If 1,200 customers register for new accounts at a social media website every day, what fraction of the first 60,000...

1. TRANSLATE the problem information

• Given information:
  • 1,200 customers register each day
  • Total of 60,000 accounts to consider
  • Need fraction registered in first 5 days

2. INFER the solution approach

• To find a fraction, we need: part/whole
• The "part" = accounts registered in 5 days
• The "whole" = 60,000 total accounts
• First step: Calculate accounts registered in 5 days

3. Calculate accounts registered in 5 days

• 5 days × 1,200 customers per day = 6,000 customers

\(\mathrm{5 \times 1{,}200 = 6{,}000}\)

4. Form the fraction

• Fraction = accounts in 5 days / total accounts
• Fraction = \(\frac{6{,}000}{60{,}000}\)

5. SIMPLIFY to match answer choices

• \(\frac{6{,}000}{60{,}000} = \frac{1}{10}\) (dividing both by 6,000)

Answer: B. \(\frac{1}{10}\)

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE skill: Students misinterpret what should be the numerator and denominator of the fraction. They might think the question asks for "what fraction of days" rather than "what fraction of accounts."

This leads them to calculate 5 days out of some total days, potentially selecting Choice A (\(\frac{1}{5}\)) if they think 5 days out of 25 days (since \(\mathrm{60{,}000 \div 1{,}200 = 50}\) days total, but they might incorrectly use 25).

Second Most Common Error:

Inadequate SIMPLIFY execution: Students correctly calculate \(\frac{6{,}000}{60{,}000}\) but fail to simplify it to \(\frac{1}{10}\). Since none of the answer choices shows \(\frac{6{,}000}{60{,}000}\), this leads to confusion and guessing.

Third Common Error:

Poor INFER reasoning: Students calculate the fraction of accounts registered in just 1 day instead of 5 days. They find \(\frac{1{,}200}{60{,}000} = \frac{1}{50}\) and select Choice D (\(\frac{1}{50}\)).

The Bottom Line:

This problem tests whether students can correctly identify what quantities form the numerator and denominator in a rate-based fraction problem, then execute the arithmetic accurately.