Concept 2 of 7
Fraction Family: Types of Fractions
Today's big idea
Comparing the top against the bottom is what names a fraction.
Top smaller means proper, top bigger means improper, 1 on top means unit.
How it works
👀 What's going on?
Some fractions are less than one whole. Some are exactly one. Some are more than one, which sounds impossible until you picture two pizzas. Fractions come in four types, and telling them apart takes one glance at the two numbers.
💡 Here's the trick
Look at the four cards above. A unit fraction has 1 on top, like 1/4. A proper fraction has a top smaller than its bottom, like 3/5, so it is less than one whole. An improper fraction has a top as big as or bigger than its bottom, like 7/4. A mixed number is a whole and a fraction together, like 2½.
🪄 How to do it
- 1.Look at the top against the bottom, the comparison the cards above are sorted by.
- 2.If the top is 1, it is a unit fraction. If the top is smaller than the bottom, it is proper.
- 3.If the top is bigger than or equal to the bottom, it is improper. Divide it out to get the mixed number.
✍️ Try it
Name the type of 9/4, then write it as a mixed number. Then name the type of 1/8.
In 9/4 the top is bigger than the bottom, so it is improper. Nine quarters is two whole ones with one quarter over, because 9 ÷ 4 = 2 remainder 1, so 9/4 = 2¼. In 1/8 the top is 1, so it is a unit fraction, and it is proper as well.
⚠️ Watch out
You might be thinking improper means bigger than one whole. 4/4 is improper too, and it is exactly one whole, not more. Improper only means the top has caught up with the bottom, and catching up counts.
🌟 Why this matters
Recipes ask for 1½ cups, races are run over 2¼ kilometres, and a shop sells three half-litre bottles. Naming the type tells you at a glance whether you are dealing with less than one thing or more.
Exam tip: Questions often hide a whole number as an improper fraction, so check whether the top has reached the bottom.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“What type of fraction is 9/5?”
- 1
Spot the top and bottom
Top (numerator) = 9. Bottom (denominator) = 5.
- 2
Compare them
Is the top > bottom? 9 > 5 → yes.
- 3
Pick the type
Top > bottom → this is an IMPROPER fraction.
- 4
Answer ✓
9/5 is an improper fraction
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Look at the bars, then tap the family this fraction belongs to.
FAMILY · ROUND 1 OF 4
1/5
Quick check
✅ VERIFICATION
Which type of fraction is 5/6?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Same Value, Different Look
Multiply top and bottom by the same number.