Multiplication and Division of Signed Mumbers - Examples, Exercises and Solutions

Question Types:
Multiplication and Division of Signed Mumbers: Solving the problemMultiplication and Division of Signed Mumbers: Dividing numbers with different signsMultiplication and Division of Signed Mumbers: Complete the equationMultiplication and Division of Signed Mumbers: Using order of arithmetic operationsMultiplication and Division of Signed Mumbers: Complete the missing numberMultiplication and Division of Signed Mumbers: Complete the missing numbersMultiplication and Division of Signed Mumbers: Division by 0Multiplication and Division of Signed Mumbers: Multiplication of signed numbersMultiplication and Division of Signed Mumbers: Division between negative numbersMultiplication and Division of Signed Mumbers: Multiplication of a negative number by a neutral numberMultiplication and Division of Signed Mumbers: Multiplication of a negative number by a positive numberMultiplication and Division of Signed Mumbers: Multiplication of negative numbersMultiplication and Division of Signed Mumbers: Complete the following equation using the appropriate signsMultiplication and Division of Signed Mumbers: Dividing a negative number by 1 and (-1)Multiplication and Division of Signed Mumbers: Determine the reciprocal of the given numberMultiplication and Division of Signed Mumbers: Substituting parametersMultiplication and Division of Signed Mumbers: Division of positive numbersMultiplication and Division of Signed Mumbers: Multiplication of positive numbersMultiplication and Division of Signed Mumbers: Determine the resulting sign from the exercise

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

Practice Multiplication and Division of Signed Mumbers

Examples with solutions for Multiplication and Division of Signed Mumbers

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

Exercise #6

Complete the following exercise:

21= 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 #7

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 #8

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 #9

What is the answer to the following exercise?

61= 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 #10

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

Exercise #11

+5:+30= +5:+30=

Video Solution

Step-by-Step Solution

Let's write the exercise in the form of a simple fraction:

530= \frac{5}{30}=

We'll break down the 30 into a multiplication exercise:

55×6= \frac{5}{5\times6}=

Let's reduce the 5 in both the numerator and denominator of the fraction, and we'll get:

16 \frac{1}{6}

Answer

16 \frac{1}{6}

Exercise #12

+24:+8= +24:+8=

Video Solution

Step-by-Step Solution

Let's write the exercise in the form of a simple fraction:

248= \frac{24}{8}=

We'll factor 24 into a multiplication exercise:

3×88= \frac{3\times8}{8}=

We'll reduce the 8 in both the numerator and denominator of the fraction and get:

31=3 \frac{3}{1}=3

Answer

3 3

Exercise #13

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 #14

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 #15

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

Topics learned in later sections

  1. Integers