Let's start with the basics: whole numbers. These are the numbers you first learned to count with, plus zero. So, 0, 1, 2, 3, and so on, forever. They don't have fractions or decimals attached.

Whole numbers have some handy properties that make arithmetic predictable. You've been using these rules for years, maybe without knowing their names.

The commutative property means order doesn't matter. $3+5$ is the same as $5+3$. The associative property means you can regroup numbers. When adding $2+8+4$, you can do $(2+8)+4$ or $2+(8+4)$ and get the same result.

There's one more that links addition and multiplication.

What about numbers less than zero? For that, we need integers. Integers include all the whole numbers, their negative opposites, and zero. Think of a thermometer: it can be 20 degrees, 0 degrees, or -20 degrees.

We can visualize all integers on a number line, with zero in the middle, positive numbers stretching to the right, and negative numbers stretching to the left.

Sometimes we only care about a number's distance from zero, not its direction. This is called absolute value, and we show it with two vertical bars.

Integers are great, but most things in life aren't perfectly whole. We often deal with parts of things, which is where fractions and decimals come in. A fraction like $3/4$ means we've split something into 4 equal parts and we have 3 of them. A decimal like 0.75 represents the same amount.

Working with them just requires a few key rules. When adding or subtracting fractions, you must have a common denominator. This means the bottom number of each fraction has to be the same.

Multiplying fractions is more direct: just multiply the numerators (top numbers) together and the denominators (bottom numbers) together. To divide, you flip the second fraction (find its reciprocal) and multiply.

With decimals, the key for addition and subtraction is to line up the decimal points. For multiplication, you multiply the numbers as if they were whole numbers, and then count the total number of decimal places in the original numbers to place the decimal point in the answer.

Fractions, decimals, and percentages are three different ways of representing the same value. Being able to switch between them is a crucial skill.

• Decimal to Percent: Move the decimal point two places to the right and add a % sign. $(0.75 \rightarrow 75\%)$
• Percent to Decimal: Move the decimal point two places to the left and remove the % sign. $(50\% \rightarrow 0.5)$
• Fraction to Decimal: Divide the numerator by the denominator. $(1/4 = 1 \div 4 = 0.25)$
• Decimal to Fraction: Write the decimal as a fraction over a power of 10, then simplify. $(0.25 = 25/100 = 1/4)$
• Percent to Fraction: Put the number over 100 and simplify. $(20\% = 20/100 = 1/5)$

Finally, let's look at how numbers relate to each other through multiplication. A factor is a number that divides evenly into another number. For instance, the factors of 12 are 1, 2, 3, 4, 6, and 12.

A multiple is what you get when you multiply a number by an integer. Multiples of 3 are 3, 6, 9, 12, and so on.

These concepts lead to two important ideas: the Greatest Common Factor (GCF) and the Least Common Multiple (LCM).

To find the GCF of 12 and 18, list the factors of each:

• Factors of 12: {1, 2, 3, 4, 6, 12}
• Factors of 18: {1, 2, 3, 6, 9, 18} The largest number in both lists is 6.

To find the LCM of 4 and 6, list the multiples of each until you find a match:

• Multiples of 4: {4, 8, 12, 16, 20, ...}
• Multiples of 6: {6, 12, 18, 24, ...} The smallest number in both lists is 12.

Now let's review these core concepts.

Ready to test your knowledge?

Understanding these different types of numbers and how they work together is the foundation for all the math that follows. From algebra to data science, it all starts here.