Transition Year Maths 8. for inscriptions.


These symbols and letters are the numbers in these systems. Algebra is different. Algebra is about using a letter for an unknown number or a variable. A letter, usually x or y, is substituted instead of a number.


Always clearly state what each variable represents. This will help avoid confusion. In Example 1 make sure to clearly write down Let x = cost of one apple


Substitution: Example 1:


You are in a shop. A sign says 6 apples for 90 cent. You can probably work out in your head how much one apple costs. But if we want to use maths to find the cost, we use algebra. We let x = cost of one apple. 6 apples costs 90 cent ⇒ 6 multiplied by (cost of one apple) = 90 cent ⇒ 6 multiplied by x = 90 ⇒ 6x = 90


or divide by 6: Example 2:


x== 90


6 15 cent each


Sign in window of Sally’s fruit shop: 8 apples for €1 Sign in window of Herb’s fruit shop: 6 apples for 72 cent Which shop is cheaper for apples? Let x = cost of one apple in Sally’s shop Let y = cost of one apple in Herb’s shop Sally’s shop: 8x = 100


x== 100


Herb’s shop: 6y = 72


y== 72


Herb’s is cheaper. 80 6 12 cent each 8 12


1 2


cent each Algebra


In Chapter 1, we saw that our number system – the decimal system – uses the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, to make all our numbers. The Romans used the letters I, V, X, L, C, D, M to represent their numbers.


The Greeks used l a vertical bar for 1 Π Pi . . . . . . . . . . . . . . . . for 5 ∆ Delta . . . . . . . . . . . . . for 10 H Eta . . . . . . . . . . . . . . . for 100 X Chi . . . . . . . . . . . . . . for 1000 M Mu . . . . . . . . . . . . . . for 10,000


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