Subjects algebra

Simplify Ratios

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1. **Stating the problem:** We need to simplify the given ratios to their lowest terms. 2. **Important rules:** - To simplify a ratio, convert all quantities to the same units. - Then express the ratio as two integers. - Finally, divide both terms by their greatest common divisor (GCD). 3. **Simplify each ratio:** - For $55\text{ cm} : 1\text{ m}$: Convert $1\text{ m} = 100\text{ cm}$. So ratio is $55 : 100$. GCD of 55 and 100 is 5. Simplified ratio: $\frac{55}{5} : \frac{100}{5} = 11 : 20$. - For $85\text{ sen} : 2.15$ (RM): Convert RM to sen: $2.15 \text{ RM} = 215 \text{ sen}$. Ratio is $85 : 215$. GCD of 85 and 215 is 5. Simplified ratio: $\frac{85}{5} : \frac{215}{5} = 17 : 43$. - For $240\text{ ml} : 0.5\text{ l}$: Convert liters to milliliters: $0.5\text{ l} = 500\text{ ml}$. Ratio is $240 : 500$. GCD of 240 and 500 is 20. Simplified ratio: $\frac{240}{20} : \frac{500}{20} = 12 : 25$. - The other ratios are already numeric: - $17 : 43$ (already simplified) - $12 : 50$; GCD is 2, simplified to $6 : 25$ - $11 : 20$ (already simplified) - $12 : 25$ (already simplified) 4. **Final simplified ratios:** - $55\text{ cm} : 1\text{ m} = 11 : 20$ - $85\text{ sen} : 2.15 = 17 : 43$ - $240\text{ ml} : 0.5\text{ l} = 12 : 25$ - $17 : 43$ (unchanged) - $12 : 50 = 6 : 25$ - $11 : 20$ (unchanged) - $12 : 25$ (unchanged)