Names: ___________________________________________________________________________ Date: _____________
Group Worksheet: Discovering Rules for Multiplying Positive and Negative Numbers
Answer Key
1. You want to purchase a gift for three of your friends. While at the mall you find a gift for $7 and
decide to buy the same gift for each friend. How does the store’s revenue change after this
transaction?
a. Multiplication Equation (with variable): 3(7) = x
b. Multiplication Equation (with solution): 3(7) = 21
c. Multiplication Equation the second factor decomposed into a negative plus a positive
addend: Answers will vary. One possible example: 3(-2 + 9) = 21
d. Rewritten equation with the distributive property: 3(-2) + 3(9) = 21
e. The two positive factors and their product. 3(9) = 27
f. Partially solved distributive property equation: 3(-2) + 27 = 21
g. Based on the equation above, what must be the product of the positive and negative
factor? 3(-2) must equal -6 to make the equation true.
2. Francine played 6 words in Scrabble that scored 18 points each. How change did these words
make in her score?
a. Multiplication Equation (with variable): 6(18) = x
b. Multiplication Equation (with solution): 6(18) = 108
c. Multiplication Equation the second factor decomposed into a positive plus a negative
addend: Answers will vary. One possible example: 6(25+ (-7)) = 108
d. Rewritten equation with the distributive property: 6(25) + 6(-7) = 108
e. The two positive factors and their product. 6(25) = 150
f. Partially solved distributive property equation: 150 + 6(-7) = 108
g. Based on the equation above, what must be the product of the positive times negative
factor? 6(-7) = -42
3. Please use the problems you solved above to answer the following items.
a. Based on your work above, what is always true about the product of a positive factor
multiplied by a positive factor? A positive times a positive equals a positive.
b. Based on your work above, what is always true about the product of a positive factor
multiplied by a negative factor? A positive times a negative equals a negative.
c. By applying the commutative property of multiplication to what you learned in 3b, what
must the answer always be for a negative factor times a positive factor? A negative
times a positive equals a negative.
4. A thief was discovered selling stolen pumpkins at a local marked for $5 each. He had already
sold 3 pumpkins when the police caught him and returned the money to the rightful owner.
What was the change in the thief’s profits after the money was returned to the rightful owner?
a. Multiplication Equation (with variable): -3(5) = x
b. Multiplication Equation (with solution): -3(5) = -15
c. Multiplication Equation the second factor decomposed into a positive plus a negative
addend: Answers will vary. One possible example: -3(16 + (-11)) = -15
d. Rewritten equation with the distributive property: -3(16) + -3(-11) = -15
e. The negative factor times the positive factor and their product? -3(16) = -48
f. Partially solved distributive property equation: -48 + -3(-11) = -15
g. What must be the product of the negative factor times the negative factor?
-3(-11) = 33 OR +33
Names: ___________________________________________________________________________ Date: _____________
5. A football team had two touchdowns called back because of penalties. If each touchdown is
worth six points, what was the effect of these penalties on the team’s final score?
a. Multiplication Equation (with variable): -2(6) = x
b. Multiplication Equation (with solution): -2(6) = -12
c. Multiplication Equation the second factor decomposed into a negative plus a positive
addend: Answers will vary. One possible example: -2((-8) +14) = -12
d. Rewritten equation with the distributive property: -2(-8) + -2(14) = -12
e. The negative factor times the positive factor and their product? -2(14) = -28
f. Partially solved distributive property equation: -2(-8) + -28 = -12
g. What must be the product of the negative factor times the negative factor?
-2(-8) = 16 OR +16
6. Please complete the table below to create a record of what you have learned so far about
multiplying positive and negative numbers.
a.
b.
c.
d.
7.
Factor 1
Positive
Positive
Negative
Negative
Factor 2
Positive
Negative
Positive
Negative
Sign of the Product
Positive
Negative
Negative
Positive
Based on what you have learned above, please write a rule statement that tells the outcome of
multiplying factors that have the same sign and the outcome of multiplying factors that have
different signs.
When you multiply factors with the same sign (positive * positive or negative * negative), the
product will always be positive.
When you multiply factors with different signs (positive * negative or negative * positive), the
product will always be negative.