Convert mixed numbers to improper fractions with this math worksheet.

Let’s solve each problem step by step.

To convert a mixed number to an improper fraction:
1. Multiply the whole number by the denominator.
2. Add the numerator to that result.
3. Keep the same denominator.

We’ll do this for all 15 problems.

---

Problem 1: 4 5/7

→ (4 × 7) + 5 = 28 + 5 = 33
→ Denominator stays 7
→ 33/7

---

Problem 2: 3 5/7

→ (3 × 7) + 5 = 21 + 5 = 26
→ Denominator stays 7
→ 26/7

---

Problem 3: 3 4/7

→ (3 × 7) + 4 = 21 + 4 = 25
→ Denominator stays 7
→ 25/7

---

Problem 4: 2 3/8

→ (2 × 8) + 3 = 16 + 3 = 19
→ Denominator stays 8
→ 19/8

---

Problem 5: 1 5/6

→ (1 × 6) + 5 = 6 + 5 = 11
→ Denominator stays 6
→ 11/6

---

Problem 6: 3 4/7

→ (3 × 7) + 4 = 21 + 4 = 25
→ Denominator stays 7
→ 25/7

*(Same as Problem 3 — that’s okay!)*

---

Problem 7: 3 1/3

→ (3 × 3) + 1 = 9 + 1 = 10
→ Denominator stays 3
→ 10/3

---

Problem 8: 2 7/9

→ (2 × 9) + 7 = 18 + 7 = 25
→ Denominator stays 9
→ 25/9

---

Problem 9: 1 3/5

→ (1 × 5) + 3 = 5 + 3 = 8
→ Denominator stays 5
→ 8/5

---

Problem 10: 2 8/9

→ (2 × 9) + 8 = 18 + 8 = 26
→ Denominator stays 9
→ 26/9

---

Problem 11: 2 2/3

→ (2 × 3) + 2 = 6 + 2 = 8
→ Denominator stays 3
→ 8/3

---

Problem 12: 1 2/7

→ (1 × 7) + 2 = 7 + 2 = 9
→ Denominator stays 7
→ 9/7

---

Problem 13: 3 2/5

→ (3 × 5) + 2 = 15 + 2 = 17
→ Denominator stays 5
→ 17/5

---

Problem 14: 4 3/6

First, simplify 3/6 → 1/2? But wait — we’re converting to improper fraction, so let’s keep it as is unless told to simplify. The question doesn’t say to simplify, so we’ll just convert.

→ (4 × 6) + 3 = 24 + 3 = 27
→ Denominator stays 6
→ 27/6

But note: 27/6 can be simplified to 9/2, but since the example in the worksheet didn’t simplify (they left 17/5), we’ll leave it as 27/6 unless instructed otherwise. However, looking at the example: they converted 3 2/5 to 17/5 and did NOT simplify further. So we follow that pattern.

BUT — wait! In the example, 3 2/5 became 17/5 — which is already simplified. Here, 27/6 reduces to 9/2. Should we reduce?

Looking again at the worksheet instructions: “Convert Mixed Numbers to Improper Fractions.” It does not say “simplify”. The example answer is 17/5 — which is already in simplest form. But if we get something like 27/6, should we reduce?

Actually, in most math classes, you are expected to simplify fractions unless told otherwise. Let me check the example again: 3 2/5 → (5×3)+2=17 → 17/5. That’s correct and simplified.

In problem 14: 4 3/6 — first, 3/6 is equal to 1/2, so maybe the mixed number should be written as 4 1/2? But the problem says 4 3/6, so we treat it as given.

However, when converting, we still do: (4 × 6) + 3 = 27 → 27/6.

Now, 27/6 simplifies by dividing numerator and denominator by 3 → 9/2.

Since the goal is to write an improper fraction, and 9/2 is also improper and simpler, I think we should simplify. But let’s see what the worksheet expects.

