Identify term, variables, and coefficients in algebraic expressions

A variable is a letter that represents an unknown number. In algebra, we use letters such as $a$, $k$, $x$, $y$, $p$, $q$, or $w$ as variables.

Examples:

• In the term $4k$, the variable is $k$
• In the term $3pq$, the variables are $p$ and $q$
• In the term $y$, the variable is $y$

A coefficient is the number multiplied by the variable in a term. It tells us how many times to take the variable.

Key point: If a term has only a variable with no number in front, the coefficient is $1$. For example, in the term $y$, the coefficient is $1$ (because $y = 1 \times y$).

Example 1: Identify the coefficient and the variable in each term.

Example 2: From the textbook example about chickens and goats.

Four families keep chickens. If $k$ represents the number of chickens in one family, then:

• The total number of chickens is: $k + k + k + k = 4k$

Here in the term $4k$:

• The coefficient is $4$
• The variable is $k$

For the goats:

• First family has $2k$ goats (twice as many as chickens)
• Second family has $3k$ goats
• Third family has $2k$ goats
• Fourth family has $4k$ goats

In each term like $2k$, $3k$, and $4k$, the number in front is the coefficient, and $k$ is the variable.

• A term is a single part of an expression (a number, a letter, or numbers and letters multiplied together)
• A variable is a letter that represents an unknown number
• A coefficient is the number multiplied by the variable in a term
• When a variable stands alone, its coefficient is $1$

Write the coefficient and variable for each term:

1. $7mn$ — coefficient: $7$, variables: $m, n$
2. $5p$ — coefficient: $5$, variable: $p$
3. $n$ — coefficient: $1$, variable: $n$
4. $pk$ — coefficient: $1$, variables: $p, k$
5. $a$ — coefficient: $1$, variable: $a$

When shopping at the market in Tanzania, you can use algebra to solve problems. For example, if the price of one kilogram of rice is $k$ shillings and you buy 5 kilograms, the total price can be written as $5k$ shillings. Here, $5$ is the coefficient and $k$ is the variable representing the unknown price per kilogram. This helps you calculate costs quickly when prices change.