Maths
STAGE 7: WORKBOOK
Expressions
You will practice how to:
• Understand that letters can be used to represent unknown numbers, variables or constants.
• Understand that a situation can be represented either in words or as an algebraic expression, and move between the two representations (linear with integer coefficients).
• Understand that the laws of arithmetic and order of operations apply to algebraic terms and expressions (four operations).
5.1 Letters for numbers
Summary of key points
In algebra, a letter is used to represent an unknown number or measurement (a variable).
An expression is a mathematical statement about a variable. For example, if you have a number, t, then add 5, you could write t + 5.
In t + 5, t and 5 are both terms in the expression. t is a variable and 5 is a constant term in the expression.
The expression 5f represents 5 × f. The 5 is called the coefficient of f
An equation is a mathematical statement where an expression is made equal to something. For example, t + 5 = 12. Equations can be solved to find the value of the unknown variable.
Exercise 1
1 Rewrite the number puzzles as equations by using a letter to represent the missing number.
= 100
2 Draw lines to match each statement to the correct algebraic expression.
‘I think of a number and add 7.’
‘I think of a number and multiply it by 7.’
‘I think of a number and subtract 7.’
‘I think of a number and divide it by 7.’
3 Use letters to represent the side lengths of these shapes.
4 Here are some statements.
c + 3 = 11 This is known as an equation.
f + g + 2 This involves two terms, f and g.
Tick the statements that are true.
A parcel has mass (m + 2) kg. This is an expression.
For the statements that are false, write the true statement.
Think about
5 Give examples to explain each of these algebraic words: variable, equation, expression and term.
5.2 Forming expressions
Summary of key points
Example
A shop sells these clothes. The price of the scarf is c dollars.
4c = 12
The coefficient of c is 12
2
The jumper costs twice as much as the scarf.
The trainers cost 10 dollars more than the jumper.
The price of the jumper can be written as 2c dollars.
An expression for the cost of the trainers is 2c + 10 dollars.
1 A shop sells boxes of crayons. Each box contains b crayons. Write down the number of crayons in each picture.
2 An apple costs a cents. A banana costs b cents. Write expressions for the cost of the fruit in each picture.
crayons
3 Nathan thinks of a number. Call his number n. Write an expression in terms of n for the result when you:
a) add 2 to Nathan’s number ………………..
b) subtract 4 from Nathan’s number ………………..
c) multiply Nathan’s number by 9 ………………..
d) multiply Nathan’s number by 4 and then add 1 ………………..
4 A pen costs p dollars. Write an expression in terms of p for the cost of 6 pens. …………… dollars
5 A hat costs h dollars. It is reduced by 4 dollars. Write an expression in terms of h for the new cost of the hat. …………… dollars
6 There are c cakes in a packet. A boy eats 3 cakes. Write an expression in terms of c for how many cakes are left. …………… cakes
7 Sheena has n badges. She shares them equally between her two children. Write an expression in terms of n for how many badges each child has. …………… badges
8 The cost of train tickets is:
Child ticket $c Adult ticket $a
What is the total cost of 5 child tickets and 2 adult tickets? $……………
9 Four people are talking about how old they are. Clara’s age is c years. Write an expression in terms of c for the age of all the other people.
Clara c years
Dimitri ‘I am two years older than Clara.’ …………… years
Eva ‘I am three times as old as Clara.’ …………… years
Faiyaz ‘I am six years younger than Eva.’ …………… years
10 Here is a triangle with side lengths as marked on the diagram.
Write an expression for the perimeter of the triangle.
The perimeter is the total distance around the edge of a shape.