Looking at the example: they didn’t have to simplify because 17/5 was already reduced. But in real practice, teachers usually want simplified answers.

Wait — actually, in the problem list, problem 14 is written as “4 3/6”, which is unusual because 3/6 reduces. Maybe it’s a trick? Or maybe it’s intentional to test if students simplify?

I think safest is to convert as given, then simplify if possible. Since 27/6 = 9/2, and 9/2 is simpler, we’ll go with 9/2.

But let’s double-check with another one.

Problem 15: 1 3/5 → (1×5)+3=8 → 8/5 — already simplified.

So for consistency, if we get a reducible fraction, we should reduce it.

Therefore, for problem 14: 27/6 = 9/2.

Alternatively, maybe the problem meant 4 3/6 as is, and wants 27/6. But that seems odd.

Actually, let’s look back at the original image description — no, we can’t refer to image. But based on standard math practice, we simplify fractions.

I’ll go with simplified form.

So:

Problem 14: 4 3/6

→ First, note that 3/6 = 1/2, so 4 3/6 = 4 1/2, but since the problem says 3/6, we compute directly:

(4 × 6) + 3 = 24 + 3 = 27 → 27/6

Simplify: divide numerator and denominator by 3 → 9/2

→ 9/2

---

Problem 15: 1 3/5

→ (1 × 5) + 3 = 5 + 3 = 8
→ Denominator stays 5
→ 8/5

---

Now, let’s list all answers clearly:

1) 33/7
2) 26/7
3) 25/7
4) 19/8
5) 11/6
6) 25/7
7) 10/3
8) 25/9
9) 8/5
10) 26/9
11) 8/3
12) 9/7
13) 17/5
14) 9/2 *(after simplifying 27/6)*
15) 8/5

Wait — problem 14: is 4 3/6 really intended to be simplified before converting? Actually, no — the conversion process doesn’t require simplifying the fractional part first. You just multiply whole number by denominator, add numerator, over denominator.

So strictly speaking, 4 3/6 converts to (4×6 + 3)/6 = 27/6.

And 27/6 is an improper fraction. Whether to simplify depends on instruction.

But in the example given in the worksheet: 3 2/5 → 17/5, which is already simplified. They didn’t show any case where simplification was needed.

However, in educational contexts, unless specified, we usually present fractions in simplest form.

Moreover, 27/6 is not wrong, but 9/2 is better.

To be safe, let’s check online or standard practice — but since I can’t, I’ll assume we simplify.

Alternatively, perhaps the problem has a typo and meant 4 3/6 as 4 1/2, but we must work with what’s given.

Another thought: in the worksheet, all denominators in the answers are the same as input, except when simplified. But in the example, denominator stayed 5.

For consistency, maybe we should not simplify unless asked.

But let’s see problem 14: 4 3/6 — if we leave as 27/6, it’s correct but not simplified. If we simplify to 9/2, it’s also correct and neater.

I recall that in many textbooks, after converting, they expect simplified form.

For instance, Khan Academy or similar platforms would reduce 27/6 to 9/2.

So I’ll go with 9/2.

Final decision: simplify all fractions to lowest terms.

Thus:

Problem 14: 27/6 = 9/2

All others are already simplified.

Let me verify each:

1) 33/7 — 33 and 7 coprime → ok
2) 26/7 — ok
3) 25/7 — ok
4) 19/8 — ok
5) 11/6 — ok
6) 25/7 — ok
7) 10/3 — ok
8) 25/9 — ok
9) 8/5 — ok
10) 26/9 — ok
11) 8/3 — ok
12) 9/7 — ok
13) 17/5 — ok
14) 27/6 = 9/2 — yes
15) 8/5 — ok

Perfect.

Final Answer:
1) 33/7
2) 26/7
3) 25/7
4) 19/8
5) 11/6
6) 25/7
7) 10/3
8) 25/9
9) 8/5
10) 26/9
11) 8/3
12) 9/7
13) 17/5
14) 9/2
15) 8/5