Write expressions from words and shapes, and substitute positive and negative numbers into them.
What you will learn
- Read and write algebraic notation
- Turn words into an expression
- Substitute numbers, including negatives
The notation
A letter stands for a number.
An expression is a mix of numbers and letters with no equals sign, such as 2n + 5. Its terms are the parts joined by + or −: 2n and 5. The number in front of a letter is its coefficient: in 2n the coefficient is 2.
- 3a means 3 × a; ab means a × b; t + t + t = 3t.
- a² means a × a, and 3a² means 3 × a × a (only the a is squared). (3a)² is 9a².
- a/b means a ÷ b.
"5 more than twice n" is 2n + 5. "Twice the sum of n and 5" is 2(n + 5): the brackets show what happens first. "4 less than k squared" is k² − 4.
Pencils at 45p and pens at 120p: the cost in pence of a pencils and b pens is 45a + 120b.
The perimeter of a shape is the distance all the way round: add every side. A rectangle 2x + 1 by x + 4 has perimeter 2(2x + 1) + 2(x + 4) = 4x + 2 + 2x + 8 = 6x + 10. (Collecting the x parts and the number parts together is in the next lesson.)
The rest of this lesson and its 7 practice questions are locked.
In this lesson
- The notation
- Substituting
- Try it: Check a substitution
7 practice questions, marked as you go; about 20 minutes in all.
Key terms
Expression, Terms, Perimeter
In this unit: Algebraic expressions
The language of algebra: writing and substituting into expressions, simplifying, expanding brackets, factorising, and telling expressions, equations, formulae and identities apart.