What Is a Fraction?
A fraction is a number for a part of something. Two numbers, one line, and one rule about equal parts that decides everything else.
What a fraction is
A fraction is a number that describes part of a whole.
Cut a chocolate bar into four equal pieces and take three of them. There is no whole number for what you are holding. It is more than nothing and less than one bar. A fraction is the number that fits in that gap.
We write it like this: 34. Say it out loud as "three quarters".
The two numbers
Every fraction has two numbers doing two different jobs. They have long names that sound alike, which is exactly why children mix them up for years.
A way to remember which is which
Denominator is down. That one word saves a lot of guessing. And the down number is the one that does the cutting, so read a fraction from the bottom up: cut into 4, take 3.
Why the parts have to be equal
This is the part that gets skipped, and it is the part that matters most.
If you snap a chocolate bar into four pieces and one of them is huge, calling that piece 14 is simply wrong. A quarter is not "one of four pieces". A quarter is one of four equal pieces.
Test your child on this with a real object. Tear a sheet of paper into four uneven bits and ask whether one piece is a quarter. The answer they give tells you whether they understand fractions or have just memorised the words.
Fractions on a number line
Shaded shapes are how fractions start, but a fraction is a number, and numbers live on a number line. Getting a child comfortable with this early makes comparing and adding much easier later.
Notice that 44 lands exactly on 1. Four quarters make one whole, which is worth saying out loud once or twice.
Reading fractions aloud
The names follow a pattern, with two odd ones at the start.
- 12 is a half, not a "onerth".
- 13 is a third.
- 14 is a quarter, and some books say "fourth".
- From five onwards it is regular: 15 a fifth, 16 a sixth, 110 a tenth.
- Change the top number and the name just gets a count in front: 35 is three fifths.
Common mistakes
1. Counting pieces instead of equal pieces
Naming any four pieces as quarters. Equal is not a detail in the definition, it is the definition. Ask "are those pieces the same size?" every single time.
2. Thinking a bigger bottom number means a bigger fraction
Reading 18 as larger than 14 because 8 is larger than 4. It is the other way round. More pieces in the same whole means each piece is smaller. Sharing one pizza between 8 people beats sharing it between 4 only if you want less pizza.
3. Forgetting what the whole was
Half of a small pizza and half of a large pizza are both called a half, but they are not the same amount of food. A fraction always describes a part of something, so the whole has to be clear before the fraction means anything.
Practice questions
Seven questions. One attempt each, and the explanation appears once the answer is in.
Check yourself
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For parents
The fastest way to check real understanding at this age is not a worksheet. Hand your child a chocolate bar, a sandwich or a sheet of paper and ask them to show you three quarters. If they hesitate about making the pieces equal, that is the thing to work on, and everything later in fractions gets easier once it clicks.
What to learn next
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