Common Mistakes
Learn
In this lesson, we will identify and correct common mistakes students make when working with equivalent fractions. Learning from these errors will help you avoid them!
Common Errors to Avoid
- Adding instead of multiplying: To find equivalent fractions, multiply (or divide) both numerator and denominator by the SAME number, not add.
- Only changing one part: You must change BOTH the numerator and denominator by the same factor.
- Not fully simplifying: Always check if you can simplify further.
- Confusing "larger denominator" with "larger fraction": 1/8 is smaller than 1/4, even though 8 > 4.
Examples
Work through these examples to see the concepts in action.
Mistake Example 1
Wrong: "1/2 = 3/4 because I added 2 to both parts"
Correct: 1/2 is NOT equal to 3/4. To find equivalent fractions, multiply both parts by the same number. 1/2 = 2/4 (multiply both by 2).
Mistake Example 2
Wrong: "6/8 simplified is 3/8 because I divided the numerator by 2"
Correct: You must divide BOTH parts. 6/8 = 3/4 (divide both by 2).
✏️ Practice
Test your understanding with these practice questions.
Practice Questions
0/4 correctIf y = 3x represents a proportional relationship, what is the constant of proportionality?
A recipe uses 2 cups of flour for every 3 cups of sugar. If you use 6 cups of flour, how many cups of sugar do you need?
Which equation represents a proportional relationship?
The table shows x: 2, 4, 6 and y: 8, 16, 24. What is the constant of proportionality?
Check Your Understanding
Test yourself with these 10 quiz questions. Click on each question to reveal the answer.
Question 1: A student says 2/3 = 4/5 because they added 2 to both parts. Is this correct?
Answer: No, this is incorrect. You must MULTIPLY (not add) both parts by the same number. 2/3 is not equal to 4/5. The correct equivalent would be 2/3 = 4/6.
Question 2: A student simplified 8/12 to 4/12. What mistake did they make?
Answer: They only divided the numerator by 2, but forgot to divide the denominator. The correct simplification is 8/12 = 4/6 = 2/3.
Question 3: True or False: 1/4 is greater than 1/2 because 4 is greater than 2.
Answer: False. 1/4 is LESS than 1/2. A larger denominator means smaller pieces, so 1/4 < 1/2.
Question 4: A student says 6/9 simplified is 3/6. Find and correct the error.
Answer: The student divided by different numbers (6 divided by 2 = 3, but 9 divided by ... = 6 doesn't work). The correct answer: 6/9 = 2/3 (divide both by 3).
Question 5: A student claims 12/16 fully simplified is 6/8. Is this the simplest form?
Answer: No. 6/8 can be simplified further to 3/4. The student should have divided by 4 instead of 2, or continued simplifying.
Question 6: What is wrong with saying 3/5 = 6/15 because you multiplied by 2 and 3?
Answer: You must multiply BOTH parts by the SAME number. 3x2=6 but 5x3=15 uses different multipliers. The correct equivalent: 3/5 = 6/10 (multiply both by 2) or 3/5 = 9/15 (multiply both by 3).
Question 7: A student says 5/10 = 1/5. Find the error and give the correct answer.
Answer: The student made a calculation error. To simplify 5/10, divide both by 5: 5/10 = 1/2 (not 1/5).
Question 8: True or False: 2/6 and 3/9 are equivalent fractions.
Answer: True. Both simplify to 1/3. 2/6 = 1/3 and 3/9 = 1/3.
Question 9: A student wrote: "To find an equivalent fraction for 1/3 with denominator 9, I add 6 to get 1/9." What is wrong?
Answer: Adding to the denominator doesn't create equivalent fractions. To convert 1/3 to ninths, multiply BOTH parts by 3: 1/3 = 3/9.
Question 10: Is 4/6 fully simplified if a student divided both numbers by 2 and stopped?
Answer: The student would get 2/3, which IS fully simplified. So yes, if they got 2/3, that's correct. The mistake would be stopping at 4/6 without simplifying at all.
Next Steps
- Review any concepts that felt challenging
- Move on to the next lesson when ready
- Return to practice problems periodically for review