Algebraic expressions are collections of numbers, variables and operations. When an equals sign is added, they become equations.
The variables are important, as it is not an algebraic equation without them – they make the outcome different depending on their value.
Letters and numbers are called terms in algebra. For example, in 6x-4, the terms are -4 and 6x.
Of course, having too many terms can be long and unwieldy, so we simplify expressions by collecting ‘like terms’ together. Like terms are terms with the same letter. 5x and -3x are like terms. Simplified together, they make 2x. We can all agree that 11x – 2y is better than 14x – x + 5y – 2x – 7y.
But not all expressions are nice and respectful and have only addition and subtraction; some have multiplication and division! Multiplication can be simplified by changing it into indices. t x t x t = t3
When you have both multiplication and number/letter terms, you multiply the numbers and letters separately, then put them back together.
3x x 5x = 15x2
Simplifying division is a bit harder.
Firstly, you turn the expression into a fraction.
6t2s4 ÷ 3ts2
Then, you divide. You divide the numbers by each other first, and then you divide the letters by cancelling out the variables which appear on both sides.
This makes 2ts2.
Evaluating expressions is simple. It is merely replacing letters with numerical values and turning the expression into an equation.
If I had the equation 2s + 3x2 and s = 4 and x = 6, it would make the expression,
2 x 4 + 3 x (6×6)
Then, I turn it into an equation, by adding an equals sign and balanced answer, in this case 80.