Liri had folded her star map into four equal parts to make it easier to carry. “One part out of four – how do I write that as a number?”
A fraction is made of three parts: the numerator (on top – how many parts you have), the fraction bar (the dividing line) and the denominator (underneath – how many equal parts the whole is divided into).
Fractions belong to the set of rational numbers (ℚ). This includes all numbers that can be written as a fraction of two whole numbers.
You will get to know the negative numbers (ℤ) in detail later – here you only see where fractions “live” overall.
Proper fraction: the numerator is smaller than the denominator (34). Improper fraction: the numerator is bigger than or equal to the denominator (54). Mixed number: a whole number plus a proper fraction (114).
If you multiply or divide the numerator AND the denominator by the same number, the value of the fraction does not change.
Some moons orbit their planet in exact fractional ratios to one another – e.g. exactly 12 or 13 of the orbital period of a neighbouring moon. This is called orbital resonance.
Without fractions, astronomers couldn’t recognise such elegant number relationships in the universe.
When simplifying or scaling up, people often change only the numerator OR only the denominator – but you must ALWAYS treat both at the same time!
Tip: whatever you do on the top, you must do the same on the bottom – otherwise the value of the fraction changes.
Liri unfolded her map again – 44, a whole, made up of four equal quarters.
Liri now understands what fractions are and can simplify and scale them up.