10.6 Multiplication and division of signed numbers

Fundamentals of mathematics Page 1 / 1

This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module discusses how to multiply and divide signed numbers. By the end of the module students should be able to multiply and divide signed numbers and be able to multiply and divide signed numbers using a calculator.

Section overview

Multiplication of Signed Numbers
Division of Signed Numbers
Calculators

Multiplication of signed numbers

Let us consider first, the product of two positive numbers. Multiply: $3 \cdot 5$ .

$3 \cdot 5$ means $5 + 5 + 5 = 15$

This suggests In later mathematics courses, the word "suggests" turns into the word "proof." One example does not prove a claim. Mathematical proofs are constructed to validate a claim for all possible cases. that

$(positive number) \cdot (positive number) = (positive number)$

More briefly,

$(+) (+) = (+)$

Now consider the product of a positive number and a negative number. Multiply: $(3) (- 5)$ .

$(3) (- 5)$ means $(- 5) + (- 5) + (- 5) = - 15$

This suggests that

$(positive number) \cdot (negative number) = (negative number)$

More briefly,

$(+) (-) = (-)$

By the commutative property of multiplication, we get

$(negative number) \cdot (positive number) = (negative number)$

More briefly,

$(-) (+) = (-)$

The sign of the product of two negative numbers can be suggested after observing the following illustration.

Multiply -2 by, respectively, 4, 3, 2, 1, 0, -1, -2, -3, -4.

We have the following rules for multiplying signed numbers.

Rules for multiplying signed numbers

Multiplying signed numbers:

To multiply two real numbers that have the same sign , multiply their absolute values. The product is positive.
$(+) (+) = (+)$
$(-) (-) = (+)$
To multiply two real numbers that have opposite signs , multiply their absolute values. The product is negative.
$(+) (-) = (-)$
$(-) (+) = (-)$

Sample set a

Find the following products.

$8 \cdot 6$

$(\begin{matrix} | 8 | & = & 8 \\ | 6 | & = & 6 \end{matrix}\}$ Multiply these absolute values.

$8 \cdot 6 = 48$

Since the numbers have the same sign, the product is positive.

Thus, $8 \cdot 6 =+ 48$ , or $8 \cdot 6 = 48$ .

		Display Reads
Type	186	186
Press		-186
Press	×	-186
Type	43	43
Press		-43
Press	=	7998

		Display Reads
Type	158.64	158.64
Press	÷	158.64
Type	54.3	54.3
Press		-54.3
Press	=	-2.921546961

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10.6 Multiplication and division of signed numbers

Section overview

Multiplication of signed numbers

Rules for multiplying signed numbers

Sample set a

Practice set a

Division of signed numbers

( + ) ( + ) = ( + ) size 12{ { { \( + \) } over { \( + \) } } = \( + \) } {}

( + ) ( − ) = ( − ) size 12{ { { \( + \) } over { \( - \) } } = \( - \) } {}

( − ) ( + ) = ( − ) size 12{ { { \( - \) } over { \( + \) } } = \( - \) } {}

( − ) ( − ) = ( + ) size 12{ { { \( - \) } over { \( - \) } } = \( + \) } {}

Rules for dividing signed numbers

Sample set b

Practice set b

Sample set c

Practice set c

Calculators

Sample set d

Practice set d

Exercises

Exercises for review

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$\frac{(+)}{(+)} = (+)$

$\frac{(+)}{(-)} = (-)$

$\frac{(-)}{(+)} = (-)$

$\frac{(-)}{(-)} = (+)$