Simplify Fractions (hard) (5) Worksheet - Free Printable
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Step-by-step solution for: Simplify Fractions (hard) (5) Worksheet
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Show Answer Key & Explanations
Step-by-step solution for: Simplify Fractions (hard) (5) Worksheet
Let's solve each of these fractions by simplifying them to their lowest terms. To do this, we find the greatest common divisor (GCD) of the numerator and denominator, then divide both by that number.
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We'll go through each problem one by one.
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1. 54/62
GCD(54, 62) = 2 → $ \frac{54 ÷ 2}{62 ÷ 2} = \frac{27}{31} $ ✔
Answer: $ \frac{27}{31} $
2. 45/99
GCD(45, 99) = 9 → $ \frac{45 ÷ 9}{99 ÷ 9} = \frac{5}{11} $
Answer: $ \frac{5}{11} $
3. 210/730
GCD(210, 730) = 10 → $ \frac{210 ÷ 10}{730 ÷ 10} = \frac{21}{73} $
Answer: $ \frac{21}{73} $
4. 348/510
GCD(348, 510) = 6 → $ \frac{348 ÷ 6}{510 ÷ 6} = \frac{58}{85} $
Answer: $ \frac{58}{85} $
5. 30/162
GCD(30, 162) = 6 → $ \frac{30 ÷ 6}{162 ÷ 6} = \frac{5}{27} $
Answer: $ \frac{5}{27} $
6. 8/36
GCD(8, 36) = 4 → $ \frac{8 ÷ 4}{36 ÷ 4} = \frac{2}{9} $
Answer: $ \frac{2}{9} $
7. 534/540
GCD(534, 540) = 6 → $ \frac{534 ÷ 6}{540 ÷ 6} = \frac{89}{90} $
Answer: $ \frac{89}{90} $
8. 7/322
GCD(7, 322) = 7 → $ \frac{7 ÷ 7}{322 ÷ 7} = \frac{1}{46} $
Answer: $ \frac{1}{46} $
9. 120/592
GCD(120, 592) = 8 → $ \frac{120 ÷ 8}{592 ÷ 8} = \frac{15}{74} $
Answer: $ \frac{15}{74} $
10. 12/76
GCD(12, 76) = 4 → $ \frac{12 ÷ 4}{76 ÷ 4} = \frac{3}{19} $
Answer: $ \frac{3}{19} $
11. 18/27
GCD(18, 27) = 9 → $ \frac{18 ÷ 9}{27 ÷ 9} = \frac{2}{3} $
Answer: $ \frac{2}{3} $
12. 160/440
GCD(160, 440) = 40 → $ \frac{160 ÷ 40}{440 ÷ 40} = \frac{4}{11} $
Answer: $ \frac{4}{11} $
13. 60/356
GCD(60, 356) = 4 → $ \frac{60 ÷ 4}{356 ÷ 4} = \frac{15}{89} $
Answer: $ \frac{15}{89} $
14. 85/180
GCD(85, 180) = 5 → $ \frac{85 ÷ 5}{180 ÷ 5} = \frac{17}{36} $
Answer: $ \frac{17}{36} $
15. 384/584
GCD(384, 584) = 8 → $ \frac{384 ÷ 8}{584 ÷ 8} = \frac{48}{73} $
Answer: $ \frac{48}{73} $
16. 6/39
GCD(6, 39) = 3 → $ \frac{6 ÷ 3}{39 ÷ 3} = \frac{2}{13} $
