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# Terms and Operations

### Terms and Operations

Terms and operations are the building blocks of algebra

Algebra uses letters to represent values.

These values are called **variables** as they might change or we might not know what they are.

We can use the four operations ($+,-,\times ,\div$) in algebra. Which one of these expressions is *not* an algebraic expression?

An algebraic expression must have letters but can have numbers too.

We saw that $4m+3$ is an algebraic expression.

Let's look at $4m+3$ more closely. What is $4m$ short for?

We leave out the $\times$ in algebra, both when we have numbers and letters or just letters. Any letters are put in alphabetical order.

$3\times x$ is written $3x$

$x\times y$ is written $xy$

We leave out the division sign in algebra too. How might we show when we are dividing our variables?

How do we best write $a$ times $b$?

We have seen how to write one letter multiplied by a different letter. But how would you write $a\times a$?

How would you write $x\times x\times x$?

The *coefficient* is the number a letter is multiplied by and always comes first in the term. What is the coefficient of $a^2$ in the expression $4a^2+7a+6$?

A coefficient can also be a fraction.

In algebra, we use top heavy fractions rather than mixed numbers. We use $\dfrac{13}{4}$ rather than $3\dfrac{1}{4}$.

What is the coefficient of $b$ in $\dfrac{5}{3}b^2+\dfrac{4}{3}b+\frac{9}{3}$?

A *term* is a collection of numbers and letters that are multiplied and/or divided together then separated by $+$ or $-$. What is the second term in this expression $3x^2+2x-6$?

Terms are written in alphabetical order with the coefficient coming first. How should you write $z\times x \times 4$?

In addition to the terms being in alphabetical order, the expressions and equations are too.

For example,We write $a+ab+b$ rather than say$b+a+ab$.

What is a better way of writing $3+4\times m-n\times 2$?

When there are powers, start with the highest and work down. What is the best way to write $7-2y^2+3x+5x^2$?

Summary! Algebra uses letters for values that are unknown or may change.

These values are known are **variables**.

We don't use the $\times$ and $\div$ symbols in algebra.

$x\times y$ is written $xy$

$x\div y$ is written $\dfrac{x}{y}$

The coefficient is a number that multiplies the variable.

In $3x^2$ the coefficient of $x^2$ is $3$ In $\dfrac{a}{4}$ the coefficient of $a$ is $\dfrac{1}{4}$

A *term* is a collections of variables and numbers multiplied or divided together.

Terms are separated by $+$ or $-$. $3a^2-4a+6$ has three separate terms: $3a^2$, $4a$ and $6$.

Individual terms should be written in alphabetical order.

We write $ab$ rather than $ba$.

An expression of several terms should be written in alphabetical order or by descending powers.

We write $a+ab+b$ rather than $b+a+ab$ We write $x^2+x+2$ rather than $2+x+x^2$