What Are Fractions
Learn what fractions are and how they represent parts of a whole.
Definition
- Numerator (top number): How many parts we have
- Denominator (bottom number): How many equal parts the whole is divided into
Try it now
Worked Examples
A chocolate bar is divided into 6 equal pieces. You eat 2 pieces. What fraction of the chocolate bar did you eat?
Count the total equal parts
The bar is divided into 6 equal pieces → Denominator = 6
Count how many parts you have
You ate 2 pieces → Numerator = 2
Write the fraction
→
Answer: You ate of the chocolate bar.
Common Mistakes
Confusing the numerator and denominator
Why it's wrong: It's easy to mix up which number goes on top. The numerator (parts we have) goes on top; the denominator (total parts) goes on the bottom.
Correct: Remember: the Denominator goes Down (both start with D). The numerator is the Number of parts you have.
Thinking a bigger denominator means a bigger fraction
Why it's wrong: A bigger denominator means the whole is cut into MORE pieces, so each piece is SMALLER.
Correct: is smaller than because cutting something into 8 pieces makes smaller pieces than cutting into 4.
Forgetting that parts must be equal
Why it's wrong: Fractions only work when all parts are the same size. Unequal parts don't form true fractions.
Correct: If a pizza is cut into 4 unequal slices, you can't say each piece is . The slices must be equal.
Interactive Visual
Click on the circle to change the fraction
Fraction Number Line
Click on tick marks to select fractions.
Interactive Sandbox
Expression Calculator
Try these:
History
No calculations yet
Practice Problems
18 problemsIn the fraction , what is the numerator?
Why It Matters
- Cooking: A recipe calls for cup of sugar
- Time: Half an hour is of an hour, or 30 minutes
- Sharing: Splitting a pizza into 8 slices means each slice is of the pizza
- Sports: A basketball player made of their free throws
Real World Applications
Cooking and Baking
Recipes use fractions to measure ingredients precisely.
Example:
A cookie recipe needs cup of flour. This means you fill a 1-cup measure to the mark.
A recipe calls for cup of sugar. You want to make half the recipe.
How much sugar do you need?
Step 1: Write the mathematical expression
Find half of :
Sharing Fairly
Fractions help us divide things equally among people.
Example:
If 3 friends share a cake equally, each person gets of the cake.
You have 1 sandwich to share equally among 4 friends.
What fraction of the sandwich does each friend get?
Step 1: Write the mathematical expression
One whole divided among 4 people:
Time
We use fractions to describe parts of an hour.
Example:
A quarter of an hour is of 60 minutes, which equals 15 minutes.
A movie starts in half an hour.
How many minutes until the movie starts?
Step 1: Write the mathematical expression
of 60 minutes:
Key Takeaways
- 1A fraction represents a part of a whole
- 2The numerator (top) tells how many parts we have
- 3The denominator (bottom) tells how many equal parts the whole is divided into
- 4All parts must be equal for the fraction to be accurate
- 5Larger denominators mean smaller pieces:
Frequently Asked Questions
Glossary
- Fraction
- A number that represents a part of a whole, written as one number over another (e.g., )
- Numerator
- The top number in a fraction; it tells how many parts you have
- Denominator
- The bottom number in a fraction; it tells how many equal parts the whole is divided into
- Whole
- The complete object or amount that is being divided into parts