Simplifying Proper Fractions worksheet with 40 problems to reduce fractions to their lowest terms.

To simplify a fraction to its lowest terms, we need to find the Greatest Common Divisor (GCD) for the numerator (top number) and the denominator (bottom number). Then, we divide both numbers by that GCD.

Here are the step-by-step solutions for each problem on the worksheet:

1. $\frac{117}{144}$
* Both numbers are divisible by 9.
* $117 \div 9 = 13$
* $144 \div 9 = 16$
* Answer: $\frac{13}{16}$

2. $\frac{297}{639}$
* Both numbers are divisible by 9.
* $297 \div 9 = 33$
* $639 \div 9 = 71$
* Answer: $\frac{33}{71}$

3. $\frac{98}{336}$
* Both numbers are divisible by 14.
* $98 \div 14 = 7$
* $336 \div 14 = 24$
* Answer: $\frac{7}{24}$

4. $\frac{5}{220}$
* Both numbers are divisible by 5.
* $5 \div 5 = 1$
* $220 \div 5 = 44$
* Answer: $\frac{1}{44}$

5. $\frac{36}{162}$
* Both numbers are divisible by 18.
* $36 \div 18 = 2$
* $162 \div 18 = 9$
* Answer: $\frac{2}{9}$

6. $\frac{252}{368}$
* Both numbers are divisible by 4.
* $252 \div 4 = 63$
* $368 \div 4 = 92$
* Answer: $\frac{63}{92}$

7. $\frac{10}{60}$
* Both numbers are divisible by 10.
* $10 \div 10 = 1$
* $60 \div 10 = 6$
* Answer: $\frac{1}{6}$

8. $\frac{32}{480}$
* Both numbers are divisible by 32.
* $32 \div 32 = 1$
* $480 \div 32 = 15$
* Answer: $\frac{1}{15}$

9. $\frac{108}{156}$
* Both numbers are divisible by 12.
* $108 \div 12 = 9$
* $156 \div 12 = 13$
* Answer: $\frac{9}{13}$

10. $\frac{60}{250}$
* Both numbers are divisible by 10.
* $60 \div 10 = 6$
* $250 \div 10 = 25$
* Answer: $\frac{6}{25}$

11. $\frac{350}{560}$
* Divide by 10 first: $\frac{35}{56}$. Both are divisible by 7.
* $35 \div 7 = 5$
* $56 \div 7 = 8$
* Answer: $\frac{5}{8}$

12. $\frac{64}{264}$
* Both numbers are divisible by 8.
* $64 \div 8 = 8$
* $264 \div 8 = 33$
* Answer: $\frac{8}{33}$

13. $\frac{45}{54}$
* Both numbers are divisible by 9.
* $45 \div 9 = 5$
* $54 \div 9 = 6$
* Answer: $\frac{5}{6}$

14. $\frac{14}{21}$
* Both numbers are divisible by 7.
* $14 \div 7 = 2$
* $21 \div 7 = 3$
* Answer: $\frac{2}{3}$

15. $\frac{24}{30}$
* Both numbers are divisible by 6.
* $24 \div 6 = 4$
* $30 \div 6 = 5$
* Answer: $\frac{4}{5}$

16. $\frac{40}{50}$
* Both numbers are divisible by 10.
* $40 \div 10 = 4$
* $50 \div 10 = 5$
* Answer: $\frac{4}{5}$

17. $\frac{141}{297}$
* Both numbers are divisible by 3.
* $141 \div 3 = 47$
* $297 \div 3 = 99$
* Answer: $\frac{47}{99}$

18. $\frac{464}{784}$
* Both numbers are divisible by 16.
* $464 \div 16 = 29$
* $784 \div 16 = 49$
* Answer: $\frac{29}{49}$

19. $\frac{456}{584}$
* Both numbers are divisible by 8.
* $456 \div 8 = 57$
* $584 \div 8 = 73$
* Answer: $\frac{57}{73}$

20. $\frac{140}{175}$
* Both numbers are divisible by 35.
* $140 \div 35 = 4$
* $175 \div 35 = 5$
* Answer: $\frac{4}{5}$

21. $\frac{120}{390}$
* Divide by 10 first: $\frac{12}{39}$. Both are divisible by 3.
* $12 \div 3 = 4$
* $39 \div 3 = 13$
* Answer: $\frac{4}{13}$

