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Thought-Process to Discover Knowledge

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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.

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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.

What is the product of 4 and 3?

By first principles, text(received:)4 is repeatedly put in 3 times.

• 43
• 12
• 12

The answer is "12"

What is the product of -4 and 3?

By first principles, text(given:)4 is repeatedly put in 3 times.

• -12
• -12
• +12

The answer is "-12"

What is the product of 4 and -3?

By first principles, text(received:)4 is repeatedly taken away 3 times.

• -12
• -12
• +12

The answer is "-12"

What is the product of -4 and -3?

By first principles, text(given:)4 is repeatedly taken away 3 times.

• -12
• +12
• +12

The answer is "+12"

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".

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