In Algebra, we use letters to represent numbers. These letters are called variables, and they help us describe general rules, find unknown values, and solve real-world problems.
Using Letters to Represent Numbers
In algebra, we often do not know the exact value of a number, or that number often changes depending on the situation. Instead of leaving a blank or a question mark, we use a letter to stand for the unknown number. This letter is called a variable.
Let’s look at an example:
John buys some apples. He eats 2 apples, and later, his brother gives him 3 more. The next day, John sells all the apples he has left for $0.50 each.
In this situation, the exact number of apples John bought is unknown. However, the number of apples he has after eating and receiving more, as well as the total money he earns, all depend on this unknown number.
To make it easier to describe these relationships, we use a letter to represent the unknown number of apples.
Let’s call it x.
Now we can express each part using algebra:
Apples left after eating 2: x − 2
Apples after his brother gives him 3 more: x − 2 + 3, which simplifies to x + 1
Total amount earned from selling them at $0.50 each: $0.5(x+1)
By using the letter x, we can write general statements and calculate easily once we know the value of x.
This is what algebra does — it helps us represent unknown numbers and show how quantities are related.
How We Show Unknown Numbers in Algebra
In algebra, a variable must be a single letter, like x, and x represents just one thing.
For example, if x refers to the number of apples, then to represent the number of pears, we have to use another letter, e.g. y.
In theory, we can use any letter we like. But here are some things to note:
- lower case alphabets are often used conventionally for algebra. we typically do not use letters like o, i and l.
- We don’t use upper case, as they are often used for other things , like in angles e.g. ∠ABC, representing physical quantities, e.g. representing volume as V, etc.
- Only a SINGLE letter is used. E.g. x, y, z, etc.
- Multiple letters represent a number of variables being multiplied together. For example, we do not use ab to represent a variable, as ab is seen as a times b rather than a single variable.
- Avoid confusing letters
- Letters like l, i, m, o are usually not used.
- l can easily be misread as “1”, similarly for i (although i also means imaginary numbers, which is not covered in secondary school Math)
- m is the symbol for metres. –> Think about writing m metres as m m. 😲
- o can be easily misread as the number “0”.
- Letters like l, i, m, o are usually not used.