Terms, Like Terms and Notation

In short: A variable is a letter that stands for a number, and a term is a number, a letter, or numbers and letters multiplied together, like $5y$. Like terms have exactly the same letters with the same powers, like $4ab$ and $9ab$.

Before you start

You only need two things you already know:

• Multiplication is repeated adding. $3\times 5$ means $5+5+5$.
• Squares and cubes. $5^2=5\times 5=25$ and $2^3=2\times 2\times 2=8$. The small raised number is called the power (or index). It tells you how many times to multiply the number by itself.

Variables

A variable (also called a pronumeral) is a letter or symbol that stands for a number we do not know yet.

Examples: $a$, $x$, $b^2$, $z^3$

The letter can change its value from question to question. That is why it is called a variable: it can vary.

Terms

A term is one of these:

• a number on its own, such as $2$, $8$ or $27$
• a variable on its own, such as $x$
• numbers and variables multiplied (or divided) together, such as $2a$, $3xy$, $\frac{1}{2}b$ or $\frac{2pq}{z}$

Terms are separated by plus and minus signs.

The number in front of a variable is called the coefficient. In $7y$ the coefficient is $7$. In $x$ the coefficient is $1$, because $x$ means $1x$.

Notation: how algebra is written

Mathematicians are lazy in a clever way. They leave out the $\times$ sign.

Two more rules for writing a term neatly:

1. Write the number first.
2. Write the letters in alphabetical order.

So $y\times 2\times x$ is written $2xy$, not $y2x$.

Like terms and unlike terms

Like terms have exactly the same letters with exactly the same powers. Only the number in front can be different.

Unlike terms have different letters, or the same letter with different powers.

• $x$, $y$ and $ab$ are unlike (different letters).
• $x$, $x^2$ and $x^5$ are unlike (same letter, different powers).

Think of like terms as the same kind of fruit. $3$ apples and $5$ apples are like terms. $3$ apples and $5$ bananas are not. An apple is not a crate of apples either, so $x$ and $x^2$ are different too.

Expressions and equations

An expression is a group of terms, like $3x+4y$. It has no equals sign.

An equation says that two things have the same value. It always has an equals sign:

$$x+3=2y-42x^2-3=15$$

The left side and the right side are balanced, like a see-saw that is level.

Quick summary

• A variable (pronumeral) is a letter that stands for an unknown number.
• A term is a number, a variable, or numbers and variables multiplied together. Plus and minus signs separate terms.
• No sign between a number and a letter means multiply: $5y=5\times y$.
• Write the number first, then the letters in alphabetical order.
• Like terms have the same letters with the same powers: $4ab$ and $9ab$.
• $x$ and $x^2$ are not like terms.
• An equation has an equals sign and says both sides have the same value.

Quiz