Multiplying And Dividing With Integers - Math Planet

Pre-Algebra / Explore and understand integers / Multiplying and dividing with integers Do excercises Show all 4 exercises

• Multiplying and dividing I
• Multiplying and dividing II
• Multiplying and dividing III
• Multiplying and dividing IV

You also have to pay attention to the signs when you multiply and divide. There are two simple rules to remember:

When you multiply a negative number by a positive number then the product is always negative.

When you multiply two negative numbers or two positive numbers then the product is always positive.

This is similar to the rule for adding and subtracting: two minus signs become a plus, while a plus and a minus become a minus. In multiplication and division, however, you calculate the result as if there were no minus signs and then look at the signs to determine whether your result is positive or negative. Two quick multiplication examples:

$$3\cdot (-4)=-12$$

3 times 4 equals 12. Since there is one positive and one negative number, the product is negative 12.

$$(-3)\cdot (-4)=12$$

Now we have two negative numbers, so the result is positive.

Turning to division, you may recall that you can confirm the answer you get by multiplying the quotient by the denominator. If you answer is correct then the product of these two numbers should be the same as the numerator. For example,

$$\frac{12}{3}=4$$

In order to check whether 4 is the correct answer, we multiply 3 (the denominator) by 4 (the quotient):

$$3\cdot 4=12$$

What happens when you divide two negative numbers? For example,

$$\frac{(-12)}{(-3)}=\: ?$$

For the denominator (-3) to become the numerator (-12), you would have to multiply it by 4, therefore the quotient is 4.

So, the quotient of a negative and a positive number is negative and, correspondingly, the quotient of a positive and a negative number is also negative. We can conclude that:

When you divide a negative number by a positive number then the quotient is negative.

When you divide a positive number by a negative number then the quotient is also negative.

When you divide two negative numbers then the quotient is positive.

The same rules hold true for multiplication.

Video lesson

Calculate the following expressions

$$(-4)\cdot (-12),\: \: \: \: \frac{-12}{3}$$

Do excercises Show all 4 exercises

• Multiplying and dividing I
• Multiplying and dividing II
• Multiplying and dividing III
• Multiplying and dividing IV

More classes on this subject Pre-Algebra Explore and understand integers: Absolute value Pre-Algebra Explore and understand integers: Adding and subtracting integers

Next Chapter:

PRE-ALGEBRA – Inequalities and one-step equations Search

• Math Playground All courses
  • • Math Playground Overview
• Programming All courses
  • • Programming Overview
• Pre-Algebra All courses
  • • Pre-Algebra Overview
    • Introducing Algebra
      • Pre-Algebra
      • Introducing Algebra
        • Overview
        • Operations in the correct order
        • Evaluate expressions
        • Identify properties
        • Equations with variables
        • Coordinate system and ordered pairs
        • Inequalities
    • Explore and understand integers
      • Pre-Algebra
      • Explore and understand integers
        • Overview
        • Absolute value
        • Adding and subtracting integers
        • Multiplying and dividing with integers
      • About Mathplanet
      • Cookie settings
    • Inequalities and one-step equations
      • Pre-Algebra
      • Inequalities and one-step equations
        • Overview
        • Different ways to solve equations
        • Calculating the area and the perimeter
        • Solving inequalities
        • Understanding inequalities and equations
    • Discover fractions and factors
      • Pre-Algebra
      • Discover fractions and factors
        • Overview
        • Monomials and adding or subtracting polynomials
        • Powers and exponents
        • Multiplying polynomials and binomials
        • Factorization and prime numbers
        • Finding the greatest common factor
        • Finding the least common multiple
    • More about the four rules of arithmetic
      • Pre-Algebra
      • More about the four rules of arithmetic
        • Overview
        • Integers and rational numbers
        • Learn how to estimate calculations
        • Calculating with decimals and fractions
        • Geometric sequences of numbers
        • Scientific notation
    • More about equation and inequalities
      • Pre-Algebra
      • More about equation and inequalities
        • Overview
        • Fundamentals in solving Equations in one or more steps
        • Calculating the circumference of a circle
    • Graphing and functions
      • Pre-Algebra
      • Graphing and functions
        • Overview
        • Linear equations in the coordinate plane
        • The slope of a linear function
        • Graphing linear inequalities
        • Solve systems of equations by graphing
    • Ratios and percent
      • Pre-Algebra
      • Ratios and percent
        • Overview
        • Rates and ratios
        • Proportions and percent
        • Solving problems with percentages
    • Probability and statistics
      • Pre-Algebra
      • Probability and statistics
        • Overview
        • The mean, the median and the mode
        • Stem-and-Leaf Plots and Box-and-Whiskers Plot
        • Calculating the outcome
        • Combinations and permutations
        • Finding the odds
        • Probability of events
    • Introducing geometry
      • Pre-Algebra
      • Introducing geometry
        • Overview
        • Geometry – fundamental statements
        • Circle graphs
        • Angles and parallel lines
        • Triangles
        • Quadrilaterals, polygons and transformations
    • Area and Volume
      • Pre-Algebra
      • Area and Volume
        • Overview
        • Measure areas
        • Pyramids, prisms, cylinders and cones
    • Right triangles and algebra
      • Pre-Algebra
      • Right triangles and algebra
        • Overview
        • Square roots and real numbers
        • The Pythagorean Theorem
        • Trigonometry
• Algebra 1 All courses
  • • Algebra 1 Overview
• Algebra 2 All courses
  • • Algebra 2 Overview
• Geometry All courses
  • • Geometry Overview
• SAT All courses
  • • SAT Overview
• ACT All courses
  • • ACT Overview