Common Mistakes: Fractions
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Fractions can be tricky! Let's learn about common mistakes so you can avoid them.
Mistake #1: Thinking Bigger Denominator = Bigger Fraction
Wrong thinking: "1/8 is bigger than 1/4 because 8 is bigger than 4"
Right: 1/4 is bigger! When the numerator is the same, a bigger denominator means smaller pieces.
Think: Would you rather have 1/4 of a pizza or 1/8? 1/4 is more!
Mistake #2: Confusing Numerator and Denominator
Wrong: Writing 4/3 when you mean 3 out of 4 parts
Right: 3/4 = 3 parts out of 4 total parts
Remember: Numerator (top) = parts you have. Denominator (bottom) = total parts.
Mistake #3: Unequal Parts
Wrong: Saying a shape is divided into fourths when the parts aren't equal size
Right: Fractions require EQUAL parts! 4 unequal pieces are not fourths.
Practice: Find the Mistake
1. A student says 1/3 is smaller than 1/6 because 3 is smaller than 6. Is this correct?
A) Yes, that's right
B) No, 1/3 is actually larger than 1/6
C) They are equal
D) You can't compare them
Answer
B) - 1/3 is larger! When you divide something into fewer pieces (3), each piece is bigger than when you divide into more pieces (6).
2. Which fraction represents "5 out of 8 equal parts"?
A) 8/5
B) 5/8
C) 5 x 8
D) 5 + 8
Answer
B) 5/8 - The number of parts you have (5) goes on top, the total parts (8) goes on bottom.
3. A circle is cut into 4 pieces, but one piece is much bigger than the others. Can we say each piece is 1/4?
A) Yes, there are 4 pieces
B) No, the pieces must be equal for fourths
C) Yes, because 4 pieces always means fourths
D) It doesn't matter
Answer
B) - Fractions require EQUAL parts. If the pieces aren't equal, they're not true fourths.
4. Which is greater: 2/4 or 2/8?
A) 2/8 because 8 is bigger
B) 2/4 because fourths are bigger pieces
C) They are equal
D) You can't tell
Answer
B) 2/4 - With the same numerator, smaller denominators mean bigger pieces. 2/4 = 1/2, while 2/8 = 1/4.
5. A student wrote that half of 10 is 10/2. What should they have written?
A) 10/2 is correct
B) 1/2 of 10 = 5
C) 2/10
D) 10 + 2
Answer
B) - Half of 10 equals 5. The fraction 10/2 = 5 is the answer, not the problem.
6. What's wrong with saying 3/3 = 0?
A) Nothing, that's correct
B) 3/3 = 1 (a whole)
C) 3/3 = 3
D) 3/3 = 6
Answer
B) - When the numerator equals the denominator, the fraction equals 1 whole. 3/3 = 1.
7. Put these in order from smallest to largest: 1/2, 1/4, 1/8
A) 1/2, 1/4, 1/8
B) 1/8, 1/4, 1/2
C) 1/4, 1/2, 1/8
D) They're all equal
Answer
B) 1/8, 1/4, 1/2 - More pieces = smaller each piece is. 1/8 is smallest, 1/2 is largest.
8. In the fraction 3/5, which number tells how many total equal parts there are?
A) 3
B) 5
C) Both
D) Neither
Answer
B) 5 - The denominator (bottom number) tells the total number of equal parts.
9. A student says 4/4 is the same as 4. Is this correct?
A) Yes, 4/4 = 4
B) No, 4/4 = 1
C) No, 4/4 = 0
D) No, 4/4 = 8
Answer
B) No, 4/4 = 1 - 4/4 means 4 out of 4 parts, which is the whole thing = 1.
10. Why is 0/5 equal to 0?
A) Because 5 - 0 = 5
B) Because you have 0 parts out of 5, which is nothing
C) Because 5 x 0 = 0
D) It's not equal to 0
Answer
B) - If you have 0 parts out of 5, you have nothing. 0/5 = 0.
Next Steps
- Draw pictures to check your fraction thinking
- Remember: bigger denominator = smaller pieces
- Always check that parts are EQUAL
- Continue to the Unit Quiz