Mixed Numbers & Improper Fractions
Learn how to convert between mixed numbers and improper fractions, and understand what they mean.
What Are Mixed Numbers?
A mixed number has a whole number part and a fraction part together. For example, 23/4 means 2 whole ones and 3 quarters.
Visualising 23/4
2 whole shapes + 3 out of 4 parts = 23/4
What Are Improper Fractions?
An improper fraction is a fraction where the numerator is bigger than (or equal to) the denominator. This means the fraction is worth 1 or more.
Example: 11/4 is an improper fraction because 11 > 4
Visualising 11/4
11 quarter-pieces = 2 wholes and 3 quarters = 23/4
How to Convert
Mixed Number → Improper Fraction
- Multiply the whole number by the denominator.
- Add the numerator.
- Write the result over the same denominator.
32/5 → (3 × 5) + 2 = 17 → 17/5
Improper Fraction → Mixed Number
- Divide the numerator by the denominator.
- The quotient is the whole number.
- The remainder is the new numerator, over the same denominator.
17/5 → 17 ÷ 5 = 3 remainder 2 → 32/5
Key Vocabulary
Mixed Number
A number made up of a whole number and a fraction (e.g. 31/2).
Improper Fraction
A fraction where the numerator is greater than or equal to the denominator (e.g. 7/2).
Numerator
The top number of a fraction — how many parts you have.
Denominator
The bottom number of a fraction — how many equal parts the whole is divided into.
Worked Examples
Convert 42/3 to an improper fraction.
Step 1: Multiply whole number by denominator: 4 × 3 = 12
Step 2: Add the numerator: 12 + 2 = 14
Answer: 14/3
Convert 23/6 to a mixed number.
Step 1: Divide 23 ÷ 6 = 3 remainder 5
Step 2: The whole number is 3, the remainder is 5.
Answer: 35/6
Convert 17/8 to an improper fraction.
Step 1: Multiply: 1 × 8 = 8
Step 2: Add: 8 + 7 = 15
Answer: 15/8
Knowledge Check
Select the correct answer for each question.
Question 1
Convert 21/4 to an improper fraction.
Question 2
Convert 19/5 to a mixed number.
Question 3
Which of these is an improper fraction?
Question 4
Convert 53/8 to an improper fraction.
Question 5
Convert 25/7 to a mixed number.
Key Concepts Summary
- ●A mixed number combines a whole number and a fraction (e.g. 31/2).
- ●An improper fraction has a numerator greater than or equal to the denominator (e.g. 7/2).
- ●To convert mixed → improper: multiply whole by denominator, add numerator.
- ●To convert improper → mixed: divide numerator by denominator, use quotient and remainder.
- ●Mixed numbers and improper fractions are just two different ways to write the same amount.