Convert Improper Fractions to Mixed Fractions worksheets - Math ... - Free Printable
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Step-by-step solution for: Convert Improper Fractions to Mixed Fractions worksheets - Math ...
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Show Answer Key & Explanations
Step-by-step solution for: Convert Improper Fractions to Mixed Fractions worksheets - Math ...
Let’s simplify each fraction step by step. We’ll find the greatest common factor (GCF) of the numerator and denominator, then divide both by that number to get the simplest form.
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1. 12/18
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 18: 1, 2, 3, 6, 9, 18
GCF = 6
→ 12 ÷ 6 = 2
→ 18 ÷ 6 = 3
✔ 2/3
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2. 15/20
Factors of 15: 1, 3, 5, 15
Factors of 20: 1, 2, 4, 5, 10, 20
GCF = 5
→ 15 ÷ 5 = 3
→ 20 ÷ 5 = 4
✔ 3/4
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3. 3/6
GCF = 3
→ 3 ÷ 3 = 1
→ 6 ÷ 3 = 2
✔ 1/2
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4. 145/500
Let’s check GCF. Both end in 5 → divisible by 5.
145 ÷ 5 = 29
500 ÷ 5 = 100
29 is prime, doesn’t divide 100 → done!
✔ 29/100
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5. 954/150
Both even → divide by 2 first:
954 ÷ 2 = 477
150 ÷ 2 = 75
Now 477 and 75 → sum of digits: 4+7+7=18 (div by 3), 7+5=12 (div by 3)
477 ÷ 3 = 159
75 ÷ 3 = 25
159 ÷ 3 = 53 (since 1+5+9=15)
25 not divisible by 3 → stop
So we divided by 2 × 3 × 3 = 18? Wait — let’s do it cleanly:
Actually, better to find GCF directly or step-by-step:
Start with 954 and 150.
Divide both by 6? Let’s try:
954 ÷ 6 = 159
150 ÷ 6 = 25
Now 159 and 25 → 25 is 5×5, 159 ÷ 5? No. 159 ÷ 3 = 53 → but 25 not divisible by 3. So GCF was 6? Wait — actually:
Wait — 954 ÷ 6 = 159? 6×159=954? 6×150=900, 6×9=54 → yes.
150 ÷ 6 = 25 → correct.
But 159 and 25 have no common factors → so simplified is 159/25
But wait — can we reduce more? 159 ÷ 3 = 53, 25 not divisible by 3 → yes, done.
But 159/25 is an improper fraction — that’s okay, question says “proper and improper”.
Alternatively, maybe we missed a bigger GCF?
Let me check GCF of 954 and 150.
Prime factors:
150 = 2 × 3 × 5²
954 ÷ 2 = 477 → 477 ÷ 3 = 159 → 159 ÷ 3 = 53 → so 954 = 2 × 3² × 53
Common factors: 2 and 3 → GCF = 6
Yes → 954 ÷ 6 = 159, 150 ÷ 6 = 25 → 159/25
✔ 159/25
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6. 150/36
Both divisible by 6?
150 ÷ 6 = 25
36 ÷ 6 = 6
25 and 6 → no common factors → done
✔ 25/6
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7. 20/25
GCF = 5
20 ÷ 5 = 4
25 ÷ 5 = 5
✔ 4/5
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8. 14/21
GCF = 7
14 ÷ 7 = 2
21 ÷ 7 = 3
✔ 2/3
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9. 84/140
Both divisible by 28? Or step by step.
Divide by 2: 42/70
Again by 2: 21/35
Now 21 and 35 → GCF = 7
21 ÷ 7 = 3
35 ÷ 7 = 5
So total divided by 2×2×7=28
84 ÷ 28 = 3
140 ÷ 28 = 5
✔ 3/5
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10. 70/20
GCF = 10
70 ÷ 10 = 7
20 ÷ 10 = 2
✔ 7/2
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11. 132/30
Both divisible by 6?
132 ÷ 6 = 22
30 ÷ 6 = 5
22 and 5 → no common factors
✔ 22/5
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12. 76/12
Both divisible by 4?
76 ÷ 4 = 19
12 ÷ 4 = 3
19 is prime → done
✔ 19/3
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13. 1092/140
Let’s find GCF.
First, both even → divide by 2:
1092 ÷ 2 = 546
140 ÷ 2 = 70
Again even → divide by 2:
546 ÷ 2 = 273
70 ÷ 2 = 35
Now 273 and 35.
35 = 5 × 7
273 ÷ 7 = 39 (because 7×39=273)
35 ÷ 7 = 5
So now we have 39/5
Total divided by 2×2×7=28
Check: 1092 ÷ 28 = ? 28×39=1092? 28×40=1120, minus 28=1092 → yes
140 ÷ 28 = 5 → yes
✔ 39/5
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14. 216/96
Both divisible by 24? Or step by step.
Divide by 8:
216 ÷ 8 = 27
96 ÷ 8 = 12
Now 27/12 → divide by 3: 9/4
So overall divided by 8×3=24
216 ÷ 24 = 9
96 ÷ 24 = 4
✔ 9/4
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15. 262/50
Both even → divide by 2:
262 ÷ 2 = 131
50 ÷ 2 = 25
131 is prime? Yes, doesn’t divide 25 → done
✔ 131/25
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16. 1160/400
Both divisible by 40? Or step by step.
