Before you can solve complex equations, you need to be confident with the basics. Think of it like learning an alphabet before you can write a story. In math, that alphabet is arithmetic. Everything in algebra is built on four fundamental operations: addition, subtraction, multiplication, and division.

You've likely been using these for years. Addition combines values, subtraction finds the difference, multiplication is just fast addition, and division is the reverse of multiplication. We won't review how to do them, but it's crucial to remember that algebra constantly uses these simple actions in new and interesting ways.

Whole numbers are great, but the world is full of pieces, slices, and parts. That's where fractions and decimals come in. They are two different ways of describing the same thing: a number that isn't whole.

A fraction has two parts. The top number is the numerator (how many parts you have), and the bottom number is the denominator (how many parts the whole is divided into). So, in the fraction $3/4$, we have three parts of a whole that's been cut into four equal pieces.

A decimal is just another way to write a fraction. Specifically, it's a fraction where the denominator is a power of 10 (like 10, 100, or 1000). The position of a digit after the decimal point tells you the denominator.

To convert any fraction to a decimal, you just divide the numerator by the denominator. To turn a decimal into a fraction, you use the place value as the denominator and simplify.

Percentages are a special type of fraction that you see everywhere, from store discounts to phone battery levels. A percentage is simply a fraction where the denominator is always 100. The word "percent" literally means "per hundred."

Since percentages, fractions, and decimals are all ways of showing parts of a whole, you can easily convert between them. To change a percent to a decimal, you just divide by 100, which means moving the decimal point two places to the left.

$50\% = 50.0 \div 100 = 0.50$

To change a decimal to a percent, you do the opposite: multiply by 100.

$0.75 \times 100 = 75\%$

Here are some common conversions that are helpful to know by heart:

When a math problem has multiple operations, the order you do them in matters. If we didn't have a set of rules, two people could get different answers from the same problem. Consider this expression:

If you work from left to right, you get $3 + 5 = 8$, and then $8 \times 2 = 16$. But if you do the multiplication first, you get $5 \times 2 = 10$, and then $3 + 10 = 13$. Which one is correct?

To avoid this confusion, mathematicians agreed on an order of operations. A common way to remember it is with the acronym PEMDAS.

It's important to remember that multiplication and division are a team—you do them in the order they appear from left to right. The same is true for addition and subtraction.

Let's revisit our problem using PEMDAS:

There are no parentheses or exponents. Multiplication comes before addition, so we do $5 \times 2$ first, which is 10. Now the problem is just $3 + 10$, which equals 13. The correct answer is 13.

Here’s a slightly more complex example:

1. Parentheses: $(2+1) = 3$. The expression becomes $10 - 3^2 \div 3$.
2. Exponents: $3^2 = 9$. Now we have $10 - 9 \div 3$.
3. Division: $9 \div 3 = 3$. The expression is now $10 - 3$.
4. Subtraction: $10 - 3 = 7$.

The final answer is 7.

These rules are essential. In algebra, you'll be working with much more complex expressions, but the order of operations will always be the same.