Algebra

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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 $2+x+x^2$