Method

Multiplying Integers With Different Signs

The product of two integers is always negative if and only if one factor is negative and the other is positive. Change the negative factor to its opposite and perform the multiplication as if both were whole numbers. Next, change the result to its opposite to get the final product. Consider the following multiplication of integers. -7*2 Follow these three steps to find the product of two integers with different signs.

Check the Signs of the Factors

Verify that one factor is positive and the other is negative. Change the negative factor to its opposite. The result is a multiplication of two positive integers. For the given example, the first factor is negative 7, so change it to its opposite 7. -7*2 ⇒ 7*2

Find the Product of the Resulting Multiplication

Next, find the product of the multiplication of two whole numbers. In this case, 7*2 means that seven equal intervals of length 2 are needed. Use a number line to find this product.

The endpoint is the product of the resulting multiplication. This means that 7*2=14.

Change the Product to Its Opposite

Change the product from the previous step to its opposite to get the product of the initial multiplication of integers with different signs. For the given example, the product of whole numbers is 14. Its opposite is -14. 7*2= 14 ⇒ -7*2= -14 In summary, multiply two integers with different signs as if they were whole numbers and change the result to its opposite to get the final product.

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