In everyday life, we often face situations where we know some information but not everything. For example, we might know that a number plus 5 equals 10, but we do not know the number itself. Letters help us express these unknown quantities.

When we use a letter to stand for a number we do not yet know, we can write mathematical statements called expressions or equations to represent the problem.

An algebraic term is made of two parts:

• The coefficient is the number in front of the letter.
• The variable is the letter that represents an unknown number.

Example 1

In the term $6a$:

• 6 is the coefficient
• $a$ is the variable

Example 2

In the term $y$:

• The coefficient is 1 (because $y$ means $1 \times y$)
• $y$ is the variable

Example 3

In the term $3pq$:

• 3 is the coefficient
• $p$ and $q$ are variables

Let us look at a simple example:

Imagine 4 families keep chickens. Each family has the same number of chickens. Let us use the letter $k$ to represent the number of chickens each family has.

• One family has $k$ chickens
• Two families have $k + k$ chickens
• Four families have $k + k + k + k$ chickens

We can write this more simply as $4k$.

This is algebra: using the letter $k$ to represent an unknown number of chickens. We can calculate or reason about the total even without knowing the exact value of $k$.

• Algebra uses letters to represent unknown numbers or quantities
• These letters are called variables
• The number in front of a variable is called the coefficient
• Together, the coefficient and variable form a term
• Algebra helps us solve problems where we do not know all the numbers

In Tanzania, algebra is useful in many daily situations. For example, when a farmer sells mangoes at the market, if each mango costs $x$ shillings and a customer buys 5 mangoes, the total price can be written as $5x$. If the farmer knows the total money received, algebra can help find the price of one mango. This skill is helpful for small business owners, traders, and anyone managing money or quantities.