Which of the following fractions compares BC to BD?

A. [tex] \frac{2}{3} [/tex]

B. [tex] \frac{5}{2} [/tex]

C. [tex] \frac{2}{5} [/tex]

D. [tex] \frac{3}{2} [/tex]



Answer :

To compare the length from point B to point C (denoted as BC) with the length from point B to point D (denoted as BD), we use the fraction [tex]\(\frac{BC}{BD}\)[/tex].

Given:
- BC is the length from B to C, which is 2 units.
- BD is the length from B to D, which is 3 units.

The fraction that compares these two lengths is:

[tex]\[ \frac{\text{BC}}{\text{BD}} = \frac{2}{3} \][/tex]

To verify, we can check this fraction:

[tex]\[ \frac{BC}{BD} = \frac{2}{3} \approx 0.6667 \][/tex]

Comparing this to the given options:
- [tex]\(\frac{2}{3} \approx 0.6667\)[/tex]
- [tex]\(\frac{5}{2} = 2.5\)[/tex]
- [tex]\(\frac{2}{5} = 0.4\)[/tex]
- [tex]\(\frac{3}{2} = 1.5\)[/tex]

Clearly, the fraction that compares BC to BD is [tex]\(\frac{2}{3}\)[/tex].

Therefore, the correct answer is:
[tex]\[ \boxed{\frac{2}{3}} \][/tex]