Question
20. Which ratio is not equivalent to \( \frac{3}{4} \) ? \[ \begin{array}{ll}\text { F. } \frac{9}{12} & \text { G. } \frac{1.5}{2} \\ \text { H. } \frac{36}{48} & \text { J. } \frac{21}{24}\end{array} \]
Ask by Boyd Flynn. in the United States
Jan 27,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
Option J, \( \frac{21}{24} \), is not equivalent to \( \frac{3}{4} \).
Solution
To determine which ratio is **not** equivalent to \( \frac{3}{4} \), let's analyze each option:
1. **Option F: \( \frac{9}{12} \)**
- Simplify by dividing numerator and denominator by 3:
\[
\frac{9 \div 3}{12 \div 3} = \frac{3}{4}
\]
- **Equivalent to \( \frac{3}{4} \).**
2. **Option G: \( \frac{1.5}{2} \)**
- Convert to fractions:
\[
1.5 = \frac{3}{2} \quad \text{so} \quad \frac{1.5}{2} = \frac{\frac{3}{2}}{2} = \frac{3}{4}
\]
- **Equivalent to \( \frac{3}{4} \).**
3. **Option H: \( \frac{36}{48} \)**
- Simplify by dividing numerator and denominator by 12:
\[
\frac{36 \div 12}{48 \div 12} = \frac{3}{4}
\]
- **Equivalent to \( \frac{3}{4} \).**
4. **Option J: \( \frac{21}{24} \)**
- Simplify by dividing numerator and denominator by 3:
\[
\frac{21 \div 3}{24 \div 3} = \frac{7}{8}
\]
- **Not equivalent to \( \frac{3}{4} \).**
**Answer:** J. \( \frac{21}{24} \)
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Simplify this solution The Deep Dive
To determine which ratio is not equivalent to \( \frac{3}{4} \), let's simplify each option. - For \( \frac{9}{12} \): Dividing both the numerator and denominator by 3 gives \( \frac{3}{4} \). - For \( \frac{1.5}{2} \): Dividing by 0.5 results in \( \frac{3}{4} \). - For \( \frac{36}{48} \): Dividing both by 12 yields \( \frac{3}{4} \). - For \( \frac{21}{24} \): Dividing both by 3 gives \( \frac{7}{8} \), which is not equivalent to \( \frac{3}{4} \). So, the answer is \( J. \frac{21}{24} \).
