Understanding Fractions - Grade 6 Maths

What You Will Learn

Understand what a fraction represents.
Identify the numerator and denominator.
Recognise proper, improper and mixed fractions.
Read and write fractions using simple examples.
Practise identifying fractions in everyday situations.

1. What Is a Fraction?

A fraction represents a part of a whole. It tells us how many equal parts we have out of the total number of equal parts.

Imagine a pizza cut into 4 equal slices. If you eat 1 slice, you have eaten one out of four equal parts.

One out of four equal parts

1 4

The shaded part represents one quarter (1/4).

Fractions are useful in everyday life. We use them when sharing food, measuring ingredients, dividing objects and describing parts of a group.

2. Parts of a Fraction

Look at this fraction:

3 5

Numerator: The top number (3). It tells us how many parts we have.

Denominator: The bottom number (5). It tells us how many equal parts make the whole.

In the fraction 3/5, a whole is divided into 5 equal parts and we are talking about 3 of those parts.

Remember: The denominator tells the total number of equal parts. The numerator tells how many of those parts are being considered.

3. Types of Fractions

A. Proper Fractions

A proper fraction has a numerator smaller than its denominator.

Examples: 1/2, 2/5 and 3/4.

Example: In 2/5, 2 is smaller than 5. Therefore, 2/5 is a proper fraction.

B. Improper Fractions

An improper fraction has a numerator greater than or equal to its denominator.

Examples: 5/4, 7/3 and 6/6.

Example: In 7/3, 7 is greater than 3. Therefore, 7/3 is an improper fraction.

C. Mixed Numbers

A mixed number contains a whole number and a proper fraction.

Examples: 1 1/2, 2 1/4 and 3 2/5.

Example: 1 1/2 means one whole and one half.

4. Step-by-Step Solved Examples

Example 1: Identify the numerator and denominator

Question: In the fraction 4/7, identify both parts.

Look at the top number: 4.
Look at the bottom number: 7.
The numerator is 4 and the denominator is 7.

Answer: Numerator = 4; Denominator = 7.

Example 2: Identify the type of fraction

Question: Is 3/8 a proper or improper fraction?

Compare the numerator (3) and denominator (8).
Since 3 is smaller than 8, it is a proper fraction.

Answer: 3/8 is a proper fraction.

Example 3: Write a fraction from a situation

Question: A chocolate bar is divided into 6 equal pieces. Sara eats 2 pieces. What fraction does she eat?

Total equal pieces = 6. This is the denominator.
Pieces eaten = 2. This is the numerator.
Write the fraction as 2/6.

Answer: Sara eats 2/6 of the chocolate bar.

5. Common Mistakes to Avoid

Mistake 1: Mixing up the numerator and denominator.
Remember: numerator is on top; denominator is below.

Mistake 2: Thinking the denominator tells how many parts are selected.
The denominator tells how many equal parts make the whole.

Mistake 3: Dividing something into unequal pieces and calling them equal fractions.
Fractions of a whole require equal-sized parts.

Mistake 4: Assuming every fraction is less than one.
Improper fractions can represent one whole or more than one whole.

6. Practice Exercises

Try these questions before checking your answers.

1. What is the numerator in 5/9?

2. What is the denominator in 3/8?

3. Is 2/7 a proper or improper fraction?

4. Is 9/5 a proper or improper fraction?

5. A cake is cut into 8 equal pieces. Ali eats 3. Write the fraction he eats.

Show practice answers

5
8
Proper fraction
Improper fraction
3/8

7. Test Your Understanding

Choose one answer for each question, then select Check Answers. Each question is worth one point.

8. Free Printable Worksheet

Use this worksheet to practise what you have learned. You can print it or save it as a PDF.

Learnora — Grade 6 Mathematics

Understanding Fractions Worksheet

Name: __________________________ Date: _______________

Instructions: Answer all questions. Show your working where needed.

Identify the numerator and denominator in 3/7.
Write one example of a proper fraction.
Write one example of an improper fraction.
Is 4/9 a proper or improper fraction? Explain.
A pizza has 8 equal slices. You eat 3 slices. What fraction did you eat?
Write the mixed number that means two wholes and one third.
What does the denominator represent?
Classify 8/8 as proper or improper.

Great work! Keep practising.

Learnora — Learn Better. Practice Smarter.

Teacher / Parent Answer Key

Numerator = 3; denominator = 7.
Any valid example such as 1/2.
Any valid example such as 5/3.
Proper fraction, because 4 is smaller than 9.
3/8.
2 1/3.
The total number of equal parts in the whole.
Improper fraction, because the numerator equals the denominator.

9. Lesson Summary

A fraction represents part of a whole.
The numerator is the top number.
The denominator is the bottom number.
A proper fraction has a smaller numerator than denominator.
An improper fraction has a numerator equal to or greater than its denominator.
A mixed number combines a whole number and a proper fraction.

Next learning goal: Once you understand fractions, you can move on to equivalent fractions and comparing fractions.