Answer: $ \frac{2}{13} $
17. 16/40
GCD(16, 40) = 8 → $ \frac{16 ÷ 8}{40 ÷ 8} = \frac{2}{5} $
Answer: $ \frac{2}{5} $
18. 144/222
GCD(144, 222) = 6 → $ \frac{144 ÷ 6}{222 ÷ 6} = \frac{24}{37} $
Answer: $ \frac{24}{37} $
19. 6/72
GCD(6, 72) = 6 → $ \frac{6 ÷ 6}{72 ÷ 6} = \frac{1}{12} $
Answer: $ \frac{1}{12} $
20. 77/273
GCD(77, 273) = 7 → $ \frac{77 ÷ 7}{273 ÷ 7} = \frac{11}{39} $
Answer: $ \frac{11}{39} $
21. 165/246
GCD(165, 246) = 3 → $ \frac{165 ÷ 3}{246 ÷ 3} = \frac{55}{82} $
Answer: $ \frac{55}{82} $
22. 6/27
GCD(6, 27) = 3 → $ \frac{6 ÷ 3}{27 ÷ 3} = \frac{2}{9} $
Answer: $ \frac{2}{9} $
23. 180/477
GCD(180, 477) = 9 → $ \frac{180 ÷ 9}{477 ÷ 9} = \frac{20}{53} $
Answer: $ \frac{20}{53} $
24. 72/84
GCD(72, 84) = 12 → $ \frac{72 ÷ 12}{84 ÷ 12} = \frac{6}{7} $
Answer: $ \frac{6}{7} $
25. 40/65
GCD(40, 65) = 5 → $ \frac{40 ÷ 5}{65 ÷ 5} = \frac{8}{13} $
Answer: $ \frac{8}{13} $
26. 64/148
GCD(64, 148) = 4 → $ \frac{64 ÷ 4}{148 ÷ 4} = \frac{16}{37} $
Answer: $ \frac{16}{37} $
27. 576/656
GCD(576, 656) = 16 → $ \frac{576 ÷ 16}{656 ÷ 16} = \frac{36}{41} $
Answer: $ \frac{36}{41} $
28. 6/10
GCD(6, 10) = 2 → $ \frac{6 ÷ 2}{10 ÷ 2} = \frac{3}{5} $
Answer: $ \frac{3}{5} $
29. 21/138
GCD(21, 138) = 3 → $ \frac{21 ÷ 3}{138 ÷ 3} = \frac{7}{46} $
Answer: $ \frac{7}{46} $
30. 18/27
GCD(18, 27) = 9 → $ \frac{18 ÷ 9}{27 ÷ 9} = \frac{2}{3} $
Answer: $ \frac{2}{3} $
31. 42/76
GCD(42, 76) = 2 → $ \frac{42 ÷ 2}{76 ÷ 2} = \frac{21}{38} $
Answer: $ \frac{21}{38} $
32. 210/530
GCD(210, 530) = 10 → $ \frac{210 ÷ 10}{530 ÷ 10} = \frac{21}{53} $
Answer: $ \frac{21}{53} $
33. 486/498
GCD(486, 498) = 6 → $ \frac{486 ÷ 6}{498 ÷ 6} = \frac{81}{83} $
Answer: $ \frac{81}{83} $
34. 14/595
GCD(14, 595) = 7 → $ \frac{14 ÷ 7}{595 ÷ 7} = \frac{2}{85} $
Answer: $ \frac{2}{85} $
35. 5/50
GCD(5, 50) = 5 → $ \frac{5 ÷ 5}{50 ÷ 5} = \frac{1}{10} $
Answer: $ \frac{1}{10} $
36. 16/348
GCD(16, 348) = 4 → $ \frac{16 ÷ 4}{348 ÷ 4} = \frac{4}{87} $
Answer: $ \frac{4}{87} $
37. 244/312
GCD(244, 312) = 4 → $ \frac{244 ÷ 4}{312 ÷ 4} = \frac{61}{78} $
Answer: $ \frac{61}{78} $
38. 12/28
GCD(12, 28) = 4 → $ \frac{12 ÷ 4}{28 ÷ 4} = \frac{3}{7} $
Answer: $ \frac{3}{7} $
39. 6/300
GCD(6, 300) = 6 → $ \frac{6 ÷ 6}{300 ÷ 6} = \frac{1}{50} $
