Multiplication and division of directed numbers - Examples, Exercises and Solutions

The method to solve an exercise with real numbers, when it involves multiplication and division, is very similar to the one we use when we have to add or subtract real numbers, with the difference that, in this case, we must make use of the multiplication and division table that we learned in elementary school.

When we have two real numbers with the same sign (plus or minus) we distinguish two cases:

When we have two real numbers with the same sign (plus or minus) we distinguish two cases
  • The product (result of the multiplication) of two positive numbers will be positive. The quotient (result of the division) of two positive numbers will be positive.
    (+2)×(+1)=+2(+2) \times (+1)= +2
    (+2):(+1)=+2(+2) :(+1)= +2
  • The product of two negative numbers will be positive. The quotient of two negative numbers will be positive.
    (−2)×(−1)=+2(-2) \times (-1)= +2
    (−2):(−1)=+2(-2) :(-1)= +2
  • When we have two numbers with different signs, that is, one with the plus sign and the other with the minus sign, the result of the multiplication or division will always be negative.
    (+2)×(−1)=−2(+2) \times (-1)= -2
    (−2):(+1)=−2(-2) :(+1)= -2
Detailed explanation

Suggested Topics to Practice in Advance

  1. Positive and negative numbers and zero
  2. Opposite numbers
  3. Elimination of Parentheses in Real Numbers
  4. Real line or Numerical line
  5. Addition and Subtraction of Real Numbers

Practice Multiplication and division of directed numbers

Question 1

What is the answer to the following exercise?

\( 1\cdot(-1)= \)

Question 2

Complete the following exercise:
\( (-7)\cdot(1)= \)

Question 3

Complete the following exercise:
\( (-16)\cdot(1)= \)

Question 4

What is the answer to the following exercise?

\( (-1)\cdot3= \)

Question 5

Complete the following exercise:

\( (-2)\cdot1= \)

examples with solutions for multiplication and division of directed numbers

Exercise #1

What is the answer to the following exercise?

1⋅(−1)= 1\cdot(-1)=

Video Solution

Step-by-Step Solution

Let's remember the rule:

(+x)×(−x)=−x (+x)\times(-x)=-x

Therefore, the sign of the exercise result will be negative:

+1×−1=−1 +1\times-1=-1

Answer

−1 -1

Exercise #2

Complete the following exercise:
(−7)⋅(1)= (-7)\cdot(1)=

Video Solution

Step-by-Step Solution

Let's recall the law:

(+x)×(−x)=−x (+x)\times(-x)=-x

Therefore, the sign of the exercise result will be negative:

−7×+1=−7 -7\times+1=-7

Answer

−7 -7

Exercise #3

Complete the following exercise:
(−16)⋅(1)= (-16)\cdot(1)=

Video Solution

Step-by-Step Solution

Let's remember the rule:

(+x)×(−x)=−x (+x)\times(-x)=-x

Therefore, the sign of the exercise result will be negative:

−16×+1=−16 -16\times+1=-16

Answer

−16 -16

Exercise #4

What is the answer to the following exercise?

(−1)⋅3= (-1)\cdot3=

Video Solution

Step-by-Step Solution

Let's recall the law:

(+x)×(−x)=−x (+x)\times(-x)=-x

Therefore, the sign of the exercise result will be negative:

−1×+3=−3 -1\times+3=-3

Answer

−3 -3

Exercise #5

Complete the following exercise:

(−2)⋅1= (-2)\cdot1=

Video Solution

Step-by-Step Solution

Let's recall the law:

(+x)×(−x)=−x (+x)\times(-x)=-x

Therefore, the sign of the exercise result will be negative:

−2×+1=−2 -2\times+1=-2

Answer

−2 -2

Question 1

Complete the following exercise:

\( 2\cdot1= \)

Question 2

Complete the following exercise:

\( (-10)\cdot(-1)= \)

Question 3

Complete the following exercise:

\( (-3)\cdot(-1)= \)

Question 4

What is the answer to the following exercise?

\( 6\cdot1= \)

Question 5

What is the answer to the following exercise?

