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Chapter 6: Algebraic expressions (Part 1)

6.1 Introduction

Imagine the teacher is reading a few pages of the book to his class and then asks three learners to take turns to read. Bandile reads 1 page less than his teacher, Aarifah reads 1 page more than her teacher, while Oratilwe reads as many pages as the teacher reads. If you know how many pages the teacher read, how would you work out the total number of pages read?

In this chapter, you will find out how to create mathematical expressions that describe similar situations. If the teacher read \(5\) pages, then Bandile read \((5 - 1) = 4\) pages, Aarifah read \((5 + 1) = 6\) pages and Oratilwe read \(5\) pages. The total number of pages read is then \(5 + 4 + 6 + 5 = 20\) pages. However, we would need to do this again if the teacher changes how many pages he reads!

An algebraic expression is a description of certain calculations that need to be done in a certain order. In this chapter, you will be introduced to the language of algebra. You will also learn about expressions that appear to be different but which produce the same results when evaluated. When we evaluate an expression, we choose or are given a value for the variable in the expression. We then carry out the operations (\(+, −, ×, ÷\)) in the expression using this value.

In the example above:

  • \(x\) is the number of pages the teacher reads
  • \(x - 1\) is the number of pages Bandile reads
  • \(x + 1\) is the number of pages Aarifah reads
  • \(x\) is also the number of pages Oratilwe reads.

Do you know the total? You might have worked this out:

\[x + (x - 1) + (x + 1) + x = 4x\]

Therefore, the total number of pages read will be four times the number of pages that the teacher read.