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Algebraic Expressions Introduction

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Algebraic Expressions Introduction

Read each prompt carefully. Use algebraic notation where asked, and show clear reasoning for the explanation questions.

Recognising expression parts

Identify the variable, coefficient and constant in each expression.

1.In 8r + 6, which symbol is the variable?

2.In 8r + 6, what is the coefficient of r?

3.In 8r + 6, identify the constant term.

4.For the expression 9p − 4, state the variable, coefficient and constant term.

5.For 5u + 2v − 11, list every variable, its coefficient, and the constant term.

Writing expressions

Translate each phrase or situation into an algebraic expression. Use the variable given.

6.Write an expression for seven times a number n.

7.Write an expression for a number k increased by twelve.

8.Write an expression for four less than three times a number a.

9.Write an expression for a number m divided by five, then increased by two.

10.A packet contains x stickers. Write an expression for the number of stickers in six identical packets.

11.A bus fare is $3.50 per ride. Write an expression for the cost of r rides, in dollars.

12.A tank holds w litres of water. After 9 litres are drained, how many litres remain? Write an expression.

13.A temperature is h degrees Celsius. Write an expression for the temperature after it rises by 6°C.

Match each phrase

Match each description to the expression that represents it.

14.Match each verbal phrase to its algebraic expression.

Twice a number q, then subtract 5
A number q increased by 9
One third of q
Four times q, then add 3
q decreased by 8

q − 8
4q + 3
2q − 5
q + 9
q/3

Algebraic notation

Use standard algebraic conventions: omit the multiplication sign and write numerical coefficients before variables.

15.Rewrite 6 × z using standard algebraic notation.

16.Rewrite 2 × c × d using standard algebraic notation.

17.Rewrite 5 × a + 3 × b using standard algebraic notation.

18.Rewrite 1 × t − 4 using standard algebraic notation.

19.Select all expressions written in standard algebraic notation.

7m
4 × n
3a + 2b
6 * p
x − 10

Explain and apply

Use precise mathematical language and show how the expression represents the situation.

20.Explain how a variable, a coefficient and a constant differ. Use 4x + 9 as an example.

21.For the expression 7s − 3, label the variable, coefficient and constant term.

22.Hana buys p pencils at $1.80 each and b books at $6 each. A $4 delivery charge is added. Write an expression for the total cost in dollars.

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More Maths Worksheets

Year 7–8

Algebraic Expressions Introduction

Algebraic Expressions Introduction

Recognising expression parts

Writing expressions

Match each phrase

Algebraic notation

Explain and apply

4 printable pages

About This Worksheet

Free in Kuraplan

Print-Ready

AI-Generated

For Teachers & Parents

Need a custom version of this worksheet?

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