Grade: Grade 5 Subject: Mathematics Unit: Fraction Operations Lesson: 5 of 6 SAT: Algebra ACT: Math

Common Mistakes in Fraction Operations

Learn to identify and avoid the most common errors students make when working with fractions. Understanding these pitfalls will help you become more accurate and confident!

Why Mistakes Happen

Learning from Errors

Everyone makes mistakes when learning fractions! The key is recognizing common patterns so you can catch and fix errors before they become habits.

Fraction operations have specific rules that differ from whole number operations. Many mistakes happen when students accidentally apply whole number rules to fractions.

Mistake #1: Adding Denominators

Wrong Way
1 4 + 1 3 = 2 7

Adding both numerators AND denominators is incorrect!

Right Way
1 4 + 1 3 = 7 12

Find the LCD first, then add only the numerators!

Remember: The denominator tells you what SIZE the pieces are. You cannot combine pieces of different sizes without converting them first!

Mistake #2: Finding LCD When Multiplying

Wrong Way

Finding a common denominator when multiplying fractions:

2 3 x 1 4 = 8 12 x 3 12

You do NOT need a common denominator for multiplication!

Right Way

Simply multiply straight across:

2 3 x 1 4 = 2 12 = 1 6

Multiply numerators together, multiply denominators together!

Mistake #3: Forgetting to Flip When Dividing

Wrong Way

Dividing without flipping the second fraction:

3 4 ÷ 1 2 = 3 8

You cannot just multiply straight across for division!

Right Way

Keep-Change-Flip (multiply by the reciprocal):

3 4 x 2 1 = 6 4 = 3 2

Keep the first, change to multiplication, flip the second!

Mistake #4: Forgetting to Simplify

Incomplete Answer
2 8 + 2 8 = 4 8

This answer is correct but not fully simplified!

Complete Answer
4 8 = 1 2

Always reduce to lowest terms by dividing by the GCF!

Pro Tip: After solving, always ask yourself: "Can both numbers be divided by the same thing?" If yes, simplify!

Practice: Spot the Mistake

For each problem, identify whether the work shown is correct or contains a mistake. Click to reveal the answer.

Question 1

Is this correct? 12 + 13 = 25

Click to see answer

Incorrect! The student added both numerators and denominators. The correct answer is 5/6 (LCD = 6, so 3/6 + 2/6 = 5/6).

Question 2

Is this correct? 34 x 25 = 620

Click to see answer

Partially correct! The multiplication is right (3x2=6, 4x5=20), but the answer needs to be simplified. 6/20 = 3/10.

Question 3

Is this correct? 58 - 14 = 38

Click to see answer

Correct! The student found the LCD (8), converted 1/4 to 2/8, then subtracted: 5/8 - 2/8 = 3/8.

Question 4

Is this correct? 23 ÷ 45 = 815

Click to see answer

Incorrect! The student multiplied instead of using Keep-Change-Flip. The correct answer: 2/3 x 5/4 = 10/12 = 5/6.

Question 5

Is this correct? 710 + 310 = 1010 = 1

Click to see answer

Correct! Same denominators, so just add numerators: 7+3=10. And 10/10 = 1 whole.

Question 6

Is this correct? 16 x 34 = 410

Click to see answer

Incorrect! The student added instead of multiplied. Correct: 1x3=3, 6x4=24, so 3/24 = 1/8.

Question 7

Is this correct? 45 - 13 = 715

Click to see answer

Correct! LCD = 15. Convert: 4/5 = 12/15 and 1/3 = 5/15. Subtract: 12/15 - 5/15 = 7/15.

Question 8

Is this correct? 56 ÷ 13 = 52

Click to see answer

Correct! Keep-Change-Flip: 5/6 x 3/1 = 15/6 = 5/2 (or 2 1/2).

Question 9

Is this correct? 29 + 16 = 315

Click to see answer

Incorrect! The student added numerators and denominators separately. Correct: LCD = 18. 4/18 + 3/18 = 7/18.

Question 10

Is this correct? 38 x 49 = 16

Click to see answer

Correct! 3x4=12, 8x9=72. Then 12/72 simplifies to 1/6 (divide both by 12).

Key Takeaways

Add/Subtract

Need same denominators. Only add/subtract numerators!

Multiply

Straight across. No common denominator needed!

Divide

Keep-Change-Flip. Multiply by the reciprocal!

Always Simplify

Reduce your final answer to lowest terms!