Fractions As Fair Sharing

You have 3 chocolate bars and 4 friends who all want the same amount. No one wants to feel shorted, so we need a fair share.

Start by making the bars easy to share. If we cut each bar into 4 equal pieces, then sharing among 4 friends becomes simple. Each friend can get 1 piece from each bar.

Now count pieces. Each bar gives 4 pieces, so 3 bars give $3\times4=12$ equal pieces. If 4 friends share those 12 pieces equally, each friend gets $12\div4=3$ pieces.

So each friend gets 3 pieces, and each piece is one fourth of a bar. That means each friend gets three fourths of a bar. We write that as $\frac{3}{4}$.

Try splitting and sharing so you can see what each friend ends up with.

The two numbers in a fraction

$\frac{3}{4}$ looks like two numbers stacked, but it really tells one story about sharing.

The bottom number, 4, is about the size of the pieces. It tells you the whole bar was cut into 4 equal parts. If the bottom number were 2, the pieces would be bigger. If it were 6, the pieces would be smaller.

The top number, 3, is about how many of those equal parts you have. Here, each friend has 3 pieces, and each piece is one fourth of a bar.

So we can say it in plain words like this.

• The top number tells how many parts you have.
• The bottom number tells how many equal parts make one whole.

Common mistake
People sometimes think the top number means bigger and the bottom number means smaller. But $\frac{1}{2}$ is bigger than $\frac{1}{4}$ even though 2 is smaller than 4. The bottom number changes the piece size, not the amount you have.

Use the chocolate bars again and match the fraction parts to what you can count.