Math worksheet for converting mixed decimals to fractions.

Let’s solve each problem step by step. We’re converting mixed decimals (like 3.25) into fractions in simplest form.

We’ll break each decimal into:
- The whole number part
- The decimal part → convert to fraction over 10, 100, or 1000 depending on places
- Then simplify the fraction if needed

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2) 3.72

Break it:
3 + 0.72
0.72 = 72/100
Simplify 72/100: divide numerator and denominator by 4 → 18/25
So: 3 18/25

Wait — let me check: 72 ÷ 4 = 18, 100 ÷ 4 = 25 → yes.
Final: 3 18/25

But wait — is that right? Let me double-check with division:
3.72 = 372/100 → simplify: divide by 4 → 93/25 → which is 3 18/25 → correct.

Actually, 372 ÷ 4 = 93, 100 ÷ 4 = 25 → so 93/25 = 3 18/25 → yes.

✔ Final for #2: 3 18/25

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3) 8.65

8 + 0.65
0.65 = 65/100
Simplify: divide by 5 → 13/20
So: 8 13/20

Check: 65 ÷ 5 = 13, 100 ÷ 5 = 20 → yes.

✔ Final for #3: 8 13/20

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4) 0.523

No whole number → just 523/1000
Can we simplify? Check GCF of 523 and 1000.

523 is a prime number? Let’s see: divisible by 2? no. 3? 5+2+3=10 → not divisible by 3. 5? doesn’t end in 0 or 5. 7? 7×74=518, 523-518=5 → not divisible. 11? 5-2+3=6 → not divisible by 11. So likely prime.

So 523/1000 is already simplified.

✔ Final for #4: 523/1000

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5) 4.32

4 + 0.32
0.32 = 32/100
Simplify: divide by 4 → 8/25
So: 4 8/25

Check: 32÷4=8, 100÷4=25 → yes.

✔ Final for #5: 4 8/25

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6) 2.025

2 + 0.025
0.025 = 25/1000
Simplify: divide by 25 → 1/40
So: 2 1/40

Check: 25÷25=1, 1000÷25=40 → yes.

✔ Final for #6: 2 1/40

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7) 1.248

1 + 0.248
0.248 = 248/1000
Simplify: find GCF of 248 and 1000.

Divide both by 8:
248 ÷ 8 = 31
1000 ÷ 8 = 125
So: 31/125 → can’t simplify further (31 is prime)

So: 1 31/125

✔ Final for #7: 1 31/125

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8) 9.072

9 + 0.072
0.072 = 72/1000
Simplify: divide by 8 → 9/125
So: 9 9/125

Check: 72÷8=9, 1000÷8=125 → yes.

✔ Final for #8: 9 9/125

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9) 2.84

2 + 0.84
0.84 = 84/100
Simplify: divide by 4 → 21/25
So: 2 21/25

Check: 84÷4=21, 100÷4=25 → yes.

✔ Final for #9: 2 21/25

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10) 5.062

5 + 0.062
0.062 = 62/1000
Simplify: divide by 2 → 31/500
So: 5 31/500

Check: 62÷2=31, 1000÷2=500 → yes.

✔ Final for #10: 5 31/500

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11) 1.967

1 + 0.967
0.967 = 967/1000
Is this simplifiable? 967 — check if divisible by small primes.

Not even, sum 9+6+7=22 → not divisible by 3. Doesn’t end in 5 or 0 → not divisible by 5. Try 7: 7×138=966 → 967-966=1 → not divisible. 11: 9-6+7=10 → not divisible. Likely prime.

So: 1 967/1000

✔ Final for #11: 1 967/1000

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12) 8.8

8 + 0.8
0.8 = 8/10 = 4/5
So: 8 4/5

✔ Final for #12: 8 4/5

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13) 5.258

5 + 0.258
0.258 = 258/1000
Simplify: divide by 2 → 129/500
Check if 129 and 500 have common factors: 129 = 3×43, 500 = 2²×5³ → no common factors.

So: 5 129/500

✔ Final for #13: 5 129/500

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14) 6.875

6 + 0.875
0.875 = 875/1000
Simplify: divide by 125 → 7/8
Because 875 ÷ 125 = 7, 1000 ÷ 125 = 8

So: 6 7/8

✔ Final for #14: 6 7/8

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Now let’s list all answers clearly:

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Final Answer:
2) 3 18/25
3) 8 13/20
4) 523/1000
5) 4 8/25
6) 2 1/40
7) 1 31/125
8) 9 9/125
9) 2 21/25
10) 5 31/500
11) 1 967/1000
12) 8 4/5
13) 5 129/500
14) 6 7/8