Simplifying Ratios worksheet with 18 ratio problems to reduce to their simplest form, including whole numbers and decimals, with a playful green dragon graphic.

To solve the problem of simplifying the given ratios, we need to reduce each ratio to its simplest form by dividing both terms by their greatest common divisor (GCD). Let's go through each ratio step by step.

1. 25 : 150

- Find the GCD of 25 and 150.
- Factors of 25: 1, 5, 25
- Factors of 150: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150
- GCD = 25
- Divide both terms by 25:
\[
\frac{25}{25} : \frac{150}{25} = 1 : 6
\]

2. 30 : 75

- Find the GCD of 30 and 75.
- Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
- Factors of 75: 1, 3, 5, 15, 25, 75
- GCD = 15
- Divide both terms by 15:
\[
\frac{30}{15} : \frac{75}{15} = 2 : 5
\]

3. 34 : 102

- Find the GCD of 34 and 102.
- Factors of 34: 1, 2, 17, 34
- Factors of 102: 1, 2, 3, 6, 17, 34, 51, 102
- GCD = 34
- Divide both terms by 34:
\[
\frac{34}{34} : \frac{102}{34} = 1 : 3
\]

4. 148 : 111

- Find the GCD of 148 and 111.
- Factors of 148: 1, 2, 4, 37, 74, 148
- Factors of 111: 1, 3, 37, 111
- GCD = 37
- Divide both terms by 37:
\[
\frac{148}{37} : \frac{111}{37} = 4 : 3
\]

5. 97 : 194

- Find the GCD of 97 and 194.
- 97 is a prime number.
- Factors of 194: 1, 2, 97, 194
- GCD = 97
- Divide both terms by 97:
\[
\frac{97}{97} : \frac{194}{97} = 1 : 2
\]

6. 52 : 130

- Find the GCD of 52 and 130.
- Factors of 52: 1, 2, 4, 13, 26, 52
- Factors of 130: 1, 2, 5, 10, 13, 26, 65, 130
- GCD = 26
- Divide both terms by 26:
\[
\frac{52}{26} : \frac{130}{26} = 2 : 5
\]

7. 112 : 320

- Find the GCD of 112 and 320.
- Factors of 112: 1, 2, 4, 7, 8, 14, 16, 28, 56, 112
- Factors of 320: 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160, 320
- GCD = 16
- Divide both terms by 16:
\[
\frac{112}{16} : \frac{320}{16} = 7 : 20
\]

8. 2.4 : 5.6

- Convert decimals to whole numbers by multiplying both terms by 10:
\[
2.4 \times 10 : 5.6 \times 10 = 24 : 56
\]
- Find the GCD of 24 and 56.
- Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
- Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56
- GCD = 8
- Divide both terms by 8:
\[
\frac{24}{8} : \frac{56}{8} = 3 : 7
\]

9. 32 : 480

- Find the GCD of 32 and 480.
- Factors of 32: 1, 2, 4, 8, 16, 32
- Factors of 480: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 80, 96, 120, 160, 240, 480
- GCD = 32
- Divide both terms by 32:
\[
\frac{32}{32} : \frac{480}{32} = 1 : 15
\]

10. 7.8 : 9.1

- Convert decimals to whole numbers by multiplying both terms by 10:
\[
7.8 \times 10 : 9.1 \times 10 = 78 : 91
\]
- Find the GCD of 78 and 91.
- Factors of 78: 1, 2, 3, 6, 13, 26, 39, 78
- Factors of 91: 1, 7, 13, 91
- GCD = 13
- Divide both terms by 13:
\[
\frac{78}{13} : \frac{91}{13} = 6 : 7
\]

11. 128 : 160

- Find the GCD of 128 and 160.
- Factors of 128: 1, 2, 4, 8, 16, 32, 64, 128
- Factors of 160: 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160
- GCD = 32
- Divide both terms by 32:
\[
\frac{128}{32} : \frac{160}{32} = 4 : 5
\]

12. 2.5 : 3.5

- Convert decimals to whole numbers by multiplying both terms by 10:
\[
2.5 \times 10 : 3.5 \times 10 = 25 : 35
\]
- Find the GCD of 25 and 35.
- Factors of 25: 1, 5, 25
- Factors of 35: 1, 5, 7, 35
- GCD = 5
- Divide both terms by 5:
\[
\frac{25}{5} : \frac{35}{5} = 5 : 7
\]

13. 42 : 280

- Find the GCD of 42 and 280.
- Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42
- Factors of 280: 1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, 280
- GCD = 14
- Divide both terms by 14:
\[
\frac{42}{14} : \frac{280}{14} = 3 : 20
\]

14. 66 : 30

- Find the GCD of 66 and 30.
- Factors of 66: 1, 2, 3, 6, 11, 22, 33, 66
- Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
- GCD = 6
- Divide both terms by 6:
\[
\frac{66}{6} : \frac{30}{6} = 11 : 5
\]

15. 84 : 156

- Find the GCD of 84 and 156.
- Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
- Factors of 156: 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156
- GCD = 12
- Divide both terms by 12:
\[
\frac{84}{12} : \frac{156}{12} = 7 : 13
\]

16. 378 : 105

- Find the GCD of 378 and 105.
- Factors of 378: 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378
- Factors of 105: 1, 3, 5, 7, 15, 21, 35, 105
- GCD = 21
- Divide both terms by 21:
\[
\frac{378}{21} : \frac{105}{21} = 18 : 5
\]

17. 250 : 750

- Find the GCD of 250 and 750.
- Factors of 250: 1, 2, 5, 10, 25, 50, 125, 250
- Factors of 750: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 125, 150, 250, 375, 750
- GCD = 250
- Divide both terms by 250:
\[
\frac{250}{250} : \frac{750}{250} = 1 : 3
\]

18. 32 : 28.8

- Convert decimals to whole numbers by multiplying both terms by 10:
\[
32 \times 10 : 28.8 \times 10 = 320 : 288
\]
- Find the GCD of 320 and 288.
- Factors of 320: 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160, 320
- Factors of 288: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 32, 36, 48, 72, 96, 144, 288
- GCD = 32
- Divide both terms by 32:
\[
\frac{320}{32} : \frac{288}{32} = 10 : 9
\]

19. 2.4 : 1.8

- Convert decimals to whole numbers by multiplying both terms by 10:
\[
2.4 \times 10 : 1.8 \times 10 = 24 : 18
\]
- Find the GCD of 24 and 18.
- Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
- Factors of 18: 1, 2, 3, 6, 9, 18
- GCD = 6
- Divide both terms by 6:
\[
\frac{24}{6} : \frac{18}{6} = 4 : 3
\]

20. 25 : 45

- Find the GCD of 25 and 45.
- Factors of 25: 1, 5, 25
- Factors of 45: 1, 3, 5, 9, 15, 45
- GCD = 5
- Divide both terms by 5:
\[
\frac{25}{5} : \frac{45}{5} = 5 : 9
\]

Final Answer:

\[
\boxed{
\begin{array}{ccc}
1 : 6 & 2 : 5 & 1 : 3 \\
4 : 3 & 1 : 2 & 2 : 5 \\
7 : 20 & 3 : 7 & 1 : 15 \\
6 : 7 & 4 : 5 & 5 : 7 \\
3 : 20 & 11 : 5 & 7 : 13 \\
18 : 5 & 1 : 3 & 10 : 9 \\
4 : 3 & 5 : 9 &
\end{array}
}
\]