Select two ratios that are equivalent to 27:927:927, colon, 9. Choose 2 answers: Choose 2 answers: (Choice A) A 3:13:13, colon, 1 (Choice B) B 9:39:39, colon, 3 (Choice C) C 6:36:36, colon, 3 (Choice D) D 9:69:69, colon, 6 (Choice E) E 12:312:3
The Correct Answer and Explanation is :
To find two ratios equivalent to (27:927:927:9), we first need to simplify the original ratio. The first step is to express the ratio in a more manageable form by dividing each term by the greatest common divisor (GCD).
Step 1: Simplifying the Original Ratio
- The ratio (27:927:927:9) consists of four components: 27, 927, 927, and 9.
- We can find the GCD of these numbers. The GCD of 27 and 9 is 9, and since 927 is divisible by 9 as well, the GCD of all four terms is 9.
Now, divide each term by 9:
- ( \frac{27}{9} = 3 )
- ( \frac{927}{9} = 103 )
- ( \frac{927}{9} = 103 )
- ( \frac{9}{9} = 1 )
Thus, the simplified form of the ratio is:
[
3:103:103:1
]
Step 2: Finding Equivalent Ratios
Next, we will check each of the choices provided to see which two are equivalent to (3:103:103:1):
- Choice A: (3:13:13:1)
This is not equivalent because 13 is not related to 103. - Choice B: (9:39:39:3)
To check for equivalence, we can simplify this ratio by dividing each term by 3:
[
3:13:13:1
]
This is not equivalent. - Choice C: (6:36:36:3)
Dividing each term by 3:
[
2:12:12:1
]
Not equivalent. - Choice D: (9:69:69:6)
Dividing by 3 gives us:
[
3:23:23:2
]
Not equivalent. - Choice E: (12:312:3)
Dividing each term by 3 yields:
[
4:104:1
]
Not equivalent.
Conclusion
Upon reviewing the choices, none of the provided ratios are equivalent to (3:103:103:1). Therefore, it seems there may have been an error in the options given for this particular problem.
Final Answer
Thus, upon analysis, no choices are equivalent to (27:927:927:9) based on the calculations performed.