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9.2 Constructing algebraic expressions

9.2 Constructing algebraic expressions

In algebraic expressions, letters represent unknown numbers.
You o$en need to construct algebraic expressions to help you solve problems.
Suppose you want to work out the price of tickets for a day out. You might choose to let a represent the
price of an adult’s ticket and c represent the price of a child’s ticket.
You can write the total price for an adult’s ticket and a child’s ticket as a + c.
You can write the di%erence between the price of an adult’s ticket and a child’s ticket as a − c.
You can write the total price of tickets for 2 adults and 2 children as 2(a + c) or 2a + 2c.
!ese expressions are written in terms of a and c.

Worked example 9.2
a Ahmad thinks of a number, n. Write down an expression, in terms of n, for the number Ahmad gets
when he:
i doubles the number then adds 5
ii divides the number by 3 then subtracts 6
iii adds 3 to the number then multiplies the result by 4
iv multiplies the number by itself then halves the result.
b Write an expression in terms of x and y for: 5x
i the perimeter ii the area of this rectangle. 2y
Write each expression in its simplest form.

a i 2n + 5 Multiply n by 2, then add 5. Write 2 × n as 2n.
n
ii n − 6 Divide n by 3 then subtract 2. Write n ÷ 3 as .
3
3
iii 4(n + 3) Add 3 to n, then multiply the result by 4. Write n + 3 inside a pair
of brackets to show this must be done before multiplying by 4.
2
iv n 2 Multiply n by itself, to give n × n, and write it as n . Write n ÷ 2
2
2 2
as n .
2
b i Perimeter = 5x + 2y + 5x + 2y Add together the lengths of the four sides to work out the perimeter.
= 10x + 4y Simplify the expression by collecting like terms.
ii Area = 5x × 2y Multiply the length by the width to work out the area.
= 10xy Simplify the expression by multiplying the numbers and the letters
together.

) Exercise 9.2

1 Xavier thinks of a number, n.
Write an expression, in terms of n, for the number Xavier gets when he:
a multiplies the number by 7 b adds 12 to the number
c subtracts 2 from the number d subtracts the number from 20
e multiplies the number by 2 then adds 9 f divides the number by 2
g divides the number by 6 then subtracts 4 h multiplies the number by itself
i divides 100 by the number j multiplies the number by 2 then subtracts 1
k adds 2 to the number then multiplies l subtracts 7 from the number then multiplies
the result by 5 the result by 8

86 9 Expressions and formulae