## 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