Ratio Worksheet: Reduce each ratio to its lowest term.

Let's solve each ratio by reducing it to its lowest terms. To do this, we find the greatest common divisor (GCD) of the two numbers and divide both numbers by that GCD.

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Step-by-step solutions:

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(1) 30 : 25
GCD of 30 and 25 is 5
→ $ \frac{30}{5} : \frac{25}{5} = 6 : 5 $

✔ 6:5

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(2) 70 : 30
GCD of 70 and 30 is 10
→ $ \frac{70}{10} : \frac{30}{10} = 7 : 3 $

✔ 7:3

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(3) 16 : 8
GCD of 16 and 8 is 8
→ $ \frac{16}{8} : \frac{8}{8} = 2 : 1 $

✔ 2:1

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(4) 20 : 30
GCD of 20 and 30 is 10
→ $ \frac{20}{10} : \frac{30}{10} = 2 : 3 $

✔ 2:3

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(5) 49 : 14
GCD of 49 and 14 is 7
→ $ \frac{49}{7} : \frac{14}{7} = 7 : 2 $

✔ 7:2

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(6) 96 : 24
GCD of 96 and 24 is 24
→ $ \frac{96}{24} : \frac{24}{24} = 4 : 1 $

✔ 4:1

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(7) 40 : 72
GCD of 40 and 72 is 8
→ $ \frac{40}{8} : \frac{72}{8} = 5 : 9 $

✔ 5:9

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(8) 81 : 63
GCD of 81 and 63 is 9
→ $ \frac{81}{9} : \frac{63}{9} = 9 : 7 $

✔ 9:7

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(9) 5 : 45
GCD of 5 and 45 is 5
→ $ \frac{5}{5} : \frac{45}{5} = 1 : 9 $

✔ 1:9

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(10) 80 : 20
GCD of 80 and 20 is 20
→ $ \frac{80}{20} : \frac{20}{20} = 4 : 1 $

✔ 4:1

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(11) 30 : 50
GCD of 30 and 50 is 10
→ $ \frac{30}{10} : \frac{50}{10} = 3 : 5 $

✔ 3:5

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(12) 12 : 36
GCD of 12 and 36 is 12
→ $ \frac{12}{12} : \frac{36}{12} = 1 : 3 $

✔ 1:3

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(13) 15 : 45
GCD of 15 and 45 is 15
→ $ \frac{15}{15} : \frac{45}{15} = 1 : 3 $

✔ 1:3

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(14) 36 : 30
GCD of 36 and 30 is 6
→ $ \frac{36}{6} : \frac{30}{6} = 6 : 5 $

✔ 6:5

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(15) 22 : 66
GCD of 22 and 66 is 22
→ $ \frac{22}{22} : \frac{66}{22} = 1 : 3 $

✔ 1:3

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(16) 44 : 88
GCD of 44 and 88 is 44
→ $ \frac{44}{44} : \frac{88}{44} = 1 : 2 $

✔ 1:2

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(17) 6 : 16
GCD of 6 and 16 is 2
→ $ \frac{6}{2} : \frac{16}{2} = 3 : 8 $

✔ 3:8

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(18) 21 : 49
GCD of 21 and 49 is 7
→ $ \frac{21}{7} : \frac{49}{7} = 3 : 7 $

✔ 3:7

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(19) 50 : 90
GCD of 50 and 90 is 10
→ $ \frac{50}{10} : \frac{90}{10} = 5 : 9 $

✔ 5:9

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(20) 2 : 22
GCD of 2 and 22 is 2
→ $ \frac{2}{2} : \frac{22}{2} = 1 : 11 $

✔ 1:11

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(21) 5 : 20
GCD of 5 and 20 is 5
→ $ \frac{5}{5} : \frac{20}{5} = 1 : 4 $

✔ 1:4

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(22) 35 : 45
GCD of 35 and 45 is 5
→ $ \frac{35}{5} : \frac{45}{5} = 7 : 9 $

✔ 7:9

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(23) 14 : 18
GCD of 14 and 18 is 2
→ $ \frac{14}{2} : \frac{18}{2} = 7 : 9 $

✔ 7:9

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(24) 13 : 78
GCD of 13 and 78 is 13
→ $ \frac{13}{13} : \frac{78}{13} = 1 : 6 $

✔ 1:6

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(25) 12 : 36
GCD of 12 and 36 is 12
→ $ \frac{12}{12} : \frac{36}{12} = 1 : 3 $

✔ 1:3

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(26) 45 : 27
GCD of 45 and 27 is 9
→ $ \frac{45}{9} : \frac{27}{9} = 5 : 3 $

✔ 5:3

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(27) 20 : 50
GCD of 20 and 50 is 10
→ $ \frac{20}{10} : \frac{50}{10} = 2 : 5 $

✔ 2:5

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✔ Final Answers:

| Problem | Reduced Ratio |
|--------|----------------|
| (1) | 6:5 |
| (2) | 7:3 |
| (3) | 2:1 |
| (4) | 2:3 |
| (5) | 7:2 |
| (6) | 4:1 |
| (7) | 5:9 |
| (8) | 9:7 |
| (9) | 1:9 |
| (10) | 4:1 |
| (11) | 3:5 |
| (12) | 1:3 |
| (13) | 1:3 |
| (14) | 6:5 |
| (15) | 1:3 |
| (16) | 1:2 |
| (17) | 3:8 |
| (18) | 3:7 |
| (19) | 5:9 |
| (20) | 1:11 |
| (21) | 1:4 |
| (22) | 7:9 |
| (23) | 7:9 |
| (24) | 1:6 |
| (25) | 1:3 |
| (26) | 5:3 |
| (27) | 2:5 |

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Let me know if you'd like a printable version or explanation for any specific one!