Mixed Numbers and Improper Fractions
A mixed number combines a whole number and a fraction.
About this topic
A mixed number such as 2 3/4 combines a whole number and a proper fraction. An improper fraction like 11/4 has a numerator larger than its denominator. They are two ways to write the same value.
To convert a mixed number, multiply the whole part by the denominator, add the numerator, and keep the denominator: 2 3/4 becomes (2 × 4 + 3)/4 = 11/4. To go back, divide the numerator by the denominator and write the remainder over it. Since 11 ÷ 4 is 2 remainder 3, we get 2 3/4. Improper fractions are easier for multiplying and dividing, while mixed numbers are easier to picture.
Imagine having 11 quarter-pizzas. You can make two whole pizzas and have 3 slices left over, so you have 2 and 3/4 pizzas. Likewise, a board 5 1/2 feet long is easier to imagine than 11/2 feet, but to cut it into 3/4 foot lengths you would convert to 11/2 and divide.
Mixed numbers are common in cooking, carpentry and everyday measurement. A frequent mistake is multiplying the whole parts and the fractions separately, so 2 1/2 × 3 1/2 is not 6 1/4. Convert to 5/2 × 7/2 = 35/4 = 8 3/4. Remember that 2 3/4 means 2 plus 3/4, not 2 times 3/4.
Key ideas
- Improper fractions have numerators at least the denominator
- Convert 7/4 to 1 3/4 by dividing
- Multiply whole by denominator and add numerator to go back
Quick check
Use cases: where Mixed Numbers and Improper Fractions helps
- Homework: review the key idea behind Mixed Numbers and Improper Fractions before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Mixed Numbers and Improper Fractions without notes.
- Visual learning: play with the interactive lab to see how Mixed Numbers and Improper Fractions changes when you adjust its inputs.
- Teaching a friend: explain Mixed Numbers and Improper Fractions in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Mixed Numbers and Improper Fractions?
A mixed number combines a whole number and a fraction.
What will I learn in Mixed Numbers and Improper Fractions?
Improper fractions have numerators at least the denominator. Convert 7/4 to 1 3/4 by dividing. Multiply whole by denominator and add numerator to go back.
Is Mixed Numbers and Improper Fractions part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Mixed Numbers and Improper Fractions lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Mixed Numbers and Improper Fractions?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.