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Chapter 2: Problem 138

In your own words, explain how to multiply two integers.

Short Answer

Expert verified
Multiply the absolute values and determine the sign based on the original integers.

Step by step solution

01

Understand the Signs

First, identify the signs of the integers you need to multiply. If both integers have the same sign (both positive or both negative), the result of the multiplication will be positive. If they have different signs (one positive and one negative), the result will be negative.
02

Multiply the Absolute Values

Next, ignore the signs and multiply the absolute values of the two integers. Absolute value refers to the number without any positive or negative sign. For example, to multiply -3 and 4, consider multiplying 3 and 4 instead.
03

Apply the Sign Rule

Finally, apply the sign rule based on the signs you analyzed in Step 1. If both numbers had the same sign, the result is positive. If they had different signs, the result is negative. Using the previous example (-3 and 4), the product of 3 and 4 is 12, and since the signs are different, the final result is -12.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Integer Multiplication Rules
Multiplying integers involves a few straightforward rules that you need to remember. If you multiply two integers, there are two main factors to focus on: the signs of the numbers and their absolute values. When you multiply:
  • Two positive numbers, the result remains positive. For example, multiplying 6 and 4 gives you 24.
  • Two negative numbers, the result is also positive, because a negative times a negative is positive. Multiplying -5 and -3 yields 15.
  • One positive and one negative number, the product is always negative. For instance, when you multiply 7 and -2, your answer is -14.
The rules are consistent and can guide you in quickly determining the sign of your product.
Absolute Value
The absolute value of a number is simply its distance from zero on the number line. It does not take into account whether the number is positive or negative.

For example, the absolute value of both 6 and -6 is 6, because each is 6 units away from zero. The mathematical notation for absolute value uses vertical bars, so you would write \(|6| = 6\) and \(|-6| = 6\).When you multiply two integers, you'll first multiply their absolute values. This initial product helps in determining the result before applying any sign rules.
For example, to multiply -7 and 3, first consider the absolute values 7 and 3, which equal 21. After this, consider the sign rules to do the final calculation.
Sign Rules in Multiplication
Determining the sign of the product when multiplying integers is crucial. The steps are simple:
  • If both integers have the same sign, whether both are positive or both are negative, their product is positive.
  • If the integers have different signs, one is negative while the other is positive, resulting in a negative product.
Remembering these sign rules helps streamline the multiplication process. If you're ever uncertain, think of these basics: - Multiplying two negatives results in a positive because the negatives "cancel out." - Mixing a positive and a negative results in a negative. By internalizing these simple rules, you'll quickly be able to multiply integers accurately.

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Most popular questions from this chapter

The deepest spot in the Pacific Ocean is the Mariana Trench, which has an elevation of 10,924 meters below sea level. The bottom of the Pacific's Aleutian Trench has an elevation 3245 meters higher than that of the Mariana Trench. Use a negative number to represent the depth of the Aleutian Trench. (Source: Defense Mapping Agency).

Write the given numbers in order from least to greatest. $$ |-1|,-|-6|,-(-6),-|1| $$

Write the given numbers in order from least to greatest. $$ 1^{4},-(-3),-|7|,|-20| $$

Insert \(<,>,\) or \(=\) between each pair of numbers to make a true statement. $$ |-8| \quad|-11| $$

Add. $$ -32+62 $$
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