## 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 step 3 you created a toolbox to make this and the next chapter very simple! You learned to expand and to simplify fractions, as well as some other tools: prime factorization, the greatest common divisor (GCD) and the least common multiple (LCM).

Finally you got to know the tool *common denominator*. Especially this you will need in this chapter!

## Page 1: Addition Fraction plus Whole Number

*When adding a whole number with a fraction, you can write the result directly as a mixed number by simply omitting the plus sign.*

==> Page 1: Adding Fractions and Whole Numbers

## Page 2: Addition Fraction plus Fraction

*Two fractions that don't have the same denominators or common denominators cannot be added directly! Instead:*

- Make the denominators the same by expanding or simplifying / reducing (→ see simplifying / reducing).
- Add the numerators - the denominator remains unchanged.
- Check, if you can simplify the fraction (to lowest terms).

==> Page 2: Adding Fractions

## Page 3: Subtraction Whole Number minus Fraction

First, convert the improper fraction into a mixed number.

The remaining task is to solve a problem of the type "subtract mixed number from whole number".

==> Page 3: Subtraction Whole Number minus Fraction

## Page 4: Subtraction Fraction minus Fraction

*Two fractions that don't have the same denominators or common denominators cannot be subtracted directly! Instead:*

- Make the denominators the same by expanding or simplifying / reducing (→ see simplifying / reducing).
- Subtract the numerators - the denominator remains unchanged.
- Check, if you can simplify the fraction (to lowest terms).

==> Page 4: Subtracting Fractions