Question

Which of the following values are equivalent to 14 over 20? Select all that apply.
A. 2 over 5

B.
7%
C.
0.7
D.
70.0

Answer 1

To determine which values are equivalent to \( \frac{14}{20} \), we can simplify the fraction and convert it to decimal and percentage forms.

1. **Convert \( \frac{14}{20} \) to its simplest form:**
- Divide both the numerator and the denominator by their greatest common divisor (GCD), which is 2:
\[
\frac{14 \div 2}{20 \div 2} = \frac{7}{10}
\]

2. **Convert \( \frac{7}{10} \) to a decimal:**
- \( \frac{7}{10} = 0.7 \)

3. **Convert \( \frac{7}{10} \) to a percentage:**
- \( \frac{7}{10} = 7 \times 10\% = 70\% \)

Now we can check the given options:

A. \( \frac{2}{5} \)
- To compare:
\[
\frac{2}{5} = 0.4 \quad \text{(not equivalent)}
\]

B. \( 7\% \)
- \( 7\% = 0.07 \quad \text{(not equivalent)} \)

C. \( 0.7 \)
- This is equivalent to \( \frac{7}{10} \quad \text{(equivalent)} \)

D. \( 70.0 \)
- This is equivalent to \( 70\% \quad \text{(equivalent)} \)

Thus, the correct equivalent values to \( \frac{14}{20} \) are **C** (0.7) and **D** (70.0).