Algebra
Grade 1-3Algebraic Notation & Vocabulary
Every algebra topic builds on being able to read and write algebraic notation fluently, translate a worded statement into an expression, and know the difference between a term, an expression, an equation, a formula and an identity. This lesson covers writing expressions from words, substituting values into an expression, key algebra vocabulary, and writing a formula from a real-world context.
What you need to know
- 3a means 3 times a; a b means a times b; a squared means a times a.
- Write terms without multiplication signs, and put the number before the letter (3a, not a3).
- a over b means a divided by b; a term is a part of an expression separated by plus or minus.
- An expression has no equals sign; an equation does.
Written by Asad, co-founder of Teachably
Video walkthrough coming soon
The written lesson below covers everything you need in the meantime.
Writing expressions from words
Translate each part of a worded statement into algebra one piece at a time. "More than" and "sum" suggest addition, "less than" suggests subtraction with the order reversed, "multiplied by" suggests writing the number directly next to the letter, and "divided by" suggests a fraction.
"4 more than n" is written as n + 4, and "6 less than y" is written as y − 6, since the 6 is subtracted from y.
Substituting values into an expression
Replace each letter with its given value, keeping any multiplication between the number and the letter, then work out the calculation following the order of operations.
To find the value of 3a + 2 when a = 4, substitute to get 3(4) + 2, which works out to 12 + 2 = 14.
Key algebra vocabulary
A term is a single part of an expression, such as 4a or 7, separated by + or − signs. The coefficient is the number in front of a letter. An expression has no equals sign, an equation is true for specific values only, a formula shows the relationship between different quantities, and an identity is true for every possible value of the letter.
In 4a + 2b − 7, there are three terms: 4a, 2b and −7. The statement 2(x + 3) ≡ 2x + 6 is an identity, since it is true for every value of x, while 3x + 7 = 22 is an equation, true only when x = 5.
Writing a formula from a real-world context
Identify the fixed part of the cost or quantity and the part that changes with a variable, then combine them using the appropriate operation.
A taxi charges a £3 fixed fee plus £2 per mile. For a journey of m miles, the total cost is the fixed fee plus £2 for each mile, giving the formula C = 3 + 2m.
Worked examples
Three exam-style questions, fully solved
Write an expression for 4 more than n.
Easy- 1.Identify that "more than" means addition, and add 4 to n
Answer: n + 4
Work out the value of 3a + 2 when a = 4.
Medium- 1.Substitute a = 4 into the expression: 3(4) + 2
- 2.Work out the multiplication first: 12 + 2
Answer: 14
A taxi charges a £3 fixed fee plus £2 per mile. Write a formula for the total cost C, in pounds, for a journey of m miles.
Hard- 1.Identify the fixed part of the cost: £3
- 2.Identify the part that depends on the number of miles: £2 per mile, or 2m
- 3.Combine the fixed fee and the per-mile cost: C = 3 + 2m
Answer: C = 3 + 2m
Practice
6 questions, marked instantly
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Practice
Now try these yourself.
Type your answer and check it. The worked solution appears once you have had a go.
Write an expression for 5 more than n.
Write an expression for 7 less than y.
Work out the value of 4a − 3 when a = 5.
Work out the value of 2x + 3y when x = 4 and y = 2.
A plumber charges a £40 call-out fee plus £30 for each hour worked. Write a formula for the total cost C, in pounds, for a job lasting h hours.
Write c × c × c × c as a single power.
Avoid these
The mistakes students make most often
Writing "less than" or "more than" statements in the wrong order, such as writing 6 − y instead of y − 6 for "6 less than y".
Forgetting the order of operations when substituting into an expression, especially when a coefficient needs to be multiplied before adding or subtracting.
Miscounting the number of terms in an expression, especially when it includes both addition and subtraction, or confusing a term with a factor.
Leaving repeated multiplication as it is instead of writing it as a single power, such as leaving c × c × c × c × c instead of writing c⁵.
Confusing the vocabulary, such as calling a formula an equation, or not recognising an identity when both sides are always equal for every value of the letter.
FAQ
Questions students and parents ask
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