Math worksheet for practicing division of fractions and whole numbers.

Let’s solve each problem step by step. Remember: when you divide a fraction by a whole number (or vice versa), you can turn the whole number into a fraction over 1, then flip the second fraction and multiply.

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1) ⅓ ÷ 7

Turn 7 into 7/1 → now it’s ⅓ ÷ 7/1
Flip the second fraction → ⅓ × 1/7 = 1/21

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2) 6 ÷

Turn 6 into 6/1 → 6/1 ÷ ⅓
Flip the second fraction → 6/1 × 3/1 = 18/1 = 18

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3) ¹⁄₁₀ ÷ 2

Turn 2 into 2/1 → ¹⁄₁₀ ÷ 2/1
Flip → ¹⁄₁₀ × 1/2 = 1/20

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4) 6 ÷ ⅓

Same as #2 → 6/1 × 3/1 = 18

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5) 5 ÷ ¾

Turn 5 into 5/1 → 5/1 ÷ ¾
Flip → 5/1 × 4/3 = 20/3 = 6 ²⁄₃ (or leave as improper fraction if needed — but mixed number is fine here)

Wait — let’s check: 20 ÷ 3 = 6 with remainder 2 → yes, 6 ²⁄₃

But sometimes worksheets want improper fractions. Let’s see what’s common — since others are simple, maybe keep as 20/3? But 6 ²⁄₃ is correct too. We’ll go with 20/3 unless specified otherwise. Actually, looking at other problems, they’re all simplified fractions or whole numbers. 20/3 is already simplified. So we’ll write 20/3.

Actually — let me double-check the instruction. The worksheet doesn’t specify format. Since 20/3 is exact and simplest form, we’ll use that.

BUT — in elementary math, often mixed numbers are preferred for answers >1. Let’s look at problem #9: 4 ÷ 4/10 — that will be 10, which is whole. Problem #8: 9 ÷ ½ = 18. So probably mixed numbers are okay. But to be safe, I’ll give both forms where needed. For now, let’s stick to simplest form — 20/3 is fine.

Actually, let’s recalculate: 5 × 4 = 20, denominator 3 → 20/3. Yes.

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6) ½ ÷ 6

Turn 6 into 6/1 → ½ ÷ 6/1
Flip → ½ × 1/6 = 1/12

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7) ⅓ ÷ 3

Turn 3 into 3/1 → ⅓ ÷ 3/1
Flip → ⅓ × 1/3 = 1/9

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8) 9 ÷ ½

Turn 9 into 9/1 → 9/1 ÷ ½
Flip → 9/1 × 2/1 = 18

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9) 4 ÷ ⁴⁄₁₀

First, simplify ⁴⁄₁₀ to ²⁄₅? Or not necessary — let’s do it as is.

4 ÷ ⁴⁄₁₀ → 4/1 ÷ ⁴⁄₁₀
Flip → 4/1 × ¹⁰⁄₄ = (4×10)/(1×4) = 40/4 = 10

Note: You could cancel the 4s first: 4/1 × 10/4 = 10/1 = 10. Same answer.

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10) ¼ ÷ 5

Turn 5 into 5/1 → ¼ ÷ 5/1
Flip → ¼ × 1/5 = 1/20

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Now let’s list all answers clearly:

1) 1/21
2) 18
3) 1/20
4) 18
5) 20/3 (or 6 ²⁄₃ — but since others are improper or whole, 20/3 is acceptable; however, let’s check if 20/3 reduces — no, so it’s fine)
Wait — actually, in many curricula, they prefer mixed numbers for final answers when greater than 1. Let me reconsider.

Looking back at the worksheet title: “Dividing Fractions and Whole Numbers” — likely expects simplified answers. 20/3 is simplified, but 6 ²⁄₃ is also correct. To match typical textbook style, I’ll use mixed number for #5.

So #5: 6 ²⁄₃

But let’s confirm calculation again: 5 ÷ 3/4 = 5 × 4/3 = 20/3 = 6 and 2/3 → yes.

Alternatively, if the worksheet expects improper fractions, 20/3 is fine. Since there’s no specification, and to be consistent with how most students are taught, I’ll go with 6 ²⁄₃ for #5.

Actually — looking at problem #9: 4 ÷ 4/10 = 10, which is whole. Others are small fractions. So perhaps mixed number is better for #5.

I think it’s safer to provide the answer as a mixed number when it’s greater than 1 and not a whole number. So:

#5: 6 ²⁄₃

Final Answers:

1) 1/21
2) 18
3) 1/20
4) 18
5) 6 ²⁄₃
6) 1/12
7) 1/9
8) 18
9) 10
10) 1/20

Let me verify #5 once more: 5 divided by 3/4 means how many 3/4 fit into 5? 3/4 fits into 1 four-thirds times, so into 5: 5 × 4/3 = 20/3 = 6.666... = 6 2/3. Correct.

All others seem solid.

Final Answer:
1) 1/21
2) 18
3) 1/20
4) 18
5) 6 ²⁄₃
6) 1/12
7) 1/9
8) 18
9) 10
10) 1/20