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

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

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?

(6)5= (-6)\cdot5=

Video Solution

Step-by-Step Solution

Remember the law:

(+x)×(x)=x (+x)\times(-x)=-x

For the sum of the angles of a triangle is always:

6×+5=30 -6\times+5=-30

Answer

Negative

Exercise #3

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

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

Video Solution

Step-by-Step Solution

To solve the exercise you need to remember an important rule: Multiplying a positive number by a negative number results in a negative number.

()×(+)=() (−)×(+)=(−)
Therefore, if we multiply negative 2 by 2 the result will be negative 4.

That is, the result is negative.

+2×2=4 +2\times-2=-4

Answer

Negative

Exercise #4

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

0.91.1:(4) \frac{-0.9}{1.1}:(-4)

Video Solution

Step-by-Step Solution

Let's see if the number is negative or positive.

As you can see, in the expression the numerator is negative and the denominator is positive.

That is, the division exercise will look like this:

+:= \frac{-}{+}:-=

The result of the expression will be a negative number, since we are dividing a negative number by a positive number.

Therefore, the exercise that will be obtained will look like this:

:=+ -:-=+

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

Answer

+

Exercise #5

ab= -a\cdot b=

Replace and calculate if a=3b=5 a=-3\text{, }b=5

Video Solution

Step-by-Step Solution

First, we replace the data in the exercise

-(-3)*5 = 

To better understand the minus sign multiplied at the beginning, we will write it like this:

-1*-3*5 = 

Now we see that we have an exercise that is all multiplication,

We will solve according to the order of arithmetic operations, from left to right:

-1*-3 = 3

3*5 = 15

Answer

15 15

Exercise #1

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

(16)(5)= (-16)\cdot(-5)=

Video Solution

Answer

Positive

Exercise #2

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

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

Video Solution

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

Answer

Positive

Exercise #4

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

1412= \frac{1}{4}\cdot\frac{1}{2}=

Video Solution

Answer

Positive

Exercise #5

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

5(12)= 5\cdot(-\frac{1}{2})=

Video Solution

Answer

Negative

Exercise #1

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

(4)12= (-4)\cdot12=

Video Solution

Answer

Negative

Exercise #2

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

63= 6\cdot3=

Video Solution

Answer

Positive

Exercise #3

Complete the following exercise:

510= 5\cdot10=

Video Solution

Answer

50

Exercise #4

Complete the following exercise:

26= 2\cdot6=

Video Solution

Answer

12

Exercise #5

Complete the following exercise:

66= 6\cdot6=

Video Solution

Answer

36

Topics learned in later sections

  1. Integers