The Algebra Tutor

Lesson #2
Multiplication Property of Equality

Lesson 2 extends the solutions of equations to include the multiplication and division property of equality. The emphasis is on solutions of equations in the form of x * a = b where a and b are real numbers. This lesson includes the explanation of  reciprocal numbers and their use in solving equations. Algebraic equations and word problems are introduced using this property. Remember the symbol "*" is often used in place of "x" for multiplication to avoid confusion with "x" as a variable.


STUDENT VOCABULARY
Variable: A term used in a mathematical equation to represent an unknown number.

Reciprocal: A reciprocal of number is its multiplicative inverse. The product of a number and its reciprocal always equals 1. e.g. 1/2 * 2/1 = 1, (­3/2) (­2/3) = 1.

Mixed Fraction: A number which has both a whole number and fraction. e.g. 3 1/2, 4 3/5

Improper Fraction: A number containing a numerator larger than the denominator. e.g. 5/3, 15/11.

Coefficient: The number part of an algebraic term. In the term 3x, 3 is the coefficient.

Positive Number : A number greater than zero.

Negative Number: A number less than zero.

Integer: A whole number that can be either positive or negative.

Product: The result of multiplication e.g. 5*2 = 10. 10 is the product.


QUESTIONS FOR THOUGHT AND FURTHER STUDY
1. What is the only number that may not be used in the denominator of a fraction?

2. How is the variable isolated in an equation involving multiplication?

3. When a number is multiplied by its reciprocal what is the result?

4. If a coefficient is a mixed fraction what is the easiest method to solve for the variable?

5. What four terms used in word problems indicate the operations of multiplication and division?

6. If the coefficient of a term is an integer what is the easiest method of isolating the variable?


STUDY QUESTION ANSWERS:
1. (Zero)

2. (Each side is multiplied by the reciprocal     of the coefficient.)

3. (1)

4. (Change mixed fraction to improper     fraction and multiply by the reciprocal)

5. (Product, times, quotient, multiply)

6. (Divide by the number.)


PRACTICE PROBLEMS
  1. 3x = 9
  2. 2x = 5
  3. 1/2 x = ­4
  4. 3/2 x = 6
  5. 4x = 1/6
  6. ­3x = ­1/9
  7. 1.2 x = 4.2
  8. 3.6 x = 9
  9. 5 1/2 x = 10
10. 4 1/3 x = 2/3

Practice Word Problems
1. Eight times what number is 128?

2. A stock boy is paid $8.00 an hour. If he was paid $320.00 for a week, how many hours did he work?

3. A number multiplied by 6 is 1/2. What is the number?

4. A concert has two prices for tickets. The loge seats are $50.00 each and the balcony seats are $25.00 each. If the theater has 1200 loge seats and 1500 balcony seats, how much money can be made on a sold out house?

5. John read half as much as David. If John read 325 pages over one week, how many pages did David read?


ANSWERS to STUDY QUESTIONS & PRACTICE PROBLEMS
Practice Problem Answers:
  1. (x = 3)
  2. (x = 2.5)
  3. (x = ­8)
  4. (x = 4)
  5. (x = 1/24)
  6. (x = 1/27)
  7. (x = 3.5)
  8. (x = 2.5)
  9. (x = 20/11)
10. (x = 2/13)

Practice Word Problem Answers:
  1. (8x = 128, x = 16.)
  2. ($8.00 x = $320.00, x = 40 hours)
  3. (6x = 1/2, x = 1/12)
  4. ($50.00(1200) + $25.00(1500) = x,       x = $60,000 + $37,500, x = $97,500)
  5. (1/2 x = 325, x = 650 pages)


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