Answer: $ \frac{1}{50} $
40. 10/820
GCD(10, 820) = 10 → $ \frac{10 ÷ 10}{820 ÷ 10} = \frac{1}{82} $
Answer: $ \frac{1}{82} $
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| # | Fraction | Simplified |
|---|--------|------------|
| 1 | 54/62 | 27/31 |
| 2 | 45/99 | 5/11 |
| 3 | 210/730 | 21/73 |
| 4 | 348/510 | 58/85 |
| 5 | 30/162 | 5/27 |
| 6 | 8/36 | 2/9 |
| 7 | 534/540 | 89/90 |
| 8 | 7/322 | 1/46 |
| 9 | 120/592 | 15/74 |
|10 | 12/76 | 3/19 |
|11 | 18/27 | 2/3 |
|12 | 160/440 | 4/11 |
|13 | 60/356 | 15/89 |
|14 | 85/180 | 17/36 |
|15 | 384/584 | 48/73 |
|16 | 6/39 | 2/13 |
|17 | 16/40 | 2/5 |
|18 | 144/222 | 24/37 |
|19 | 6/72 | 1/12 |
|20 | 77/273 | 11/39 |
|21 | 165/246 | 55/82 |
|22 | 6/27 | 2/9 |
|23 | 180/477 | 20/53 |
|24 | 72/84 | 6/7 |
|25 | 40/65 | 8/13 |
|26 | 64/148 | 16/37 |
|27 | 576/656 | 36/41 |
|28 | 6/10 | 3/5 |
|29 | 21/138 | 7/46 |
|30 | 18/27 | 2/3 |
|31 | 42/76 | 21/38 |
|32 | 210/530 | 21/53 |
|33 | 486/498 | 81/83 |
|34 | 14/595 | 2/85 |
|35 | 5/50 | 1/10 |
|36 | 16/348 | 4/87 |
|37 | 244/312 | 61/78 |
|38 | 12/28 | 3/7 |
|39 | 6/300 | 1/50 |
|40 | 10/820 | 1/82 |
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✔ All fractions are now in lowest terms.
Let me know if you'd like this as a printable PDF or need explanations for any specific one!
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🔷 Step-by-step Simplification:
We'll go through each problem one by one.
---
1. 54/62
GCD(54, 62) = 2 → $ \frac{54 ÷ 2}{62 ÷ 2} = \frac{27}{31} $ ✔
Answer: $ \frac{27}{31} $
2. 45/99
GCD(45, 99) = 9 → $ \frac{45 ÷ 9}{99 ÷ 9} = \frac{5}{11} $
Answer: $ \frac{5}{11} $
3. 210/730
GCD(210, 730) = 10 → $ \frac{210 ÷ 10}{730 ÷ 10} = \frac{21}{73} $
Answer: $ \frac{21}{73} $
4. 348/510
GCD(348, 510) = 6 → $ \frac{348 ÷ 6}{510 ÷ 6} = \frac{58}{85} $
Answer: $ \frac{58}{85} $
5. 30/162
GCD(30, 162) = 6 → $ \frac{30 ÷ 6}{162 ÷ 6} = \frac{5}{27} $
Answer: $ \frac{5}{27} $
6. 8/36
GCD(8, 36) = 4 → $ \frac{8 ÷ 4}{36 ÷ 4} = \frac{2}{9} $
Answer: $ \frac{2}{9} $
7. 534/540
GCD(534, 540) = 6 → $ \frac{534 ÷ 6}{540 ÷ 6} = \frac{89}{90} $
Answer: $ \frac{89}{90} $
8. 7/322
GCD(7, 322) = 7 → $ \frac{7 ÷ 7}{322 ÷ 7} = \frac{1}{46} $
Answer: $ \frac{1}{46} $
