Introduction to Algebraic Notation
Algebraic notation is the set of writing conventions used whenever letters stand for unknown or variable numbers. Multiplication signs are dropped (3 x a is written 3a, always with the number before the letter), repeated multiplication of the same letter is written using powers (a x a = a^2), and division is written as a fraction (a divided by 4 is a/4).
Before you start
No specific prerequisites - this is a good place to start.
Method
- Understand that a letter stands for an unknown or variable number, not a fixed value.
- Write multiplication without the x sign: 3 x a becomes 3a, with the number always written before the letter.
- Write repeated multiplication of the same letter using powers: a x a = a^2, and a x a x a = a^3.
- Write division using a fraction bar instead of a division sign: a divided by 4 becomes a/4.
- Know the difference between a term (e.g. 5x), an expression (e.g. 5x + 3, no equals sign), an equation (contains an equals sign), and a formula (links two or more different letters).
- Identify the coefficient (the number multiplying a letter) and the constant term (a number with no letter attached) in an expression.
Worked example
Write the following using correct algebraic notation: 'multiply n by 5, then add 4', and identify the coefficient and the constant term in your answer.
- 'Multiply n by 5' is written as 5n, with the number placed before the letter and no multiplication sign.
- 'Then add 4' appends + 4 to give the expression 5n + 4.
- In 5n + 4, the coefficient of n is 5, the number multiplying the letter n.
- In 5n + 4, the constant term is 4, the number with no letter attached.
Practice questions
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Q1Write 'p multiplied by 7' using correct algebraic notation.Show answer
Answer: 7p
Q2Write 'y multiplied by itself' using correct algebraic notation.Show answer
Answer: y^2
Q3Write 't divided by 6' using correct algebraic notation.Show answer
Answer: t/6
Q4Write 4 x a x a x b using correct algebraic notation.Show answer
Answer: 4a^2b (a x a becomes a^2, and the number is written first)
Q5State the coefficient of x in the expression 9x - 2.Show answer
Answer: 9
Q6State the constant term in the expression 3x + 11.Show answer
Answer: 11
Q7Is 3x + 7 = 22 a term, an expression, or an equation? Explain your answer.Show answer
Answer: An equation, because it contains an equals sign linking two sides that are equal.
Exam-style questions
Written in the style of a KS3 Maths exam paper, with a full mark scheme.
Write each of the following using correct algebraic notation: (a) k multiplied by 8, (b) w multiplied by itself three times, (c) m divided by 5, all added to 2.
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The expression 6x^2 - 4x + 9 has three terms. (a) State the coefficient of x^2. (b) State the coefficient of x. (c) State the constant term.
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Free printable worksheet
Want more practice on paper? Download the introduction to algebraic notation worksheet pack - 7 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 19 of KS3 Maths Workbook 1, the whole course as one free printable PDF.
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