# Algebra I/Content/Working with Numbers/Rational Numbers

Back to Table of Contents Algebra I

## Contents

## Vocabulary

- rational numbers
- fraction

## Lesson

A **rational number** is a fraction, written p/q where p and q are integers.
p is called the *numerator* and q the *denominator*.
Applied to a cake, it means p parts of a cake divided equally into q parts.
For example 1/2 means a half. But note that p and q can be negative.
+1/2 means gaining a half and -1/2 means losing a half.

## Example Problems

I have been given 1 piece of cake, my father who is very hungry has received 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?

1/10 + 2/10 + 1/10 + 1/10 = 5/10 of the cake, which is the half

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

## Fractions of negative numbers

If p and q are positive, then the fraction or **rational number** is *positive*. This is the way we commonly think of fractions (1/3 of a cake...).

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

Finally, if p and q 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 -p/-q *is* the fraction p/q.

## Practice Games

put links here to games that reinforce these skills

## Practice Problems

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