How to Apply Integers Multiplication and Division Rules?

Multiplying and dividing integers are two basic operations performed on integers. Multiplying integers is the same as repetitive additions, which means adding an integer a specific number of times.

Related Topics

• How to Multiply and Divide Integers?
• How to Apply Integers Addition and Subtraction Rules?

A step-by-step guide to applying multiplication and division rules

Rules for multiplication integers

Multiplication of integers is the process of repetitive addition that involves positive and negative numbers, or we can say, integers. When it comes to case multiplication of integers, the following should be considered:

• Multiplying \(2\) positive numbers: When you multiply integers by two positive signs, \(\color{blue}{positive\:\times \:positive\:=\:positive}\)
• Multiplying \(1\) positive and \(1\) negative number: When you multiply integers with one negative sign and one positive sign, \(\color{blue}{negative\:\times \:positive\:=\:negative\:}\)
• Multiplying \(2\) negative numbers: When you multiply integers with two negative signs, \(\color{blue}{negative\:\times \:negative\:=\:positive}\)

Rules for dividing integers

Integer division involves grouping items. It includes both positive and negative numbers. Just like multiplication, dividing integers involves the same thing:

• Dividing \(2\) positive numbers: When you divide integers with two positive signs, \(\color{blue}{positive\:\div \:positive\:=\:positive\:}\)
• Dividing \(2\) negative numbers: When you divide integers with two negative signs, \(\color{blue}{negative\:\div \:negative\:=\:positive}\)
• Dividing \(1\) positive and \(1\) negative numbers: When you divide integers with one negative sign and one positive sign, \(\color{blue}{negative\:\div \:positive\:=\:negative}\)

Two important things to keep in mind when multiplying or dividing integers are:

1. When the signs are different, the answer is always negative.
2. When the signs are the same, the answer is always positive.

Applying Multiplication and Division Rules – Example 1:

Solve the given expression by using the division of integers rules: \((–30) ÷ (–5) ÷ (–2)\).

Solution:

Here, we have to divide three integers, so we follow the BODMAS rule here because there is more than one operation in this statement. The first step is \((-30÷ -5)\). Now, by dividing \(-30\) by \(-5\), we get \(6\) as the answer. \(6\) is a positive integer, as \(negative\:\div \:negative\:=\:positive\). So, the new expression is \((6) ÷ (-2)\). Now, if we divide \(6\) by \(-2\), we get \(-3\), as \(positive\:\div \:negative\:=\:negative\).

Therefore, \((-30) ÷ (-5) ÷ (-2) = -3\).

Exercises for Applying Multiplication and Division Rules

Perform the following calculations using the addition and subtraction rules.

1. \(\color{blue}{-22\times -14}\)
2. \(\color{blue}{375\div \left(-5\right)}\)
3. \(\color{blue}{\:−110\:×\left(−6\right)×\left(−7\right)}\)
4. \(\color{blue}{-1,266\div \left(-2\right)}\)

1. \(\color{blue}{308}\)
2. \(\color{blue}{-75}\)
3. \(\color{blue}{-4,620}\)
4. \(\color{blue}{633}\)