Shaquan has 7 red cards and 28 blue cards. What is the ratio of red cards to blue cards that...

1. TRANSLATE the problem information

• Given information:
  • 7 red cards
  • 28 blue cards
  • Need the ratio of red cards to blue cards (in that order)

• This tells us we need to set up: \(\mathrm{red : blue = 7 : 28}\)

2. SIMPLIFY the ratio to lowest terms

• Look for the greatest common factor of 7 and 28
• \(\mathrm{7 = 7 × 1}\) and \(\mathrm{28 = 7 × 4}\), so GCF = 7
• Divide both parts by 7: \(\mathrm{7÷7 : 28÷7 = 1 : 4}\)

Answer: A. 1 to 4

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak TRANSLATE reasoning: Students mix up the order and set up the ratio as blue to red instead of red to blue.

They see "28 blue cards" first or think "there are more blue cards" and write \(\mathrm{28:7}\). When they simplify this correctly (\(\mathrm{28÷7 : 7÷7 = 4:1}\)), they get the backwards ratio.

This leads them to select Choice B (4 to 1).

Second Most Common Error:

Poor SIMPLIFY execution: Students set up the ratio correctly as \(\mathrm{7:28}\) but make calculation errors when reducing it.

They might divide incorrectly or forget to divide both parts by the same number, leading to ratios like \(\mathrm{1:7}\) through faulty arithmetic.

This may lead them to select Choice C (1 to 7).

The Bottom Line:

This problem tests whether students can carefully read what ratio is being asked for and maintain that order throughout their solution. The key insight is that "ratio of A to B" always means \(\mathrm{A:B}\), regardless of which quantity is larger.