\( (-4)\cdot(-1)= \)

examples with solutions for multiplication and division of directed numbers

Exercise #1

Complete the following exercise:

2⋅1= 2\cdot1=

Video Solution

Step-by-Step Solution

Let's remember the rule:

(+x)×(+x)=+x (+x)\times(+x)=+x

Therefore, the sign of the exercise result will be positive:

+2×+1=+2 +2\times+1=+2

Answer

2 2

Exercise #2

Complete the following exercise:

(−10)⋅(−1)= (-10)\cdot(-1)=

Video Solution

Step-by-Step Solution

Let's remember the rule:

(−x)×(−x)=+x (-x)\times(-x)=+x

Therefore, the sign of the exercise result will be positive:

−10×−1=+10 -10\times-1=+10

Answer

10 10

Exercise #3

Complete the following exercise:

(−3)⋅(−1)= (-3)\cdot(-1)=

Video Solution

Step-by-Step Solution

Let's recall the rule:

(−x)×(−x)=+x (-x)\times(-x)=+x

Therefore, the sign of the exercise result will be positive:

−3×−1=+3 -3\times-1=+3

Answer

3 3

Exercise #4

What is the answer to the following exercise?

6⋅1= 6\cdot1=

Video Solution

Step-by-Step Solution

Let's recall the law:

(+x)×(+x)=+x (+x)\times(+x)=+x

Therefore, the sign of the exercise result will be positive:

+6×+1=+6 +6\times+1=+6

Answer

6 6

Exercise #5

What is the answer to the following exercise?

(−4)⋅(−1)= (-4)\cdot(-1)=

Video Solution

Step-by-Step Solution

Let's recall the rule:

(−x)×(−x)=+x (-x)\times(-x)=+x

Therefore, the sign of the exercise result will be positive:

−4×−1=+4 -4\times-1=+4

Answer

4 4

Question 1

What will be the sign of the result of the next exercise?

\( (-2)\cdot(-4)= \)

Question 2

What will be the sign of the result of the next exercise?

\( (-3)\cdot(-4)= \)

Question 3

What will be the sign of the result of the next exercise?

\( (-2)\cdot(-\frac{1}{2})= \)

Question 4

Will the result of the exercise below be positive or negative?

\( 5\cdot(-\frac{1}{2})= \)

Question 5

What will be the sign of the result of the next exercise?

\( (-4)\cdot12= \)

examples with solutions for multiplication and division of directed numbers

Exercise #1

What will be the sign of the result of the next exercise?

(−2)⋅(−4)= (-2)\cdot(-4)=

Video Solution

Step-by-Step Solution

It's important to remember: when we multiply a negative by a negative, the result is positive!

You can use this guide:

Answer

Positive

Exercise #2

What will be the sign of the result of the next exercise?

(−3)⋅(−4)= (-3)\cdot(-4)=

Video Solution

Step-by-Step Solution

Let's remember the rule:

(−x)×(−x)=+x (-x)\times(-x)=+x

Therefore, the sign of the exercise result will be positive:

−3×−4=+12 -3\times-4=+12

Answer

Positive

Exercise #3

What will be the sign of the result of the next exercise?

(−2)⋅(−12)= (-2)\cdot(-\frac{1}{2})=

Video Solution

Step-by-Step Solution

Let's recall the law:

(−x)×(−x)=+x (-x)\times(-x)=+x

Therefore, the sign of the exercise result will be positive:

−2×−12=+1 -2\times-\frac{1}{2}=+1

Answer

Positive

Exercise #4

Will the result of the exercise below be positive or negative?

5⋅(−12)= 5\cdot(-\frac{1}{2})=

Video Solution

Step-by-Step Solution

Let's remember the rule:

(+x)×(−x)=−x (+x)\times(-x)=-x

Therefore, the sign of the exercise result will be negative:

+5×−12=−212 +5\times-\frac{1}{2}=-2\frac{1}{2}

Answer

Negative

Exercise #5

What will be the sign of the result of the next exercise?

(−4)⋅12= (-4)\cdot12=

Video Solution

Step-by-Step Solution

Let's remember the rule:

(+x)×(−x)=−x (+x)\times(-x)=-x

Therefore, the sign of the exercise result will be negative:

−4×+12=−48 -4\times+12=-48

Answer

Negative

Topics learned in later sections

  1. Integers