Server Error

Server Not Reachable.

This may be due to your internet connection or the nubtrek server is offline.

Thought-Process to Discover Knowledge

Welcome to nubtrek.

Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

Read in the blogs more about the unique learning experience at nubtrek.
mathsIntegersInteger Multiplication & Division

### Integer Multiplication: Simplified Procedure

This page extends the multiplication in first principles into a simplified procedure for multiplication of integers, which is called sign property of integer multiplication.

click on the content to continue..

In whole numbers, we had studied the following.

Multiplication by Place-value with Regrouping - Simplified Procedure : Two numbers are multiplied as illustrated in the figure. Note: The procedure combines 10 units into 1 ten as carry over and so on for higher place-values.

The product of whole numbers 4xx3 = 12 is understood in integers as:

text(received:)4 is repeatedly put in 3 times.

The product of integers -4 xx 3 = -12 is understood as text(given:)4 is repeatedly put in 3 times.

The product of integers 4 xx -3 = -12 is understood as text(received:)4 is repeatedly taken away 3 times.

The product of integers -4 xx -3 = +12 is understood as text(given:)4 is repeatedly taken away 3 times.

Summary of integer multiplication illustrative examples:

•  4xx3 = 12
text(received:)4 is put-in 3 times

•  (-4)xx3 = -12
text(given:)4 is put-in 3 times

•  4xx(-3) = -12
text(received:)4 is taken-away 3 times

•  (-4)xx(-3) = 12
text(given:)4 is taken-away 3 times

Based on this, the multiplication is simplified as

•  +ve xx +ve = +ve

•  -ve xx +ve = -ve

•  +ve xx -ve = -ve

•  -ve xx -ve = +ve

Integer Multiplication -- Simplified Procedure : The sign of the product is decided by signs of multiplicand and multiplier as follows.

Sign-Property of Integer Multiplication
•  positive xx positive = positive
•  positive xx negative = negative
•  negative xx positive = negative
•  negative xx negative = positive

The absolute value of the product is calculated by whole number multiplication of absolute values of the multiplicand and multiplier.

Solved Exercise Problem:

Find the product of the multiplication 22 xx (-1)

• -11
• -22
• -22

The answer is "-22"

Solved Exercise Problem:

Find the product of the multiplication 0xx(-32)

• 0
• -0
• both the above
• both the above

The answer is "both the above"

Solved Exercise Problem:

Find the product of the multiplication -222 xx (-88)

• -19536
• 19536
• 19536

The answer is "a positive number".

switch to interactive version