22. $\frac{160}{320}$
* Both numbers are divisible by 160.
* $160 \div 160 = 1$
* $320 \div 160 = 2$
* Answer: $\frac{1}{2}$

23. $\frac{245}{448}$
* Both numbers are divisible by 7.
* $245 \div 7 = 35$
* $448 \div 7 = 64$
* Answer: $\frac{35}{64}$

24. $\frac{119}{322}$
* Both numbers are divisible by 7.
* $119 \div 7 = 17$
* $322 \div 7 = 46$
* Answer: $\frac{17}{46}$

25. $\frac{245}{320}$
* Both numbers are divisible by 5.
* $245 \div 5 = 49$
* $320 \div 5 = 64$
* Answer: $\frac{49}{64}$

26. $\frac{130}{520}$
* Both numbers are divisible by 130.
* $130 \div 130 = 1$
* $520 \div 130 = 4$
* Answer: $\frac{1}{4}$

27. $\frac{48}{624}$
* Both numbers are divisible by 48.
* $48 \div 48 = 1$
* $624 \div 48 = 13$
* Answer: $\frac{1}{13}$

28. $\frac{140}{220}$
* Divide by 10 first: $\frac{14}{22}$. Both are divisible by 2.
* $14 \div 2 = 7$
* $22 \div 2 = 11$
* Answer: $\frac{7}{11}$

29. $\frac{376}{472}$
* Both numbers are divisible by 8.
* $376 \div 8 = 47$
* $472 \div 8 = 59$
* Answer: $\frac{47}{59}$

30. $\frac{120}{260}$
* Divide by 10 first: $\frac{12}{26}$. Both are divisible by 2.
* $12 \div 2 = 6$
* $26 \div 2 = 13$
* Answer: $\frac{6}{13}$

31. $\frac{50}{60}$
* Both numbers are divisible by 10.
* $50 \div 10 = 5$
* $60 \div 10 = 6$
* Answer: $\frac{5}{6}$

32. $\frac{38}{76}$
* Both numbers are divisible by 38.
* $38 \div 38 = 1$
* $76 \div 38 = 2$
* Answer: $\frac{1}{2}$

33. $\frac{234}{378}$
* Both numbers are divisible by 18.
* $234 \div 18 = 13$
* $378 \div 18 = 21$
* Answer: $\frac{13}{21}$

34. $\frac{196}{332}$
* Both numbers are divisible by 4.
* $196 \div 4 = 49$
* $332 \div 4 = 83$
* Answer: $\frac{49}{83}$

35. $\frac{4}{10}$
* Both numbers are divisible by 2.
* $4 \div 2 = 2$
* $10 \div 2 = 5$
* Answer: $\frac{2}{5}$

36. $\frac{3}{12}$
* Both numbers are divisible by 3.
* $3 \div 3 = 1$
* $12 \div 3 = 4$
* Answer: $\frac{1}{4}$

37. $\frac{624}{632}$
* Both numbers are divisible by 8.
* $624 \div 8 = 78$
* $632 \div 8 = 79$
* Answer: $\frac{78}{79}$

38. $\frac{264}{360}$
* Both numbers are divisible by 24.
* $264 \div 24 = 11$
* $360 \div 24 = 15$
* Answer: $\frac{11}{15}$

39. $\frac{54}{450}$
* Both numbers are divisible by 18.
* $54 \div 18 = 3$
* $450 \div 18 = 25$
* Answer: $\frac{3}{25}$

40. $\frac{368}{656}$
* Both numbers are divisible by 16.
* $368 \div 16 = 23$
* $656 \div 16 = 41$
* Answer: $\frac{23}{41}$

Final Answer:
1. 13/16
2. 33/71
3. 7/24
4. 1/44
5. 2/9
6. 63/92
7. 1/6
8. 1/15
9. 9/13
10. 6/25
11. 5/8
12. 8/33
13. 5/6
14. 2/3
15. 4/5
16. 4/5
17. 47/99
18. 29/49
19. 57/73
20. 4/5
21. 4/13
22. 1/2
23. 35/64
24. 17/46
25. 49/64
26. 1/4
27. 1/13
28. 7/11
29. 47/59
30. 6/13
31. 5/6
32. 1/2
33. 13/21
34. 49/83
35. 2/5
36. 1/4
37. 78/79
38. 11/15
39. 3/25
40. 23/41