Page 27 - Mathematics Coursebook

2.4 Constructing expressions

2.4 Constructing expressions

In algebra you can use a letter to represent an unknown number.
Example: n + 3 = 7
You can see that the
value of the letter n is 4 because: 4 + 3 = 7
So you can write: n = 4
To solve problems you sometimes have to use a letter to represent an unknown number.
Example: Here is a bag of sweets. You don’t know how many
sweets there are in the bag.
Let n represent the unknown number of sweets in the bag.
"ree sweets are taken out of the bag. n sweets
Now there are n − 3 sweets le# in the bag.

n − 3 is called an expression and the letter n is called the variable.
An expression can contain numbers and letters but not an equals sign. n – 3 sweets

Worked example 2.4

Mathew is x years old. David is 4 years older than Mathew. Adam is 2 years younger than
Mathew. Kathryn is 3 times older than Mathew. Ella is half Mathew’s age.
Write down an expression for each of their ages.

Mathew is x years old. This is the information you are given to start with.
David is x + 4 years old. You are told David is 4 years older than Mathew, so add 4 to x.
Adam is x − 2 years old. You are told Adam is 2 years younger than Mathew, so subtract 2 from x.
Kathryn is 3x years old. You are told Kathryn is 3 times as old as Mathew, so multiply 3 by x.
You write 3 × x as 3x. Always write the number before the letter.
Ella is x 2 years old. You are told Ella is half Mathew’s age, so divide x by 2.
x
You write x ÷ 2 as .
2

) Exercise 2.4

1 Avani has a bag that contains n counters.
Write an expression for the total number of counters she has in the bag when:
a she puts in 2 more b she takes 3 out.
2 The temperature on Tuesday was t °C.
Write an expression for the temperature when it is:
a 2 Celsius degrees higher than it was on Tuesday b twice as warm as it was on Tuesday.

26 2 Sequences, expressions and formulae