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Answer :
To solve the problem of renaming the opening times of the Colby and Wave drawbridges using different common denominators, let's go through the solution step by step:
1. Understanding the Problem:
- We have two drawbridges on the Dell River: the Colby and Wave drawbridges.
- Colby opens at [tex]\( \frac{3}{4} \)[/tex] of an hour.
- Wave opens at [tex]\( \frac{1}{6} \)[/tex] of an hour.
2. Using 60 as a Common Denominator:
- To express each opening time in terms of minutes using 60 as the common denominator (since there are 60 minutes in an hour):
- Colby Bridge:
[tex]\[ \frac{3}{4} \times 60 \text{ minutes} = 45 \text{ minutes} \][/tex]
- Wave Bridge:
[tex]\[ \frac{1}{6} \times 60 \text{ minutes} = 10 \text{ minutes} \][/tex]
3. Choosing Another Common Denominator:
- Let's use 12 as another common denominator to express these fractions.
- Convert each opening time using 12:
- Colby Bridge:
[tex]\[ \frac{3}{4} \times 12 = 9 \][/tex]
- This multiplication simplifies to saying: Colby opens 9 parts out of 12.
- Wave Bridge:
[tex]\[ \frac{1}{6} \times 12 = 2 \][/tex]
- This implies the Wave bridge opens 2 parts out of 12.
4. Conclusion:
- In terms of minutes, the Colby drawbridge opens at 45 minutes past the hour, and in terms of a fraction out of 12, it opens at 9/12 (75% of the hour).
- The Wave drawbridge opens at 10 minutes past the hour, and in terms of a fraction out of 12, it opens at 2/12 (16.67% of the hour).
By performing these conversions, we successfully renamed the opening times of the two drawbridges using the specified common denominators.
1. Understanding the Problem:
- We have two drawbridges on the Dell River: the Colby and Wave drawbridges.
- Colby opens at [tex]\( \frac{3}{4} \)[/tex] of an hour.
- Wave opens at [tex]\( \frac{1}{6} \)[/tex] of an hour.
2. Using 60 as a Common Denominator:
- To express each opening time in terms of minutes using 60 as the common denominator (since there are 60 minutes in an hour):
- Colby Bridge:
[tex]\[ \frac{3}{4} \times 60 \text{ minutes} = 45 \text{ minutes} \][/tex]
- Wave Bridge:
[tex]\[ \frac{1}{6} \times 60 \text{ minutes} = 10 \text{ minutes} \][/tex]
3. Choosing Another Common Denominator:
- Let's use 12 as another common denominator to express these fractions.
- Convert each opening time using 12:
- Colby Bridge:
[tex]\[ \frac{3}{4} \times 12 = 9 \][/tex]
- This multiplication simplifies to saying: Colby opens 9 parts out of 12.
- Wave Bridge:
[tex]\[ \frac{1}{6} \times 12 = 2 \][/tex]
- This implies the Wave bridge opens 2 parts out of 12.
4. Conclusion:
- In terms of minutes, the Colby drawbridge opens at 45 minutes past the hour, and in terms of a fraction out of 12, it opens at 9/12 (75% of the hour).
- The Wave drawbridge opens at 10 minutes past the hour, and in terms of a fraction out of 12, it opens at 2/12 (16.67% of the hour).
By performing these conversions, we successfully renamed the opening times of the two drawbridges using the specified common denominators.
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