Question
7. The following are equivalent to \( \frac{10}{12} \) except: a. \( 5: 6 \) b. \( 100: 120 \) c. \( 6: 5 \) d. Ratio of .1 to .12
Ask by Vaughn Floyd. in the United States
Mar 18,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Option c, \( 6:5 \), is not equivalent to \( \frac{10}{12} \).
Solution
To determine which of the options is not equivalent to \( \frac{10}{12} \), we first simplify \( \frac{10}{12} \):
1. Simplify \( \frac{10}{12} \):
\[
\frac{10}{12} = \frac{5}{6}
\]
Now, we will check each option to see if it is equivalent to \( \frac{5}{6} \).
### Option a: \( 5:6 \)
This ratio can be expressed as:
\[
\frac{5}{6}
\]
This is equivalent to \( \frac{10}{12} \).
### Option b: \( 100:120 \)
This ratio can be expressed as:
\[
\frac{100}{120}
\]
Now, simplify \( \frac{100}{120} \):
\[
\frac{100 \div 20}{120 \div 20} = \frac{5}{6}
\]
This is also equivalent to \( \frac{10}{12} \).
### Option c: \( 6:5 \)
This ratio can be expressed as:
\[
\frac{6}{5}
\]
This is not equivalent to \( \frac{5}{6} \).
### Option d: Ratio of 0.1 to 0.12
This ratio can be expressed as:
\[
\frac{0.1}{0.12}
\]
To simplify, we can multiply the numerator and denominator by 100:
\[
\frac{10}{12} = \frac{5}{6}
\]
This is equivalent to \( \frac{10}{12} \).
### Conclusion
The only option that is not equivalent to \( \frac{10}{12} \) is:
**c. \( 6:5 \)**.
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The Deep Dive
To determine the option that is not equivalent to \( \frac{10}{12} \), we can simplify \( \frac{10}{12} \) to \( \frac{5}{6} \). The ratio \( 5:6 \) is equivalent, as well as \( 100:120 \) (which is also \( \frac{5}{6} \) simplified). However, \( 6:5 \) is the inverse of \( \frac{5}{6} \) and not equivalent. The ratio of \( 0.1 \) to \( 0.12 \) simplifies to \( \frac{10}{12} \) when expressed as a fraction. Thus, the answer is **c. \( 6: 5 \)**.