## Summary:

In step 1 you have learned what a fraction is and especially the meaning of the fraction bar:"divided by".

In step 2 you have learned that by calculating this division you get a number which corresponds to the value of the fraction.
So you can say that a fraction is a number. The set of all fractions forms the set of *Rational Numbers*, the set of *Natural Numbers* is contained in it.

Conversely, **every** number can also be represented as a fraction - and not only that: it can be represented as a fraction in an infinite number of ways!

In order to represent the same fraction in different ways, you need the tools **Expand** and **Simplify/Reduce** (sometimes some other small tools). That is what you will learn in this chapter:

## Page 1: Expanding fractions

**Expand**a fraction by multiplying the numerator and the denominator with the same number. The value of the fraction does not change!Here you can find Page 1: Expanding Fractions

## Page 2: Simplifying/Reducing fractions

**Symplify**or**reduce**a fraction by dividing the numerator and the denominator by the same number. The value of the fraction does not change!Here you can find Page 2: Simplifying/Reducing fractions

## Page 3: Prime Factorization

*A prime number exactly has 2 factors: 1 and itself. The number 1 is not a prime number, since its only factor is 1.*

Life is much easier if you memorize at least the first prime numbers: 2, 3, 5, 7, 11, 13, 17, 19 ...

The numbers used for multiplication are called **factors**. The result is called **product**:

*Factor * Factor = Product*

If all factors are prime numbers then they are called **prime factors**.

**Prime Factorization** means to disassemble a number into its prime factors.

Here you can find Page 3: Prime Factorization

## Page 4: Greatest Common Divisor (GCD)

The **Greatest Common Divisor (GCD)** of two numbers A and B is the greatest factor that is common for A and B.
One way to calculate the GCD works with prime factorization.

If you simplify a fraction with the GCD of its numerator and denominator, you can reduce it directly to a Lowest Terms Fraction.

Here you can find Page 4: Greatest Common Divisor (GCD)

## Page 5: Least Common Multiple (LCM)

The **Least Common Multiple (LCM)** of two numbers A and B is the lowest number that is divisible by A and B.
One way to calculate the LCM works with prime factorization.

You need the Least Common Multiple (LCM) to find the *Common Denominator* of two fractions.

Here you can find Page 5: Least Common Multiple (LCM)

## Page 6: Common Denominator

Here you can find Page 6: Common Denominator