A fraction is part of a whole
Cut a pizza into 4 equal slices. Take 1 slice. You have one out of four equal pieces. We write that as:
1/4
Say it as "one quarter" or "one fourth."
What the two numbers mean
- The bottom number is how many equal pieces the whole thing was cut into.
- The top number is how many of those pieces you have.
So 3/4 means the pizza was cut into 4 equal slices and you have 3 of them. The pieces have to be equal. If one slice is huge and the others are tiny, they are not quarters.
A bigger bottom number means smaller pieces
This is the part that confuses almost everyone. 1/8 is smaller than 1/4, even though 8 is bigger than 4.
Think about the pizza. Cut it into 8 slices and each slice is small. Cut it into 4 and each slice is bigger. The more pieces you cut, the smaller each piece gets.
Different fractions can be the same amount
Cut a pizza into 4 slices and take 2. You have 2/4. That is exactly half the pizza. So:
2/4 = 1/2
In the same way, 4/8 is also one half. They look different but they are the same amount of pizza.
When the top and bottom match, you have the whole thing
4/4 means cut into 4 pieces, and you have all 4. That is the whole pizza, so 4/4 = 1. The same goes for 8/8 or 2/2.
A fraction is also a division
The line in a fraction means "divided by." 3/4 is the same as 3 ÷ 4. If 4 friends share 3 pizzas equally, each friend gets 3/4 of a pizza. If division is still shaky, read division in plain English first.
Adding fractions with the same bottom number
You eat 1/4 of the pizza, then 2/4 more. How much have you eaten? Count the slices: 1 slice and 2 slices is 3 slices. The slices are still quarters.
1/4 + 2/4 = 3/4
Add the top numbers. Leave the bottom number alone, because the size of the slices hasn't changed.
See it with real things
Fold a sheet of paper in half, then in half again, and open it up. You'll see four equal parts. Colour one. That is 1/4. Fold it once more and you get eighths, and you can see that each part got smaller.
Practice the idea underneath
Fractions sit on top of sharing equally. Fun With Learning is a free app with no ads and nothing to buy, and its sharing and grouping games build that idea with pictures you can tap. There are no timers. See the math games and activities, or print a division sharing mat.
