The Algebra Tutor

Lesson #4
Removing Grouping Symbols

Lesson #4 introduces the distributive property to remove grouping symbols commonly known as parentheses. Previous techniques introduced in Lessons #1, #2, and #3 are integrated into this lesson to allow the student to solve more difficult problems involving several operations simultaneously. The student should be comfortable with previous lessons before attempting to use the distributive property.


QUESTIONS FOR THOUGHT AND FURTHER STUDY
1. If a negative is written outside a parentheses, what is implied?
2. What step is necessary first if a parentheses is in an equation?
3. What algebraic symbol indicates that distributive property must be used?
4. What step will be used next after eliminating the grouping symbol?
5. What is a common error that occurs using the distributive property?
6. What is the difference between consecutive integers and consecutive even or odd integers?
7. What formula is necessary to know when working with perimeter?
8. In problems involving age, what special set­up must be made?

ANSWERS:
1. (A negative one is present outside the () and
    must be distributed throughout the parentheses.)
2. (The distributive property must be used first to remove grouping symbols.)
3. (Parentheses)
4. (Combining like terms on both sides of the equation).
5. (The term outside the () is not distributed to every term in the ().
7. (P = 2 lengths + 2 widths).
8. (A box or chart must distinguish between ages
    at present for people and ages in the past and/or future for those same people).


STUDENT VOCABULARY
Consecutive Even/Odd Integers: (Whole numbers spaced by 2. e.g. x, x + 2, x + 4, :).

Consecutive Integers: (Whole numbers spaced by 1. e.g. x, x + 1,
x + 2, :).

Distributive Property: Property which allows grouping symbols known as parentheses to be removed. For any numbers a, b, c: a(b + c) = ab + ac.

Grouping Symbols: Parentheses ( ).

Least Common Denominator: The smallest common multiple of the denominators of two or more fractions.


PRACTICE PROBLEMS
  1. 3(x + 1) ­ 5 = 2x ­ 4

  2. 2(2d + 5 ) + 1 = 5 ­ 2( 3 ­ d )

  3. What properties are necessary in order to solve the problem 2x ­ 6 = 8, x = 7?

  4. 10(t ­ 3/5) = 8

  5. 8(x ­ 9) = ­ 8 (x + 5)

  6. Find three consecutive even integers whose sum is ­12.

  7. The lengths of the sides of a triangle are consecutive odd integers. The perimeter is 27. What are the lengths of the sides?

  8. Frank is 8 years older the Ralph. The sum of Frank's age and Ralph's age is 38. How old are Ralph and Frank?

  9. Marie is 6 years older than her sister Danielle. Their father's age is twice the sum of their ages. How old are both girls if the father is 32?
10. The length of a rectangle is 4 cm more than twice the width. The perimeter is 116 cm. What are the length and width of the rectangle?

11. Find three consecutive odd integers whose sum is 261.

12. ­8 ­ (9 ­ 4x) = 11

13. Tim's age is eight times Mary's age now. Three years ago Tim's age was 17 years more than 10 times Mary's age. How old is each now?

14. 8x ­ 1/3 x = 46

15. 7y + 9 = 3 (y + 3)

Answers:
  1. (x = ­2),  2. (d = ­ 6)
  3. (The addition and multiplication properties)
  4. (t = 7/5),  5. (x = 2)
  6. (­6, ­4 , and ­ 2),  7. (7, 9, and 11)
  8. (Ralph is 15 years old and Frank is 23 years old.)
  9. (Marie is 11 and Danielle is 5)
10. (Length is 40 cm and width is 18 cm)
11. (85, 87, 89),  12. (x = 7)
13. (Tim is 40 and Mary is 5)
14. (x = 6),  15. (y = 0)


COLLECT THE WHOLE SERIES
Volume 1
The Addition Property of Equality

Volume 2
The Multiplication Property of Equality

Volume 3
The Addition & Multiplication Property of Equality

Volume 4
Removing Grouping Symbols

Volume 5
Exponents & Properties of Exponents