This section looks at some skills you will need as you start to learn about algebra.
It starts with some work on codes, then moves on to work with letters and formulae.
Remember that the outer ring contains the uncoded letters and the inner ring contains the coded letters.
If we see an expression which contains these letters, we need to replace the letters by their
corresponding numbers to find the value of the expression. Look at the examples below:
(a) Find the value of 6 + b:|
Replacing b by 7 gives 6 + 7.
The answer is 13.
(b) Find the value of 2a + b:|
Remember that 2a means 2 × a.
Replacing a by 4 and b by 7 gives 2×4 + 7.
The answer is 15.
(c) Find the value of ab:|
Remember that ab means a × b.
Replacing a by 4 and b by 7 gives 4 × 7.
The answer is 28.
(d) Find the value of a(b - c):|
You need to know that a(b - c) means a × (b - c).
Replacing a by 4, b by 7, and c by 3 gives 4 × (7 - 3).
The answer is 16.
Calculate the value of each expression below and then to see whether you are correct.
In this question, a = 2, b = 5 and c = 1.
(a) What is the value of b + 5?
(b) What is the value of 3a - c?
(c) What is the value of ab?
(d) What is the value of b(a + c)?
(a) Simplify 2x + 5x.
2x is the same as x + x.
5x is the same as x + x + x + x + x.
Therefore, 2x + 5x must be the same as (x + x) + (x + x + x + x + x), which is 7x.
(b) Simplify 9y - 5y.
We have 9 lots of y and we are taking away 5 lots of y.
This will leave 4 lots of y, so 9y - 5y = 4y.
(c) Simplify 3a + 8b + 5a - 2b.
We can only collect together the terms which have the same letter (the like terms).
We have 3a and 5a which add together to make 8a.
We also have 8b and we are subtracting 2b, which will give 6b.
The 8a and 6b are added together to give 8a + 6b.
(a) Simplify 3p + 5q.
We can not combine these terms because they contain different letters.
Therefore, 3p + 5q is already simplified.
Simplify each expression below, and then click to see whether you are correct.
(a) Simplify 2x + 4x.
(b) Simplify 5p + 7q - 3p + 2q.
(c) Simplify y + 8y - 5y.
(d) Simplify 3t + 4s.
|We want to work out formulae for the area and perimeter of the rectangle.|
To find the area, we multiply the length (x) by the width (y).|
This is x × y which is the same as xy
The formula is Area = xy
To find the perimeter, we add up the lengths.|
This is x + y + x + y which is the same as 2x + 2y
The formula is Perimeter = 2x + 2y