9. 120/592
GCD(120, 592) = 8 → $ \frac{120 ÷ 8}{592 ÷ 8} = \frac{15}{74} $
Answer: $ \frac{15}{74} $
10. 12/76
GCD(12, 76) = 4 → $ \frac{12 ÷ 4}{76 ÷ 4} = \frac{3}{19} $
Answer: $ \frac{3}{19} $
11. 18/27
GCD(18, 27) = 9 → $ \frac{18 ÷ 9}{27 ÷ 9} = \frac{2}{3} $
Answer: $ \frac{2}{3} $
12. 160/440
GCD(160, 440) = 40 → $ \frac{160 ÷ 40}{440 ÷ 40} = \frac{4}{11} $
Answer: $ \frac{4}{11} $
13. 60/356
GCD(60, 356) = 4 → $ \frac{60 ÷ 4}{356 ÷ 4} = \frac{15}{89} $
Answer: $ \frac{15}{89} $
14. 85/180
GCD(85, 180) = 5 → $ \frac{85 ÷ 5}{180 ÷ 5} = \frac{17}{36} $
Answer: $ \frac{17}{36} $
15. 384/584
GCD(384, 584) = 8 → $ \frac{384 ÷ 8}{584 ÷ 8} = \frac{48}{73} $
Answer: $ \frac{48}{73} $
16. 6/39
GCD(6, 39) = 3 → $ \frac{6 ÷ 3}{39 ÷ 3} = \frac{2}{13} $
Answer: $ \frac{2}{13} $
17. 16/40
GCD(16, 40) = 8 → $ \frac{16 ÷ 8}{40 ÷ 8} = \frac{2}{5} $
Answer: $ \frac{2}{5} $
18. 144/222
GCD(144, 222) = 6 → $ \frac{144 ÷ 6}{222 ÷ 6} = \frac{24}{37} $
Answer: $ \frac{24}{37} $
19. 6/72
GCD(6, 72) = 6 → $ \frac{6 ÷ 6}{72 ÷ 6} = \frac{1}{12} $
Answer: $ \frac{1}{12} $
20. 77/273
GCD(77, 273) = 7 → $ \frac{77 ÷ 7}{273 ÷ 7} = \frac{11}{39} $
Answer: $ \frac{11}{39} $
21. 165/246
GCD(165, 246) = 3 → $ \frac{165 ÷ 3}{246 ÷ 3} = \frac{55}{82} $
Answer: $ \frac{55}{82} $
22. 6/27
GCD(6, 27) = 3 → $ \frac{6 ÷ 3}{27 ÷ 3} = \frac{2}{9} $
Answer: $ \frac{2}{9} $
23. 180/477
GCD(180, 477) = 9 → $ \frac{180 ÷ 9}{477 ÷ 9} = \frac{20}{53} $
Answer: $ \frac{20}{53} $
24. 72/84
GCD(72, 84) = 12 → $ \frac{72 ÷ 12}{84 ÷ 12} = \frac{6}{7} $
Answer: $ \frac{6}{7} $
25. 40/65
GCD(40, 65) = 5 → $ \frac{40 ÷ 5}{65 ÷ 5} = \frac{8}{13} $
Answer: $ \frac{8}{13} $
26. 64/148
GCD(64, 148) = 4 → $ \frac{64 ÷ 4}{148 ÷ 4} = \frac{16}{37} $
Answer: $ \frac{16}{37} $
27. 576/656
GCD(576, 656) = 16 → $ \frac{576 ÷ 16}{656 ÷ 16} = \frac{36}{41} $
Answer: $ \frac{36}{41} $
28. 6/10
GCD(6, 10) = 2 → $ \frac{6 ÷ 2}{10 ÷ 2} = \frac{3}{5} $
Answer: $ \frac{3}{5} $
29. 21/138
GCD(21, 138) = 3 → $ \frac{21 ÷ 3}{138 ÷ 3} = \frac{7}{46} $
Answer: $ \frac{7}{46} $
30. 18/27
GCD(18, 27) = 9 → $ \frac{18 ÷ 9}{27 ÷ 9} = \frac{2}{3} $
Answer: $ \frac{2}{3} $
31. 42/76
GCD(42, 76) = 2 → $ \frac{42 ÷ 2}{76 ÷ 2} = \frac{21}{38} $
