Understanding Fractions
Learn what fractions are, how to read them, and how they represent parts of a whole.
What Are Fractions?
A fraction represents a part of a whole. When we divide something into equal parts and take some of those parts, we are using fractions.
For example, if you cut a pizza into 4 equal slices and eat 1 slice, you have eaten 1/4 (one quarter) of the pizza.
Visual: Fraction Bars
1 whole
Halves ( 1/2)
Thirds ( 1/3)
Quarters ( 1/4)
Three quarters ( 3/4) — 3 out of 4 parts shaded
Key Vocabulary
Numerator
The top number of a fraction. It tells us how many parts we have.
Denominator
The bottom number of a fraction. It tells us how many equal parts the whole is divided into.
Fraction
A number that represents a part of a whole, written as one number over another.
Whole
The complete object or group before it is divided into parts. A whole = 1.
Parts of a Fraction
Worked Examples
What fraction of this shape is shaded?
Step 1: Count the total number of equal parts. There are 5 parts.
Step 2: Count the shaded parts. There are 2 shaded parts.
Answer: The fraction shaded is 2/5 (two fifths).
A cake is cut into 8 equal slices. Sam eats 3 slices. What fraction did Sam eat?
Step 1: The whole cake is divided into 8 equal slices, so the denominator is 8.
Step 2: Sam ate 3 slices, so the numerator is 3.
Answer: Sam ate 3/8 (three eighths) of the cake.
What is the numerator and denominator in 5/6?
Step 1: The top number is 5. This is the numerator. It tells us we have 5 parts.
Step 2: The bottom number is 6. This is the denominator. It tells us the whole is divided into 6 equal parts.
Answer: Numerator = 5, Denominator = 6.
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
A chocolate bar is broken into 6 equal pieces. You eat 2 pieces. What fraction did you eat?
Question 2
In the fraction 7/10, what is the denominator?
Question 3
What fraction of this bar is shaded? (amber = shaded, grey = not shaded)
3 sections are shaded out of 4 total sections.
Question 4
Which fraction means "one half" — one piece out of two equal pieces?
Each option shows the fraction next to a bar split into equal pieces, with shaded pieces = the fraction.
Question 5
There are 10 marbles in a bag. 4 are red and the rest are blue. What fraction of the marbles are red?
Key Concepts Summary
- ● A fraction represents a part of a whole.
- ● The numerator (top number) tells how many parts we have.
- ● The denominator (bottom number) tells how many equal parts the whole is divided into.
- ● Fractions can be shown as fraction bars, pie charts, or written as numbers (e.g. 3/4).
- ● The denominator must never be zero (you cannot divide into zero parts).