Equations


 * Objectives**


 * Understand the terms expression and equation.

You may have heard that Algebra is a difficult topic. Don't worry - it's not! The first thing to grasp is the difference between an expression and an equation.


 * Expression**
 * a mathematical phrase made up of numbers and/or variables connected by operations.

five more than a number x + 5 three less than a number n - 3 three subtract a number 3 - m five times a number 5x five times a number, then add 3 5n + 3 three more than five times a number 5n + 3 one hundred divided by a number 100/n a number divided by 100 n/100

An algebraic expression can help you solve similar problems more efficiently. Evaluating algebraic expressions is an important skill. Carpenters, computer scientists, designers, electricians and auto machanics all use this skill to solve problems on the job.

 8 = 8 That is an **equation**. Simple enough? Now we change the equation a little by introducing simple arithmetic operation that you already know: 5 + 3 = 8
 * Equation**
 * a mathematical statement in symbols. It has an = sign and each side of the equal sign is equivalent or exactly the same. Let's start with:

8 = 2 × 4

Thus: 5 + 3 = 2 × 4 Easy to follow so far? OK, the next step is something you may have done in arithmetic quizzes. 5 + = 2 × 4 If you are asked to fill in the box, you can do the simple arithmetic and know that the answer should be 3. Now we are ready for basic algebra. Let's substitute the box with the letter 'k' and we have: 5 + k = 2 × 4

K is just like the box above and k = 3.


 * Sample Problem**

You buy 10 yoyos for $2.00. How much does one yoyo cost? We can do that in our head but to write an equation for that on paper it might look like this.

10 * yoyo = $2.00 (* means times)

Mathematicians use a shorthand for the above. Instead of writing the whole word yoyo, a letter is used and instead of using a multiplication sign just the number and letter are used.

10y = $2.00 (This means 10 x y = $2.00)

This means whatever is left of the equal sign must be equal to whatever is right of the equal sign. We know that 10 X $.20 is $2.00 and therefore we can say that each yoyo would cost $.20

You have used numbers and letters to create an algebraic expression.


 * Assignment**

Go to [|BBC Maths for School] and read using letters for numbers.

Write the following in your notebook and tell which are equations and which are expressions. a) 4x = 48 b) 3d + 5 c) 6z + 1 = 67 d) 2n - 3 = 27 e) 4y = 24 f) 5x + 5 = 30