Math Core

Whole numbers count whole things: 1 apple, 2 apples, 3 apples. But what if you only have part of an apple? Fractions are numbers for parts of a whole. They all start with one simple building block: the unit fraction.

Cutting a whole into equal parts

Here is a granola bar cut into 4 equal parts. One part is shaded.

A bar cut into 4 equal parts. 1 part is shaded.

The shaded part is one fourth of the bar. We write it like this:

\frac{1}{4}

The bottom number tells how many equal parts the whole is cut into. The top number tells how many of those parts we are talking about. Here we are talking about just 1 part.

Definition

Unit fraction

A unit fraction is 1 equal part of a whole. It always has a 1 on top.

$\dfrac{1}{b}$ means: cut the whole into $b$ equal parts and take one of them.

Naming unit fractions

The bottom number gives the fraction its name.

Equal parts	One part is called	Written
2	one half	$\dfrac{1}{2}$
3	one third	$\dfrac{1}{3}$
4	one fourth	$\dfrac{1}{4}$
6	one sixth	$\dfrac{1}{6}$
8	one eighth	$\dfrac{1}{8}$

You can also show parts with squares. This strip has 6 equal parts, and 1 is colored:

🟦⬜⬜⬜⬜⬜

The colored square is $\dfrac{1}{6}$ of the strip.

Common mistake

The parts must be equal. If a sandwich is cut into 3 pieces of different sizes, one piece is not $\dfrac{1}{3}$ of the sandwich. Always check that every part is the same size.

Bigger bottom number, smaller piece

Think about sharing one pizza. If 2 people share it, each gets a big slice. If 8 people share it, each slice is much smaller.

More parts means smaller parts

When the same whole is cut into more equal parts, each part is smaller. So $\dfrac{1}{8}$ is smaller than $\dfrac{1}{2}$ .

Worked example: Name the fraction

A ribbon is cut into 3 equal pieces. What fraction of the ribbon is one piece?

The ribbon has 3 equal parts, so the bottom number is 3. One piece is $\dfrac{1}{3}$ , or one third.

Worked example: How many parts make a whole?

How many sixths make one whole?

$\dfrac{1}{6}$ means the whole was cut into 6 equal parts. So it takes 6 sixths to make the whole.

Worked example: Which piece is bigger?

Mia gets $\dfrac{1}{3}$ of a cake. Leo gets $\dfrac{1}{4}$ of the same cake. Who gets the bigger piece?

Thirds come from cutting the cake into 3 parts. Fourths come from cutting it into 4 parts. Fewer parts means bigger parts, so Mia gets the bigger piece.

Practice

Practice 1

A pie is cut into 8 equal slices. What fraction of the pie is one slice?

Practice 2

How many thirds make one whole?

Type a number.

Practice 3

What unit fraction is colored? 🟩⬜⬜⬜

Type your answer like 1/2.

Type a number.

Practice 4

A cookie is broken into 2 pieces. One piece is much bigger than the other. Is each piece $\dfrac{1}{2}$ of the cookie?

Practice 5

A garden is split into equal beds. Each bed is $\dfrac{1}{6}$ of the garden. How many beds are there?

Type a number.

Practice 6

Which piece of the same sandwich is the biggest?

Practice 7

Sam says $\dfrac{1}{8}$ is bigger than $\dfrac{1}{4}$ because 8 is bigger than 4. Is he right?