What is an Expression?

An expression in mathematics is a group of numbers, letters and signs written together to show a mathematical idea. An expression does not have an equal sign (=). It only shows a mathematical thought, not a full sentence.

Examples:

5 + 2
(6 + 4) × 3
2x + 5
(8 − 3) ÷ 5

What Are Brackets?

Brackets are special marks we use to group numbers or parts of an expression together. They help us know which part of the calculation to do first. We cannot solve things in any order we like — brackets tell us the part to do first.

Types of Brackets

1. Parentheses ( ) — called “small brackets”.


2. Braces { } — called “curly brackets”.


3. Square brackets [ ] — called “big brackets”.

Why We Use Brackets

Look at these two expressions to see why brackets matter:

Example A: 5 + 3 × 2
Example B: (5 + 3) × 2

Solving:

Example A → 5 + 3 × 2 = 5 + 6 = 11
Example B → (5 + 3) × 2 = 8 × 2 = 16

Same numbers, different answers because the bracket changed the order. Brackets say “do this first”.

The BODMAS Rule

BODMAS tells the order in which we must do operations:

1. B — Brackets (do inside brackets first)


2. O — Of (used for expressions like "of", i.e. multiplication)


3. D — Division (÷)


4. M — Multiplication (×)


5. A — Addition (+)


6. S — Subtraction (−)

Start with Brackets, then follow the rest in that order.

Examples on Brackets

(3 + 2) × 4

6 + (8 − 3)

(2 + 3) × (4 + 1)

{(3 + 2) × 4} − 5

What Are Fractions?

A fraction shows a part of a whole. It is written with two numbers — one at the top (the numerator) and one at the bottom (the denominator).

Example: 3/4 means 3 parts out of 4 equal parts.

Types of Fractions

1. Proper fraction: numerator is smaller than denominator (e.g. 1/2, 2/3).


2. Improper fraction: numerator is larger than denominator (e.g. 5/3, 7/4).


3. Mixed fraction: a whole number and a fraction together (e.g. 1½, 2¾).

How to Work with Fractions

You can add, subtract, multiply and divide fractions — but there are rules.

1. Addition of Fractions

If denominators (bottom numbers) are the same, add the numerators (top numbers):

2/5 + 1/5 = 3/5

If denominators are different, make them the same (find a common denominator):

1/2 + 1/3 → common denominator 6
1/2 = 3/6, 1/3 = 2/6 → 3/6 + 2/6 = 5/6

2. Subtraction of Fractions

3/4 − 1/4 = 2/4 = 1/2

Different denominators example:

3/5 − 1/10 → make denominator 10:
3/5 = 6/10 → 6/10 − 1/10 = 5/10 = 1/2

3. Multiplication of Fractions

Multiply top × top and bottom × bottom:

2/3 × 4/5 = 8/15

4. Division of Fractions

Flip (take reciprocal) of the second fraction and multiply:

2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6

Expressions with Brackets and Fractions

When brackets and fractions are together, always do the brackets first (BODMAS), then handle the fractions as required.

(1/2 + 1/4) × 8

(6 − 3/2) ÷ 3/4

(2/3 + 1/6) × 12

(4 + 1/2) × 3

Summary

1. An expression is a group of numbers and signs without an equal sign.


2. Brackets show which operation to do first.


3. Use the BODMAS rule when solving expressions.


4. A fraction shows parts of a whole: numerator (top) and denominator (bottom).


5. Add or subtract fractions only after making denominators the same.


6. Multiply fractions by multiplying numerators and denominators.


7. Divide fractions by flipping the second fraction and multiplying.


8. When expressions have both fractions and brackets, solve the brackets first and show work step by step to avoid mistakes.