Let’s go through each problem step by step. We’ll simplify the fraction first (divide numerator and denominator by their greatest common factor), then convert to a mixed number if needed.
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1. 4368 / 497
Find GCF of 4368 and 497 → It’s 7
4368 ÷ 7 = 624
497 ÷ 7 = 71
→ 624/71
Now divide: 624 ÷ 71 = 8 with remainder 56
→
8 56/71
✔ Matches answer key.
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2. 21 / 12
GCF of 21 and 12 is 3
21 ÷ 3 = 7
12 ÷ 3 = 4
→ 7/4
7 ÷ 4 = 1 R3 →
1 3/4
✔ Correct.
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3. 585 / 72
GCF? Let’s try 9:
585 ÷ 9 = 65
72 ÷ 9 = 8
→ 65/8
65 ÷ 8 = 8 R1 →
8 1/8
✔ Correct.
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4. 2250 / 990
GCF? Try 90:
2250 ÷ 90 = 25
990 ÷ 90 = 11
→ 25/11
25 ÷ 11 = 2 R3 →
2 3/11
✔ Correct.
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5. 1470 / 546
GCF? Try 42:
1470 ÷ 42 = 35
546 ÷ 42 = 13
→ 35/13
35 ÷ 13 = 2 R9 →
2 9/13
✔ Correct.
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6. 567 / 162
GCF? Try 81:
567 ÷ 81 = 7
162 ÷ 81 = 2
→ 7/2
7 ÷ 2 = 3 R1 →
3 1/2
✔ Correct.
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7. 418 / 144
GCF? Try 2:
418 ÷ 2 = 209
144 ÷ 2 = 72
→ 209/72
209 ÷ 72 = 2 R65 →
2 65/72
✔ Correct.
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8. 1550 / 220
GCF? Try 10:
1550 ÷ 10 = 155
220 ÷ 10 = 22
→ 155/22
155 ÷ 22 = 7 R1 →
7 1/22
✔ Correct.
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9. 690 / 320
GCF? Try 10:
690 ÷ 10 = 69
320 ÷ 10 = 32
→ 69/32
69 ÷ 32 = 2 R5 →
2 5/32
✔ Correct.
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10. 880 / 200
GCF? Try 40:
880 ÷ 40 = 22
200 ÷ 40 = 5
→ 22/5
22 ÷ 5 = 4 R2 →
4 2/5
✔ Correct.
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11. 312 / 54
GCF? Try 6:
312 ÷ 6 = 52
54 ÷ 6 = 9
→ 52/9
52 ÷ 9 = 5 R7 →
5 7/9
✔ Correct.
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12. 3592 / 480
GCF? Try 8:
3592 ÷ 8 = 449
480 ÷ 8 = 60
→ 449/60
449 ÷ 60 = 7 R29 →
7 29/60
✔ Correct.
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13. 490 / 155
GCF? Try 5:
490 ÷ 5 = 98
155 ÷ 5 = 31
→ 98/31
98 ÷ 31 = 3 R5 →
3 5/31
✔ Correct.
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14. 110 / 40
GCF? Try 10:
110 ÷ 10 = 11
40 ÷ 10 = 4
→ 11/4
11 ÷ 4 = 2 R3 →
2 3/4
✔ Correct.
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15. 5320 / 686
GCF? Try 14:
5320 ÷ 14 = 380
686 ÷ 14 = 49
→ 380/49
380 ÷ 49 = 7 R37 →
7 37/49
✔ Correct.
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16. 1164 / 252
GCF? Try 12:
1164 ÷ 12 = 97
252 ÷ 12 = 21
→ 97/21
97 ÷ 21 = 4 R13 →
4 13/21
✔ Correct.
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17. 1340 / 236
GCF? Try 4:
1340 ÷ 4 = 335
236 ÷ 4 = 59
→ 335/59
335 ÷ 59 = 5 R40 →
5 40/59
✔ Correct.
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18. 1042 / 168
GCF? Try 2:
1042 ÷ 2 = 521
168 ÷ 2 = 84
→ 521/84
521 ÷ 84 = 6 R17 →
6 17/84
✔ Correct.
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19. 1472 / 632
GCF? Try 8:
1472 ÷ 8 = 184
632 ÷ 8 = 79
→ 184/79
184 ÷ 79 = 2 R26 →
2 26/79
✔ Correct.
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20. 1005 / 174
GCF? Try 3:
1005 ÷ 3 = 335
174 ÷ 3 = 58
→ 335/58
335 ÷ 58 = 5 R45 →
5 45/58
✔ Correct.
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All answers match the provided key. Each was simplified correctly and converted to a mixed number properly.
Final Answer:
All 20 problems have been solved correctly as shown in the original worksheet. The simplified fractions and mixed numbers are accurate based on dividing by the greatest common factor and converting improper fractions to mixed numbers.
Parent Tip: Review the logic above to help your child master the concept of hard fraction worksheet.
