# Basic Algebra/Working with Numbers/Rational Numbers

## Vocabulary[edit]

- Rational numbers
- Fraction

## Lesson[edit]

### Rational numbers[edit]

A **rational number** is a fraction, written where and are integers.
is called the *numerator* and the *denominator*.
Applied to a cake, it means parts of a cake divided equally into parts.
For example means a half. But note that and can be negative.
means gaining a half and means losing a half.

### Fractions of negative numbers[edit]

If and are positive, then the fraction or **rational number** is *positive*. This is the way we commonly think of fractions ( of a cake...).

There is no difference whether is negative or is negative. The reason for this is simple : if you talk about losing parts of a cake ( ), or about parts of a lost cake ( ), in both cases, you talk about lost parts. In these cases, the fraction is said to be *negative*.

Finally, if and are negative, then their effect is canceled by each other and the fraction is *positive*. As rational numbers are on one axis, the second time you take the opposite you obtain the original fraction. Thus, the fraction *is* the fraction .

## Example Problems[edit]

I have been given 1 piece of cake, my father who is very hungry has taken 2. My mother has taken 1 and my sister has taken 1 too. There were 10 pieces. What fraction of the cake has been eaten?

of the cake, which is half of the cake.

Note that in this case, the addition is very simple because the *denominator* is always 10. We just have to add the *numerators*.

## Practice Games[edit]

put links here to games that reinforce these skills

## Practice Problems[edit]

(Note: put answer in parentheses after each problem you write)