Algebra is fun!

But it is not fun if you think that Algebra is just mathematical alphabet soup. To help you clarify for yourself and your child exactly what algebra is, we are sharing this definition and WONDERFUL examples provided by one of our wonderful tutors, Jancis Dienes.

Algebra is the study of mathematical statements which are generally true.

In algebra, the statements we study form a pattern which is true no matter what number we put in that pattern.

For example:

(4+2) = (2+4)

(6+8) = (8+6)

(9+3) = (3+9)

So we can say:

(a+b) = (b+a)

This shows the pattern “a” and “b” are used to show that any number can be put there and the statement will be true. We call “a” and “b” variables because they can vary. In algebra, the variables are shown by a letter. Any letter can be used. Algebra is mostly about mathematical statements dealing with variables. In algebra, the letters show us the pattern which we call a formula. A formula is a mathematical statement which is generally true. For example, (a + b) = (b + a) is a formula.

Another example is this:  Take any three numbers that follow each other and follow the steps below.

Example 1:

a. Take 3, 4 and 5

b.  Multiply the first and last number: 3 x 5 = 15

c.  Take the number between these two which is 4

d.  Multiply 4 by itself: 4 x 4 = 16

e.  Notice that 3 x 5 = (4 x 4) -1

Example 2:

a. Take 5, 6 and 7

b.  Multiply the first and last number: 5 x 7 = 35

c.  Take the number between these two which is 6

d.  Multiply 6 by itself: 6 x 6 = 36

e.  Notice that 5 x 7 = (6 x 6) -1

Example 3:

a.  Take 2, 3 and 4

b.  Multiply the first and last number: 2 x 4 = 8

c.  Take the number between these two which is 3

d.  Multiply 3 by itself: 3 x 3 = 9

e.  Notice that 2 x 4 = (3 x 3) -1

Do you see the pattern?

If we call the middle number “n” we can then say: (n-1) x (n+1) = (n x n) -1

This will always be true!

The word “algebra” comes from an Arabic word meaning “putting together the broken parts.” It is as if each particular example such as:

(4 + 2) = (2 + 4) and

(6 + 8) = (8 + 6) and

(9 + 3) = (3 + 9) etc.

are the broken parts and the formula

(a + b) = (b + a)

is the truth which brings all the “broken parts” together.