Dividing Fractions
Learn how to divide fractions using the 'Keep, Change, Flip' method and understand why it works.
Definition
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Worked Examples
Calculate
Keep the first fraction
stays as →
Change division to multiplication
becomes →
Flip the second fraction
becomes →
Multiply numerators and denominators
→
Simplify if possible
→
Answer: This makes sense: How many quarter-pieces fit in a half? Two!
Common Mistakes
Flipping the wrong fraction
Why it's wrong: Students sometimes flip the first fraction instead of the second, or flip both fractions.
Correct: Only flip the SECOND fraction (the divisor). The first fraction stays exactly the same.
Forgetting to change division to multiplication
Why it's wrong: After flipping, students continue dividing instead of multiplying.
Correct: Keep-Change-Flip: you must CHANGE the operation to multiplication, then FLIP.
Not simplifying the final answer
Why it's wrong: Students stop after multiplying without checking if the fraction can be reduced.
Correct: Always check if your answer can be simplified. should become .
Getting confused when dividing by a whole number
Why it's wrong: Students forget that a whole number like 3 is the same as .
Correct: Write whole numbers as fractions first: , then apply Keep-Change-Flip.
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Practice Problems
15 problemsWhat is the reciprocal of ?
Why It Matters
- Cooking: If a recipe needs cup of flour and you want to make of it, how much flour do you need?
- Construction: How many -meter pieces can you cut from a -meter board?
- Time: If you can complete of a task in one hour, how long for the whole task?
Real World Applications
Cooking and Recipes
Chefs divide fractions when scaling recipes up or down.
Example:
A cake recipe calls for cup of sugar. If you want to make half the recipe, you need cup.
You have cup of butter. Each cookie needs cup of butter.
How many cookies can you make?
Step 1: Write the mathematical expression
Set up the division:
Construction and Measurement
Builders divide fractions when cutting materials into equal pieces.
Example:
A -meter rope needs to be cut into -meter pieces. You can cut pieces.
A board is meter long. You need pieces that are meter each.
How many full pieces can you cut?
Step 1: Write the mathematical expression
Divide the board length by piece length:
Time Management
Fraction division helps calculate rates and durations.
Example:
If you read of a book in hour, your reading rate is of the book per hour.
You completed of a project in of an hour.
At this rate, what fraction of the project can you complete per hour?
Step 1: Write the mathematical expression
Divide work done by time:
Key Takeaways
- 1To divide fractions, use Keep-Change-Flip: keep the first fraction, change to , flip the second
- 2The reciprocal of is (flip numerator and denominator)
- 3Dividing by a fraction is the same as multiplying by its reciprocal
- 4Always simplify your final answer
- 5When dividing whole numbers by fractions, write the whole number as first
Frequently Asked Questions
Glossary
- Reciprocal
- A fraction flipped upside down. The reciprocal of is . Example: reciprocal of is
- Dividend
- The number being divided (the first fraction in a division problem)
- Divisor
- The number you divide by (the second fraction in a division problem)
- Quotient
- The result of a division problem