decimals, and they are taught to identify them.

So for accuracy, I'll provide the exact decimal representation.

To make it neat, I'll write:

For 2/3: 0.\overline{6}

Similarly for others.

In text, I can write "1.666..." but bar is better.

Since the final answer will be in text, I'll use the following convention:

- For terminating decimals: write as is

- For repeating decimals: write with bar over the repeating digit(s)

So:

2. 1 \overline{6} (meaning 1.666...)

9. 7.4\overline{3} (since 13/30 = 0.4333... = 0.4\overline{3})

16. 2 \overline{6}

Let me confirm 13/30:

13 ÷ 30 = 0.4333... yes, because 30*0.4=12, remainder 1, then 10/30=1/3=0.333..., so 0.4 + 0.0333... = 0.4333... so the '3' repeats, so 0.4\overline{3}

Similarly, 2/3 = 0.\overline{6}

Now for the list:

1. 4.72

2. 1.\overline{6}

3. 10.5

4. 8.86

5. 10.25

6. 7.84

7. 8.8

8. 2.6

9. 7.4\overline{3}

10. 4.5

11. 4.84

12. 9.375

13. 1.82

14. 6.5

15. 6.375

16. 2.\overline{6}

But in the final answer, how to format? Probably as a list.

Since the user said "Final Answer: [Provide only the final correct answer]", and it's multiple items, I should list them numbered.

Also, for 7.8, is it 8.8 or 8.80? Usually we write 8.8, same as 2.6.

For 10.5, etc.

Now, double-check calculations:

1. 18/25: 25*0.72=18, yes.

2. 2/3≈0.6667, but exact is repeating.

3. 1/2=0.5, yes.

4. 86/100=0.86, yes.

5. 1/4=0.25, yes.

6. 42/50=84/100=0.84, yes.

7. 4/5=0.8, yes.

8. 6/10=0.6, yes.

9. 13/30: let's calculate: 30*0.4333=30*0.4=12, 30*0.0333=0.999, total 12.999≈13, yes. Exact: 13/30 = 130/300 = 13/30, decimal 0.4333...

10. 1/2=0.5, yes.

11. 21/25=84/100=0.84, yes.

12. 3/8=0.375, since 8*0.375=3, yes.

13. 41/50=82/100=0.82, yes.

14. 5/10=0.5, yes.

15. 3/8=0.375, yes.

16. Same as 2.

All good.

For the final answer, I'll list them as:

1. 4.72
2. 1.666... (but to be precise, I'll use bar notation in text as "1.\overline{6}")

Since this is plain text, perhaps write "1.6 repeating" but that's informal.

I think for the context, since it's a math problem, using the overline is acceptable, but in text, we can write it as 1.(6) or something, but standard is overline.

Upon reflection, in many digital platforms, they use "1.666..." for repeating.

To avoid confusion, and since the worksheet likely expects the decimal value as calculated, I'll write the answers with repeating decimals indicated by ellipsis for simplicity, as it's common in such contexts.

So:

2. 1.666...

9. 7.4333...

16. 2.666...

But for 9, it's 7.4333..., which is 7.4 followed by repeating 3s.

Similarly, for 2 and 16, repeating 6s.

In the final answer, I'll list them clearly.

Perhaps the system expects all answers as decimals without specification, but that would be inaccurate for repeating ones.

Another thought: in some curricula, they might want the fraction converted by dividing, and write the result as is.

I think I'm overcomplicating. Let me provide the answers as per calculation, and for repeating, use the bar notation in the final answer as it's mathematically accurate.

So for Final Answer:

1. 4.72
2. \( 1.\overline{6} \)
3. 10.5
4. 8.86
5. 10.25
6. 7.84
7. 8.8
8. 2.6
9. \( 7.4\overline{3} \)
10. 4.5
11. 4.84
12. 9.375
13. 1.82
14. 6.5
15. 6.375
16. \( 2.\overline{6} \)

But since the output is text, and LaTeX might not render, perhaps write in words or use alternative.

Given that, and to keep it simple, I'll write the repeating decimals as "1.666..." etc., as it's understandable.

So:

Final Answer:
1. 4.72
2. 1.666...
3. 10.5
4. 8.86
5. 10.25
6. 7.84
7. 8.8
8. 2.6
9. 7.4333...
10. 4.5
11. 4.84
12. 9.375
13. 1.82
14. 6.5
15. 6.375
16. 2.666...

For 9, 7.4333... is correct, but technically it's 7.43 with 3 repeating, so 7.4333... implies the 3 repeats, which is fine.

To be precise, for 9, it's 7.4333... with the 3 repeating, so writing 7.4333... is acceptable.

Similarly for others.

I think this is fine.

So I'll go with that.