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Algebraic Expressions Introduction

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Algebraic Expressions Introduction

For each expression, identify its parts or translate the description into algebra. Use any letter you like for an unspecified number.

Recognising expression parts

1.In the expression 8p − 5, which symbol is the variable?

8
p
−5

2.In 8p − 5, what is the coefficient of p?

8
p
−5

3.In 8p − 5, identify the constant term.

8
p
−5

4.For 6r + 11, state the variable, its coefficient, and the constant term.

5.For 5u + 2v − 9, list both variables, each variable's coefficient, and the constant term.

6.For 14 − 4q, state the variable, its coefficient, and the constant term.

Translating descriptions into expressions

7.Write an algebraic expression for nine multiplied by an unknown number.

8.Write an expression for an unknown number reduced by 13.

9.Write an expression for four less than three times an unknown number.

10.Write an expression for the sum of an unknown number and seven times that number.

11.At a kite festival, Mele buys k ribbons costing $3.20 each. Write an expression for her total ribbon cost in dollars.

12.At the kite festival, Ruben walks d kilometres to the field and then travels another 18 kilometres by bus. Write an expression for the total distance in kilometres.

13.A kite-festival afternoon begins at t degrees Celsius, then the temperature falls by 6 degrees. Write an expression for the later temperature.

14.Oliver buys h kite-festival snacks at $4.75 each and pays a one-off $2.50 service fee. Write an expression for his total cost in dollars.

Match each phrase to an expression

Use each expression once.

Check your understanding

15.Which of these are algebraic expressions? Select all that apply.

4x − 3
21
7p + 2 = 16
3a − 5b
m = 12
9 − 2n

16.True or false: In the term −11z, the coefficient of z is −11.

TrueFalse

17.True or false: In 6a + b, the coefficient of b is 1.

TrueFalse

18.True or false: In 2x + 5, the value of the constant term changes whenever x changes.

TrueFalse

19.In your own words, distinguish a variable, a coefficient and a constant term in an algebraic expression.

20.Create an expression containing the variable r, a coefficient of −3 and a constant term of 8. Label the variable, coefficient and constant.

21.At a kite festival, Mele starts with m dollars. She spends $9 on lunch, then earns an amount equal to twice the money she started with. Write and simplify an expression for how much money she has afterwards.