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🍰 Mixed Numbers and Improper Fractions

Go beyond one whole: learn what improper fractions and mixed numbers are, and how to switch smoothly between the two.

3
lessons
~30 min
to learn
🔢 Math
subject
Ages 6–12
level
Start the course →

What you’ll learn

  1. When Fractions Get BigRecognise improper fractions (top number bigger than bottom) and understand they are worth more than one whole.Fractions can be worth more than one whole. When the top number is bigger than the bottom, like 5/4 or 3/2, the fraction is called improper. On a number line an improper fraction lands past 1, because it holds more parts than it takes to make one whole.
  2. Whole Plus a BitUnderstand mixed numbers as a whole number combined with a fraction, and read them in words.A mixed number writes an amount as a whole number next to a fraction, like 1 3/4 — one whole and three quarters. The whole part counts the full wholes and the fraction part counts the leftover. Mixed numbers are how we usually say amounts, like 'two and a half'.
  3. Switching Between ThemConvert improper fractions to mixed numbers and mixed numbers to improper fractions.Improper fractions and mixed numbers are two names for the same amount. To go from improper to mixed, divide the top by the bottom: 7/4 = 1 3/4. To go from mixed to improper, multiply the whole by the bottom and add the top: 2 1/3 = 7/3. Every improper fraction has a matching mixed number.

Questions this course answers

A fraction where the top number is bigger than the bottom number is called...

When the top is bigger than the bottom, the fraction is improper and worth more than one whole.

Which of these is an improper fraction?

7/4 has a top number bigger than its bottom number, so it is improper.

The fraction 5/4 is worth...

Four quarters make one whole, so five quarters is more than one whole.

What kind of number is 1 3/4?

A whole number written next to a fraction is a mixed number.

'Three and a quarter' written as a mixed number is...

Three whole and one quarter is written 3 1/4.

Change 7/4 into a mixed number.

4 fits into 7 once with 3 left over, so 7/4 = 1 3/4.

Grounded in trusted sources

  • Khan Academy
  • BBC Bitesize — Maths
  • NCTM
  • Math is Fun
  • Nrich (University of Cambridge)

Every Wunder lesson is built from real, reputable sources — never invented.

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