Grade: 5 Subject: SAT/ACT Skills Unit: Ratios Introduction Lesson: 6 of 6 SAT Math: ProblemSolving+DataAnalysis ACT Section: Math

Review Mistakes

Learn from common ratio mistakes and turn errors into opportunities for improvement.

Learn

Mistakes Help You Learn

Every mistake contains a lesson. When you understand WHY you made an error, you become better at avoiding it next time!

Why Analyze Your Mistakes?

  • Find patterns: You might make the same type of error repeatedly
  • Understand traps: Test writers use predictable tricks
  • Build confidence: Knowing what to avoid helps you feel prepared
  • Save time: Focus on your specific weak areas

Common Ratio Mistakes

1. Wrong Order

Mistake: "Dogs to cats is 3:5" written as 5:3
Fix: The first item mentioned goes first. "Dogs to cats" = dogs:cats

2. Not Simplifying

Mistake: Writing 6:9 when asked for simplest form
Fix: Always check if both numbers share a common factor. 6:9 = 2:3

3. Part vs. Whole Confusion

Mistake: Writing boys:girls when asked for boys:total
Fix: Read carefully! Part-to-whole needs the TOTAL, not another part.

4. Scaling Errors

Mistake: If 2:3 = 4:?, answering 5 instead of 6
Fix: Multiply BOTH parts by the same number. 2x2=4, so 3x2=6

The Error Review Process

1

Identify the Problem Type

Was it a simplify question? Equivalent ratio? Word problem? Part-to-whole?

2

Find Your Mistake

Wrong order? Didn't simplify? Confused part and whole? Scaling error?

3

Understand the Correct Answer

Work through the problem correctly. What steps did you miss?

4

Write It Down

Keep an error log to track patterns and review before tests.

Examples

Example: Analyzing a Wrong Order Mistake

Question: A store has 8 apples and 12 oranges. What is the ratio of oranges to apples?

Student's Answer: 8:12

Correct Answer: 12:8 = 3:2

1

Problem Type: Part-to-Part Ratio

2

Mistake: Wrong Order

The student wrote apples:oranges instead of oranges:apples

3

Correct Process

"Oranges to apples" means oranges first: 12:8, then simplify to 3:2

4

Lesson Learned

Circle the ORDER in the question before writing the ratio!

Practice

For each scenario, identify what mistake was made.

Question 1

A student was asked to write the ratio of cats to dogs if there are 6 cats and 4 dogs. They wrote 4:6.

What mistake did they make?

Question 2

Asked to simplify 15:20, a student answered 15:20.

What mistake did they make?

Question 3

In a class with 10 boys and 15 girls, a student was asked for the ratio of boys to total students. They answered 10:15.

What mistake did they make?

Question 4

If 3:4 = 9:?, a student answered 10.

What mistake did they make?

Check Your Understanding

Test your ability to identify mistakes with this 10-question quiz!

Mistake Detective Quiz

Score: 0 / 10
Question 1 of 10

Quiz Complete!

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Next Steps

Key Takeaways

  • The four common ratio mistakes: wrong order, not simplifying, part/whole confusion, scaling errors
  • Use the 4-step error review process to learn from mistakes
  • Keep an error log to track patterns in your mistakes
  • Review mistakes within 24 hours for best retention
  • Start your own error log for ratio problems
  • Review this unit and practice any areas that challenge you
  • Move on to the next unit when you feel confident with ratios