You're already familiar with integers, both positive and negative. The best way to visualize them is on a number line, stretching infinitely in both directions from zero. Moving right means adding a positive number. Moving left means subtracting a positive number.

But what about adding or subtracting negative numbers? Adding a negative number is the same as moving to the left. For example, $5 + (-3)$ means you start at 5 and move 3 units to the left, landing on 2.

Subtracting a negative number is a bit different. It's like removing a debt. If someone takes away a $50 debt from you, you are $50 richer. So, subtracting a negative number is the same as adding a positive one. The expression $2 - (-4)$ means you start at 2 and move 4 units to the right, ending up at 6.

This leads to two important concepts: the additive inverse and absolute value.

The other key idea is absolute value, which measures distance.

The rules for adding and subtracting apply to all rational numbers, including fractions and decimals. The rules for multiplication and division are even more straightforward. They all come down to the signs.

When you multiply or divide two rational numbers:

• If the signs are the same (both positive or both negative), the result is always positive.
• If the signs are different (one positive and one negative), the result is always negative.

Why does multiplying two negatives make a positive? Imagine you owe 3 people $4 each. Your total debt is $3 \times (-4) = -12$. Now, what if those 3 debts are forgiven? That's like taking away the debts, an act of negation. So, $(-3) \times (-4)$ means taking away 3 debts of $4, which makes you $12 richer.

Every rational number can be written as a fraction $\frac{a}{b}$, where $a$ and $b$ are integers and $b$ is not zero. To convert a fraction into a decimal, you simply perform the division: $a \div b$.

The result will be one of two things: a terminating decimal or a repeating decimal.

A terminating decimal is one that ends. For example, to convert $\frac{3}{8}$ to a decimal, we calculate $3 \div 8$.

A repeating decimal is one that has a digit or a block of digits that repeats forever. Take the fraction $\frac{4}{11}$. When you divide 4 by 11, the pattern emerges quickly.

This works in reverse, too. Every terminating or repeating decimal can be converted back into a fraction, which is why they are all part of the set of rational numbers. These conversions are essential for comparing numbers in different formats and for performing calculations in algebra.

Working with rational numbers is a foundational skill in mathematics, from managing personal finances to understanding scientific data.