Fractions
A fraction tells you into how many equal pieces you divide something and how many pieces you take. Different fractions can be the same piece.
You can start right here: nothing needed first.
Why
You share a pizza with four friends. How much does each of you get?
Whole numbers do not get you far when you want to share fairly. Five people, one pizza: nobody gets a whole one.
A fraction gives that piece a name: each person gets 1/5 of the pizza. And whoever takes two pieces has 2/5.
See it
Slide the numerator and the denominator. Watch how the bar changes and which other fractions are exactly as long.
Description of the picture
A bar divided into equal boxes, some of them coloured. Below the bar are fractions of the same length, such as 1/2, 2/4 and 3/6.
Get it
In a fraction like 3/4 the denominator is at the bottom: into how many equal pieces you divide the whole. The numerator is at the top: how many of those pieces you take.
If you cut every piece in two again, you have twice as many pieces, but they are half as big. 3/4 becomes 6/8: another name for the same part.
The other way round, you can simplify a fraction. Divide the numerator and the denominator by the same number until you cannot any more.
If you multiply or divide the numerator and the denominator by the same number (not zero), the fraction keeps its value: a/b=
Worked example
Simplify 18/24 as far as you can.
Look for the largest number that divides both 18 and 24. That is 6.
18:
6= 3and24: 6= 4 Divide the numerator and the denominator by 6.
18/24=
3/4 3 and 4 have no common divisor other than 1, so you are done.
- Answer
18/24=
3/4
Do it
Pick a level. You get a new exercise every time, checked straight away.
Pitfalls
Wrong: 1/8 is bigger than 1/4, because 8 is bigger than 4.
The denominator tells you into how many pieces you divide. The more pieces, the smaller each piece.
Right: 1/8 is smaller than 1/4: a pizza cut into eight gives smaller slices than one cut into four.
Wrong: 2/3=
4/5, because I added 2 to the numerator and the denominator. Adding changes the ratio. Only multiplying or dividing by the same number keeps the fraction equal.
Right: 2/3=
4/6: numerator and denominator both times 2. Wrong: For 3/4 of a cake it does not matter how big the pieces are.
A fraction only works with equal pieces. Four unequal pieces are not quarters.
Right: First divide into four equal pieces, then take three of them.
In real life
- A recipe for four people uses 3/4 of a litre of milk.
- At the bakery you ask for half a loaf: that is 1/2.
- A quarter of an hour is 1/4 of an hour, so 15 minutes.
- With a half-price (1/2) Belgian rail ticket you pay half.
History
The ancient Egyptians already calculated with fractions, mostly with unit fractions such as 1/2, 1/3 and 1/4. They wrote other fractions as a sum of such unit fractions.
More about that time in SpoorAt the table
Cut an apple into pieces. How many pieces do you take if you want half, and why does that work with different numbers of pieces?
A question to talk about together, for parents and children. There is no wrong answer.