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Arithmetic Laws of indices BIDMAS Collecting like terms How to work out perimeter Area Angle rulesThis topic is relevant for:
Here we will learn about algebraic notation, including writing expressions and forming equations.
There are also worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.
Algebraic notation is a system for writing mathematical expressions and equations using letters, symbols, and operations.
It can be used to solve problems posed in worded form or added to the annotation of a diagram in geometrical problems to make a solution easier to find. Writing expressions using algebraic notation is a skill vital for GCSE Mathematics.
To do this we must first understand how to convert a mathematical expression in word form into algebraic notation. We need to know how to apply algebraic notation to the operations of addition, subtraction, multiplication and division.
The phrase “ more than ” can be written as
“ less than ” can be written as
“ less than ” can be written as
In algebra, when numbers and letters are written next to each other it indicates that they are multiplied together.
For example,
We write as
Multiplication is commutative so is the same as but that does not mean we write When using algebraic notation for multiplication we always put the numerical coefficient before the letter.
When letters, or numbers and letters, are being divided, they are written in fraction form.
For example,
would be written in algebraic notation as
So if we had a problem that said the length of a rectangle is one more than times the width. We could write where is the length and is the width.
Algebraic notation is used across mathematics and science. In GCSE Mathematics and GCSE Science you will see many algebraic expressions and formulae.
Across both subjects you will use algebraic notation when plotting graphs, solving equations, inequalities, expanding brackets, factorising, simplifying expressions or algebraic fractions.
In order to use algebraic notation:
Get your free algebraic notation worksheet of 20+ simplifying expressions questions and answers. Includes reasoning and applied questions.
DOWNLOAD FREEGet your free algebraic notation worksheet of 20+ simplifying expressions questions and answers. Includes reasoning and applied questions.
DOWNLOAD FREEA triangle has side lengths of and
Write an expression for the perimeter of the triangle.
The perimeter of a shape is found by finding the sum of the sides. We need to add the side lengths together.
2Use letters to represent any variables.
We already have been told that the variable is called
3Write the expression with any multiplications without the multiplication symbol and divisions as fractions.
There are no multiplications or divisions, just additions.
4Collect any like terms.
We can collect the and to give the perimeter as
Sally is tall. Her little brother Peter is shorter than Sally. Peter is tall.
Write an expression for the difference in their heights.
Read the worded phrase to identify the mathematical operations.
The difference in their heights is found by subtracting Peter’s height from Sally’s height.
Use letters to represent any variables.
We already have been told that Sally’s height is the variable
Write the expression with any multiplications without the multiplication symbol and divisions as fractions.
There are no multiplications or divisions, just a subtraction. Because Sally is taller than Peter, we need to subtract Peter’s height from Sally’s height.
Collect any like terms.
There are no like terms to collect.
The difference in their heights is
A rectangle has a length of and a width of
Write an expression for the area of the rectangle.
Read the worded phrase to identify the mathematical operations.
The area of a rectangle is found by multiplying the length by the width.
Use letters to represent any variables.
We already have been told that the variable is called
Write the expression with any multiplications without the multiplication symbol and divisions as fractions.
We need to do
This is written with the number first without the multiplication symbol,
Collect any like terms.
There are no like terms to collect.
The area of the rectangle is
Amrit has a bag of counters. He knows one quarter of the counters are blue counters in the bag but does not know how many counters there are in total.
Write an expression for the number of blue counters.
Read the worded phrase to identify the mathematical operations.
The number of blue counters will be the number of counters divided by
Use letters to represent any variables.
We have not been given a letter to represent the total number of counters so let’s call this variable
Write the expression with any multiplications without the multiplication symbol and divisions as fractions.
There is a division so we will write this as a fraction. is being divided by
So will be the numerator and will be the denominator.
Collect any like terms.
There are no like terms to collect.
The number of blue counters is
A triangle has three angles. The middle sized angle is more than the smallest angle. The largest angle is less than double the smallest angle.
Form an equation that could be used to find the size of the smallest angle.
Read the worded phrase to identify the mathematical operations.
The sum of the angles in a triangle is Therefore, we have to add the three angles together. The largest angle is less than double the smallest angle, therefore there is a multiplication and a subtraction.
Use letters to represent any variables.
We have not been given a letter to represent the size of the smallest angle, let’s call this variable
Write the expression with any multiplications without the multiplication symbol and divisions as fractions.
The smallest angle is
The middle angle is
The largest angle is
We need the sum of these terms which is equal to
Collect any like terms.
We can collect like terms to give
This equation can be solved to give
The smallest angle of the triangle is
The middle angle of the triangle is
The largest angle of the triangle is
To find the original price of an item in a sale, we can divide the sale price by the percentage remaining if written as a decimal or fraction.
Write a formula to find the original price of an item in a sale with a sale price
Read the worded phrase to identify the mathematical operations.
The formula will involve a division.
Use letters to represent any variables.
We have been given the variables and
Write the expression with any multiplications without the multiplication symbol and divisions as fractions.
To get the percentage remaining as a decimal or fraction we need to first subtract from , and then divide by
This will be written as
We then need to divide by this fraction.
is the the same as
This can be written as
Collect any like terms.
There are no term to collect but we need to finish writing the formula with as the subject.
It is important to write as and not
A common error is to write as when it should be
less than is and not
1. Write “ more than ” using algebraic notation.
“ more” involves adding so we add onto to make the expression
2. Write “ less than ” using algebraic notation.
“ less” involves subtracting so we subtract from to make the expression
3. Write “ less than ” using algebraic notation.
“ less” involves subtracting so we subtract from to make the expression
4. Write “ less than times ” using algebraic notation.
“ times ” is written as “ less” means subtracting so we subtract from to make the expression
5. A rectangle has a length which is less than times its width. Write an expression for the perimeter of the rectangle.
Let be the width of the rectangle.
The length of the rectangle will be
The perimeter will be the sum of all sides of the rectangle,
Collecting the like terms will simplify this expression to
6. The price of apples and bananas is The price of apples and bananas is Write this information as a pair of simultaneous equations where is the cost of one apple and is the cost of one banana.
The first piece of information can be written as
The second piece of information can be written as
These can be solved as simultaneous equations to give and
This means that the cost of one apple is and the cost of one banana is also
1. Each small square on a chessboard used in a chess game has a side length of
(a) Write an expression for the perimeter of the chessboard.
(b) Write an expression for the area of the chessboard.
(4 marks)
(a)
Side length
(1)
Perimeter
(1)
(b)
(1)
(1)
2. The width of a rectangle is less than half its length.
(a) Write an expression for the perimeter of the rectangle if its length is
(b) Given that the perimeter of the rectangle is find its area.
(7 marks)
(a)
(1)
(1)
(1)
(b)
(1)
(1)
(1)
(1)
3. To give the correct dose of a medicine (in ) to a child, the following steps must be taken.
Divide the child’s mass (in ) by then add
Write a formula for the dose, of a child of mass,
(3 marks)
(1)
(1)
(1)
You have now learned how to:
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