Unit 5 sec 2.1 Expression and what is an expression.

Unit 5 sec 2.1 Expression and what is an expression.

16 December 2015

00:22

In this section some terminology used in algebra, and a useful technique - collecting like terms.

  An algebraic expression, or just expression for short, is a collection of letters, numbers and/or mathematical symbols (such as +, -, ×, ÷, brackets, and so on), arranged in such a way that numbers are substituted for the letters, then you can work out the value of the expression.

  To make expressions easier to work with, we concisely in the way you saw earlier in the module. In particular, we usually omit multiplication signs; things that are multiplied. I just rated next to each other instead.

  When you are working with expressions, the following is the key thing to remember.

Letters represent numbers, so the normal rule of arithmetic applied to them in exactly the same way as they apply to numbers.

Example 1 evaluating and expression

evaluate the expression

4x² - 5y

When x = 2 and y = -3

Solution

If x = 2 and y = -3, then

4x² - 5y = 4 × 2² - 5 ×(-3)

= 4 ×4 – (-15)

= 16 +15

= 31

Every expression can be written new ways.

If two expressions are really just the same, written differently, then we say that they different forms of the same expression, or that their equivalent to each other.

  When we write an expression in a different way, we say that where rearranging, manipulating or rewriting the expression. Often, the aim of doing this is to make the expression simpler, as with the formula for the Bakers profit. In this case we say that where simplifying the expression.

 We use equal signs when working with expressions, but expressions do not contain equal signs. For example, the statements

X +x =2x and 1.24n -0.69n +0.55n

Aren’t expressions - their equations. An equation is made up of two expressions, with an equal sign between them.

 The equation is correct for only one value of N (it turned out to be 500). In contrast, the equations

X + x = 2x and 1.24n – 0.69n = 0.55n

are correct for every value of x and n, respectively. Equations like these which are true to all values of the variables, are called identities.

There are similar differences in the use of letters to represent numbers. The letter N represented a particular number -it was just that we did not know what that number was. This type of letter is called an unknown. A letter that represents any number (or any number of a particular type, such as any integer) is called a variable, usually you do not need to think about whether a letter is an unknown or unbearable.