Chapter 2: Arithmetic Expressions

When you write $5 + 3 \times 2$, do you mean first add then multiply (giving $16$) or first multiply then add (giving $11$)? Without a clear rule, the same string of symbols could mean different things to different people. This chapter teaches you the universal rule.

You will meet expressions , strings of numbers joined by operations like $+$, $-$, $\times$, $\div$. You will learn how to read them aloud, how to evaluate them step by step, and how to use brackets to change the order when you want to.

You will also see why multiplication and division are stronger than addition and subtraction, why brackets always win, and how a simple memory aid like BODMAS captures all this in one word.

Finally, you will discover useful properties , like the distributive property $a \times (b + c) = a \times b + a \times c$ , that let you rewrite an expression into an easier form. These properties are the foundation of all the algebra you will study next.

What's inside

1. What is an expression? , terms, operations and reading them aloud.
2. Order of operations: BODMAS , the universal priority rule.
3. Brackets and removing them , controlling the order yourself.
4. The distributive property , turning $a(b+c)$ into $ab+ac$.
5. Word problems and real-life expressions , translating sentences into symbols.

Key results

How to read this chapter

Try evaluating every expression yourself before reading the worked solution. Whenever you place a bracket in your own work, double-check by reading it aloud , "first do the inside". By the end of the chapter you should be able to look at any nested expression and know exactly what step comes next.