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### Theory:

**While multiplying \(2\) integers, depending upon the sign of the two or more than two numbers, the answer can change.**

**1. Any one number has a negative sign:**

In multiplication operation, if any one of the numbers is negative, then the result will have a negative sign \((+ve) × (-ve) = -ve\).

Example:

**1.**$265\times (-2)=-530$

**2.**$(-127)\times (-86)=10922$

**3.**$3\times (-86)=-258$

**2. Both numbers have a negative sign:**

In multiplication operation, when both the numbers are negative, then the result will have a positive sign \((-ve)×(-ve) = +ve\). This is according to the great mathematician Euler who proved, \((-1)×(-1)=+1\).

Example:

**1.**\((-9) × (-10) = 90\)

**2.**\((-12) × (-6) = 72\)

**3.**\((-10) × (-10) = 100\)

**4.**\((-5) × (-5) = 25\)

**3. Both numbers have positive sign:**

In multiplication, when both the numbers are positive, the result will be a positive sign \((+ve) × (+ve) =+ve\)

Example:

**1.**\(12 × 10 = 120\)

**2.**\(10 × 6 = 60\)

**3.**\(10 × 5 = 50\)

**4.**\(8 × 6 = 48\)

**Multiplication with zero:**

Any integer \(×\) \(0 = 0\). Irrespective of nature and sign of integer, when an integer is multiplied by zero, the result is \(0\).

Example:

**1.**\(40 × 0 = 0\)

**2.**−127 \(× 0 =\) 0