The portion of students that are female and white is 2,550/17,000. Which of the following represent fractions that are equivalent to 2,55017,000? Check all that apply.

Question

answers:
510/1,700
510/3,400
5,100/34,000
255/1,700

Answer 1

To determine which of the given fractions are equivalent to \( \frac{2550}{17000} \), we can simplify \( \frac{2550}{17000} \) and then compare it to the other fractions.

1. Simplifying \( \frac{2550}{17000} \):
   • Find the greatest common divisor (GCD) of 2550 and 17000. The GCD is 50.
   • Now divide both the numerator and the denominator by 50: \[ \frac{2550 \div 50}{17000 \div 50} = \frac{51}{340} \]

Now we will simplify each of the provided fractions to see if any are equivalent to \( \frac{51}{340} \).

2. Checking \( \frac{510}{1700} \):

   • GCD of 510 and 1700 is 10.
   • Simplifying: \[ \frac{510 \div 10}{1700 \div 10} = \frac{51}{170} \] This is not equivalent to \( \frac{51}{340} \).

3. Checking \( \frac{510}{3400} \):

   • GCD of 510 and 3400 is 10.
   • Simplifying: \[ \frac{510 \div 10}{3400 \div 10} = \frac{51}{340} \] This is equivalent to \( \frac{51}{340} \).

4. Checking \( \frac{5100}{34000} \):

   • GCD of 5100 and 34000 is 100.
   • Simplifying: \[ \frac{5100 \div 100}{34000 \div 100} = \frac{51}{340} \] This is equivalent to \( \frac{51}{340} \).

5. Checking \( \frac{255}{1700} \):

   • GCD of 255 and 1700 is 5.
   • Simplifying: \[ \frac{255 \div 5}{1700 \div 5} = \frac{51}{340} \] This is equivalent to \( \frac{51}{340} \).

Summary of Equivalent Fractions:

The fractions that are equivalent to \( \frac{2550}{17000} \) are:

• \( \frac{510}{3400} \)
• \( \frac{5100}{34000} \)
• \( \frac{255}{1700} \)

Conclusion:

The correct answers are:

• \( \frac{510}{3400} \)
• \( \frac{5100}{34000} \)
• \( \frac{255}{1700} \)