Answer: $ \frac{21}{38} $
32. 210/530
GCD(210, 530) = 10 → $ \frac{210 ÷ 10}{530 ÷ 10} = \frac{21}{53} $
Answer: $ \frac{21}{53} $
33. 486/498
GCD(486, 498) = 6 → $ \frac{486 ÷ 6}{498 ÷ 6} = \frac{81}{83} $
Answer: $ \frac{81}{83} $
34. 14/595
GCD(14, 595) = 7 → $ \frac{14 ÷ 7}{595 ÷ 7} = \frac{2}{85} $
Answer: $ \frac{2}{85} $
35. 5/50
GCD(5, 50) = 5 → $ \frac{5 ÷ 5}{50 ÷ 5} = \frac{1}{10} $
Answer: $ \frac{1}{10} $
36. 16/348
GCD(16, 348) = 4 → $ \frac{16 ÷ 4}{348 ÷ 4} = \frac{4}{87} $
Answer: $ \frac{4}{87} $
37. 244/312
GCD(244, 312) = 4 → $ \frac{244 ÷ 4}{312 ÷ 4} = \frac{61}{78} $
Answer: $ \frac{61}{78} $
38. 12/28
GCD(12, 28) = 4 → $ \frac{12 ÷ 4}{28 ÷ 4} = \frac{3}{7} $
Answer: $ \frac{3}{7} $
39. 6/300
GCD(6, 300) = 6 → $ \frac{6 ÷ 6}{300 ÷ 6} = \frac{1}{50} $
Answer: $ \frac{1}{50} $
40. 10/820
GCD(10, 820) = 10 → $ \frac{10 ÷ 10}{820 ÷ 10} = \frac{1}{82} $
Answer: $ \frac{1}{82} $
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✔ Final Answers:
| # | Fraction | Simplified |
|---|--------|------------|
| 1 | 54/62 | 27/31 |
| 2 | 45/99 | 5/11 |
| 3 | 210/730 | 21/73 |
| 4 | 348/510 | 58/85 |
| 5 | 30/162 | 5/27 |
| 6 | 8/36 | 2/9 |
| 7 | 534/540 | 89/90 |
| 8 | 7/322 | 1/46 |
| 9 | 120/592 | 15/74 |
|10 | 12/76 | 3/19 |
|11 | 18/27 | 2/3 |
|12 | 160/440 | 4/11 |
|13 | 60/356 | 15/89 |
|14 | 85/180 | 17/36 |
|15 | 384/584 | 48/73 |
|16 | 6/39 | 2/13 |
|17 | 16/40 | 2/5 |
|18 | 144/222 | 24/37 |
|19 | 6/72 | 1/12 |
|20 | 77/273 | 11/39 |
|21 | 165/246 | 55/82 |
|22 | 6/27 | 2/9 |
|23 | 180/477 | 20/53 |
|24 | 72/84 | 6/7 |
|25 | 40/65 | 8/13 |
|26 | 64/148 | 16/37 |
|27 | 576/656 | 36/41 |
|28 | 6/10 | 3/5 |
|29 | 21/138 | 7/46 |
|30 | 18/27 | 2/3 |
|31 | 42/76 | 21/38 |
|32 | 210/530 | 21/53 |
|33 | 486/498 | 81/83 |
|34 | 14/595 | 2/85 |
|35 | 5/50 | 1/10 |
|36 | 16/348 | 4/87 |
|37 | 244/312 | 61/78 |
|38 | 12/28 | 3/7 |
|39 | 6/300 | 1/50 |
|40 | 10/820 | 1/82 |
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✔ All fractions are now in lowest terms.
Let me know if you'd like this as a printable PDF or need explanations for any specific one!
Parent Tip: Review the logic above to help your child master the concept of simplest form fractions worksheet.
