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Algebraic Expressions Basics

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Algebraic Expressions Basics

Identify parts of expressions, collect like terms and write expressions for situations. Show working where useful.

Recognising Parts and Like Terms

1.For the expression 8p + 11, name the variable, the coefficient and the constant.

2.In 12k − 7, which number is the coefficient of k?

−7
1
7
12

3.Select every pair of like terms.

4r and −9r
3b and 3c
8 and −2
5mn and 5m

4.How many terms are in the expression 6u − 2v + 9 − 3u?

5.Match each algebra word to its description.

Variable
Coefficient
Constant
Term

A number multiplying a variable
A fixed number with no variable attached
A part of an expression separated by + or − signs
A letter that represents a number

Simplifying Expressions

6.Simplify 7x + 6x.

7.Simplify 10y − 4y + 3.

8.Simplify 3a + 8 − 5 + 4a.

9.Simplify 11m − 6m + 2n + 5n.

10.Simplify 4q + 2 − q + 9.

Using Expressions in Context

11.At a library makerspace, Harper has x packs of modelling pieces. Each pack contains 4 pieces. Write an expression for the total number of pieces Harper has.

12.Grace has c circuit boards for a makerspace project. Arjun has twice as many boards as Grace, plus 6 more. Write a simplified expression for the number of boards Arjun has.

13.A makerspace room is t°C at opening. Its temperature rises by 5°C, then later falls by 2°C. Write a simplified expression for the temperature after both changes.

14.In your own words, explain one reason why combining like terms can be useful.