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Algebraic Notation Practice

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Algebraic Notation Practice

Write expressions using standard algebraic notation. Show brackets where needed to make the meaning clear.

Writing and reading expressions

1.Rewrite 6 × p using standard algebraic notation.

2.Write 4 × q × 3 without multiplication signs, simplifying the numerical factors.

3.Rewrite r × s × 5 using standard algebraic notation.

4.Rewrite 8 × a + 3 × b using standard algebraic notation.

5.Write an algebraic expression for twice n, then add 9.

6.Write an expression for 11 less than three times k.

7.Write an expression for the sum of five times u and twice v.

8.Write an expression for the result of dividing 18 by x, then subtracting 4.

Parts of an expression

Expression: 6x - 2y + 7

Terms: 6x, -2y, 7

Coefficients: 6 and -2; constant: 7

9.For 9a - 4b + 6, state the coefficient of a.

10.For 9a - 4b + 6, state the coefficient of b.

11.For 9a - 4b + 6, identify the constant term.

12.For 9a - 4b + 6, list the variables.

13.How many terms are in 9a - 4b + 6?

14.In the term -7m, what is the coefficient?

15.In the term 13cd, what is the numerical coefficient?

16.What is the implied coefficient of t in the term t?

Check your understanding

17.True or false: 5p means 5 multiplied by p.

TrueFalse

18.True or false: mn means m plus n.

TrueFalse

19.True or false: 12 + r has the same value as r + 12.

TrueFalse

20.True or false: 4z + 6z simplifies to 10z.

TrueFalse

21.True or false: the coefficient of -w is -1.

TrueFalse

Fixing and matching notation

22.Rewrite 3 × h × j using standard algebraic notation.

23.Remove the stray × from 5 + × 2.

24.Rewrite 4a × 3b using standard algebraic notation and simplify the numerical factors.

25.Rewrite z × 1 in its simplest form.

26.Match each description to its expression: triple x; x increased by 8; 8 divided by x; x reduced by 8.

Triple x
x increased by 8
8 divided by x
x reduced by 8

8/x
3x
x - 8
x + 8

Algebra in everyday situations

27.A pear costs $3. Write an expression for the cost of p pears.

28.Tevita is 4 years younger than her brother, whose age is b. Write an expression for Tevita's age.

29.A rectangle has length L and width W. Write an expression for its perimeter.

30.Each of n notebooks costs $7, and delivery costs $5. Write an expression for the total cost in dollars.

31.A streaming subscription costs $18 each month, plus $0.25 for every extra download. If d is the number of extra downloads, write an expression for the monthly cost in dollars.

Explain and apply

32.Explain one reason algebra usually writes 4x rather than 4 × x.

33.Write an expression with exactly three terms that uses the variable c and has a constant term of 4. Then state its coefficients and its constant term.