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:

  1. Make the denominators the same by expanding or simplifying / reducing (→ see simplifying / reducing).
  2. Add the numerators - the denominator remains unchanged.
  3. 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:

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

==> Page 4: Subtracting Fractions


Let's continue with: "Adding Fractions and Whole Numbers"