FORMULABANK

Algebra is a branch of mathematics where both numbers and letters are used in calculations. The letters serve as variables representing unknown numbers, meaning they stand in for values that are not yet known.

Algebra involves general rules for performing calculations, including the order of operations (hierarchy of operations). A letter can also be replaced by a number.

Algebra is commonly encountered when simplifying expressions (reduction) and is frequently used in formulas.
For example, the volume of a box is represented as:

$V=l\cdot w\cdot h$

where:

• $V$ stands for volume
• $l$ for length
• $w$ for width
• $h$ for height

Algebra is also used to explain various mathematical concepts, such as how to divide an integer by a fraction:

$\frac{a}{\frac{b}{c}}=a\cdot \frac{c}{b}$

Note:

Identical values are represented by the same letter. Different values are represented by different letters.
For example, the expression $5+5+4=14$ can be written as:

$a+a+b=c$

The multiplication of a number and a variable can be written without a visible multiplication symbol:
$2\cdot a$ is written as $\mathrm{2a}$. There is an implicit multiplication sign between the number and the letter.

Difference between multiplication and addition:

$s\cdot s=s^2$

$s+s=\mathrm{2s}$

Remember that the equals sign ($=$) indicates that the values on both sides of the equation must be exactly the same.