Mixed Numbers
A whole number plus a proper fraction; convert to improper fractions to calculate.
Key idea
A whole number plus a proper fraction; convert to improper fractions to calculate.
In depth
A mixed number combines a whole number and a fraction: 2¾ = 2 + 3/4. Convert to an improper fraction to calculate: whole × denominator + numerator, over the denominator.
Worked example
2¾ = (2×4 + 3)/4 = 11/4.
Formula
Real-world uses
- Measuring with a tape to fractions of an inch or centimetre
- Carpentry and cooking quantities
Common mistake
Multiplying mixed numbers part by part. Convert to improper fractions first.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Mixed Numbers?
A whole number plus a proper fraction; convert to improper fractions to calculate. It is a topic at the intermediate level in Arithmetic & Number Sense.
What is the formula for Mixed Numbers?
The key formula is 2 1/3 = 7/3.
Where is Mixed Numbers used in real life?
Real-world examples: Measuring with a tape to fractions of an inch or centimetre; Carpentry and cooking quantities.
What should I learn before Mixed Numbers?
Make sure you are comfortable with Dividing Fractions, the previous topic in Arithmetic & Number Sense.
What is a common mistake with Mixed Numbers?
Multiplying mixed numbers part by part. Convert to improper fractions first.
How can I practise Mixed Numbers?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Mixed Numbers?
Move on to Reciprocals next.
Related intermediate topics in Arithmetic & Number Sense
- Long Multiplication – Multiply by each digit of the multiplier, shift by place value, then add partial products.
- Long Division – Divide, multiply, subtract and bring down repeatedly to get the quotient.
- Factors and Multiples – Factors divide a number exactly; multiples are its products with whole numbers.
- Divisibility Rules – Quick tests: by 2 last digit even, by 3 digit-sum divisible by 3, by 5 ends 0/5, by 9 digit-sum divisible by 9.
- Prime Numbers – A prime has exactly two positive divisors: 1 and itself.
- Composite Numbers – Numbers greater than 1 with more than two factors.