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Chapter 3: Problem 217

In the following exercises, multiply each pair of integers. $$9(-7)$$

Short Answer

Expert verified
-63

Step by step solution

01

- Identify the numbers

You are asked to multiply two integers: 9 and -7.
02

- Recall multiplication rules for integers

Remember that multiplying a positive number by a negative number results in a negative number.
03

- Perform the multiplication

Multiply the absolute values of the numbers: \[ 9 \times 7 = 63 \].
04

- Apply the sign rule

Because one integer is positive and the other is negative, the result is negative. Thus, \[ 9 \times (-7) = -63 \].

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Key Concepts

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

multiplication rules
When dealing with integer multiplication, it is very important to follow a set of rules to get the correct result. Here鈥檚 how you can remember them easily:
  • Multiply the absolute values of the numbers first. This means you ignore the signs and multiply the numbers as if they are all positive.
  • The result's sign depends on the signs of the numbers you are multiplying:
    - If both numbers are positive, the result is positive.
    - If both numbers are negative, the result is also positive.
    - If one number is positive and one is negative, the result is negative.
Using these simple rules consistently will help you get the correct result every time. For example, in our exercise, multiplying 9 by -7 means we first multiply their absolute values, 9 and 7, to get 63. Then we apply the sign rule and because one is negative, our final result is -63.
positive and negative numbers
Positive and negative numbers can sometimes be a bit tricky, but with practice, they become much easier to handle.

Positive numbers are any numbers greater than zero, and they don't have a plus sign in front of them; we just write the number. For example: 1, 2, 3.

Negative numbers are less than zero, and they always have a minus sign in front of them. For example: -1, -2, -3.

When multiplying positive and negative numbers:
  • Two positive numbers always give a positive result.
  • Two negative numbers also give a positive result because the negatives cancel each other out.
  • A positive and a negative number give a negative result, as seen in our exercise where 9 times -7 equals -63.
Understanding and recognizing these properties will help you a lot in solving multiplication problems easily.
absolute value
Absolute value is a concept used to describe the distance of a number from zero on the number line, regardless of its direction.

Here鈥檚 how to understand it better:
  • The absolute value of a positive number is the number itself. For instance, the absolute value of 7 is 7, written as \(|7|\right = 7\).
  • The absolute value of a negative number is also positive. It means how far the number is from zero without considering its sign. For example, the absolute value of -7 is 7, written as \(|-7|\right = 7\).
In multiplication, absolute values help to simplify the process because you multiply the numbers without thinking about their signs first. Once you have the product of the absolute values, you then decide the final sign based on the rules of multiplying positives and negatives. This method is what we used in our example when we multiplied the absolute values 9 and 7 before applying the sign rules to get the final answer of -63.

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Most popular questions from this chapter

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