Divide by 10: 116/40
Again by 4: 29/10
So total divided by 40? 1160 ÷ 40 = 29, 400 ÷ 40 = 10 → yes
✔ 29/10
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Final Answer:
1. 2/3
2. 3/4
3. 1/2
4. 29/100
5. 159/25
6. 25/6
7. 4/5
8. 2/3
9. 3/5
10. 7/2
11. 22/5
12. 19/3
13. 39/5
14. 9/4
15. 131/25
16. 29/10
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1. 12/18
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 18: 1, 2, 3, 6, 9, 18
GCF = 6
→ 12 ÷ 6 = 2
→ 18 ÷ 6 = 3
✔ 2/3
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2. 15/20
Factors of 15: 1, 3, 5, 15
Factors of 20: 1, 2, 4, 5, 10, 20
GCF = 5
→ 15 ÷ 5 = 3
→ 20 ÷ 5 = 4
✔ 3/4
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3. 3/6
GCF = 3
→ 3 ÷ 3 = 1
→ 6 ÷ 3 = 2
✔ 1/2
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4. 145/500
Let’s check GCF. Both end in 5 → divisible by 5.
145 ÷ 5 = 29
500 ÷ 5 = 100
29 is prime, doesn’t divide 100 → done!
✔ 29/100
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5. 954/150
Both even → divide by 2 first:
954 ÷ 2 = 477
150 ÷ 2 = 75
Now 477 and 75 → sum of digits: 4+7+7=18 (div by 3), 7+5=12 (div by 3)
477 ÷ 3 = 159
75 ÷ 3 = 25
159 ÷ 3 = 53 (since 1+5+9=15)
25 not divisible by 3 → stop
So we divided by 2 × 3 × 3 = 18? Wait — let’s do it cleanly:
Actually, better to find GCF directly or step-by-step:
Start with 954 and 150.
Divide both by 6? Let’s try:
954 ÷ 6 = 159
150 ÷ 6 = 25
Now 159 and 25 → 25 is 5×5, 159 ÷ 5? No. 159 ÷ 3 = 53 → but 25 not divisible by 3. So GCF was 6? Wait — actually:
Wait — 954 ÷ 6 = 159? 6×159=954? 6×150=900, 6×9=54 → yes.
150 ÷ 6 = 25 → correct.
But 159 and 25 have no common factors → so simplified is 159/25
But wait — can we reduce more? 159 ÷ 3 = 53, 25 not divisible by 3 → yes, done.
But 159/25 is an improper fraction — that’s okay, question says “proper and improper”.
Alternatively, maybe we missed a bigger GCF?
Let me check GCF of 954 and 150.
Prime factors:
150 = 2 × 3 × 5²
954 ÷ 2 = 477 → 477 ÷ 3 = 159 → 159 ÷ 3 = 53 → so 954 = 2 × 3² × 53
Common factors: 2 and 3 → GCF = 6
Yes → 954 ÷ 6 = 159, 150 ÷ 6 = 25 → 159/25
✔ 159/25
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6. 150/36
Both divisible by 6?
150 ÷ 6 = 25
36 ÷ 6 = 6
25 and 6 → no common factors → done
✔ 25/6
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7. 20/25
GCF = 5
20 ÷ 5 = 4
25 ÷ 5 = 5
✔ 4/5
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8. 14/21
GCF = 7
14 ÷ 7 = 2
21 ÷ 7 = 3
✔ 2/3
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9. 84/140
Both divisible by 28? Or step by step.
Divide by 2: 42/70
Again by 2: 21/35
Now 21 and 35 → GCF = 7
21 ÷ 7 = 3
35 ÷ 7 = 5
So total divided by 2×2×7=28
84 ÷ 28 = 3
140 ÷ 28 = 5
✔ 3/5
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10. 70/20
GCF = 10
70 ÷ 10 = 7
20 ÷ 10 = 2
✔ 7/2
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11. 132/30
Both divisible by 6?
132 ÷ 6 = 22
30 ÷ 6 = 5
22 and 5 → no common factors
✔ 22/5
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12. 76/12
Both divisible by 4?
76 ÷ 4 = 19
12 ÷ 4 = 3
19 is prime → done
✔ 19/3
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13. 1092/140
Let’s find GCF.
First, both even → divide by 2:
1092 ÷ 2 = 546
140 ÷ 2 = 70
Again even → divide by 2:
546 ÷ 2 = 273
70 ÷ 2 = 35
Now 273 and 35.
35 = 5 × 7
273 ÷ 7 = 39 (because 7×39=273)
35 ÷ 7 = 5
So now we have 39/5
Total divided by 2×2×7=28
Check: 1092 ÷ 28 = ? 28×39=1092? 28×40=1120, minus 28=1092 → yes
140 ÷ 28 = 5 → yes
✔ 39/5
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14. 216/96
Both divisible by 24? Or step by step.
Divide by 8:
216 ÷ 8 = 27
96 ÷ 8 = 12
Now 27/12 → divide by 3: 9/4
So overall divided by 8×3=24
216 ÷ 24 = 9
96 ÷ 24 = 4
✔ 9/4
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15. 262/50
Both even → divide by 2:
262 ÷ 2 = 131
50 ÷ 2 = 25
131 is prime? Yes, doesn’t divide 25 → done
✔ 131/25
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16. 1160/400
Both divisible by 40? Or step by step.
Divide by 10: 116/40
Again by 4: 29/10
So total divided by 40? 1160 ÷ 40 = 29, 400 ÷ 40 = 10 → yes
✔ 29/10
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Final Answer:
1. 2/3
2. 3/4
3. 1/2
4. 29/100
5. 159/25
6. 25/6
7. 4/5
8. 2/3
9. 3/5
10. 7/2
11. 22/5
12. 19/3
13. 39/5
14. 9/4
15. 131/25
16. 29/10
Parent Tip: Review the logic above to help your child master the concept of converting improper fractions to mixed numbers worksheet.
