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Chapter 2: Problem 20

Multiply the integers. $$8(-3)$$

Short Answer

Expert verified
-24

Step by step solution

01

Identify the integers

The problem involves multiplying two integers: 8 and -3.
02

Understand the rule of multiplication with a negative number

When multiplying a positive number by a negative number, the result is always negative.
03

Multiply the numbers

Perform the multiplication operation: \[ 8 \times (-3) = -24 \]

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Key Concepts

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

Integer Multiplication
When we talk about integer multiplication, we mean multiplying whole numbers. Integers include positive numbers, negative numbers, and zero. Unlike decimals and fractions, integers do not have fractional parts. It's important to understand that multiplication of two positive integers gives a positive result, and a multiplication of a positive and negative integer gives a negative result.
Let's illustrate this with a simple example: ewline For instance, if we multiply 2 and 3, we get: ewline 2 脳 3 = 6
Notice both are positive, so the result is positive. This is straightforward, but as soon as we add negative numbers to the mix, things change.
Negative Numbers
Negative numbers are less than zero and are represented with a minus sign (-). When thinking of negative numbers, it鈥檚 like stepping back on a number line. For instance, -3 is three steps down from zero.
They come into play often in multiplication asking us to understand how they interact with positive numbers. For example, in the exercise given where 8 is multiplied by -3, it means:
  • 8 is positive
  • -3 is negative
ewline Understanding that negative numbers can change the nature of your answer (making it negative in this case) is crucial.
Multiplication Rules
The rules for multiplying integers are simple once you understand them:
  • Positive 脳 Positive = Positive
  • Positive 脳 Negative = Negative
  • Negative 脳 Negative = Positive
Let鈥檚 look at our solution again using these rules.ewline Given: ewline 8脳(-3)
Following our rule of Positive 脳 Negative= Negative, our answer will be positive 24:
8 脳 (-3) = -24
This aligns with the multiplication rules. Practice these rules, and it will soon become second nature to determine the sign of the product quickly.
Remember:
  • Always identify the sign of each integer first.
  • Apply the multiplication rules to determine the sign of the result.
  • Multiply the absolute values of the integers as normal numbers.
Following these steps will help you solve similar problems with ease.

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Most popular questions from this chapter

Rank the numbers from least to greatest. $$-15,-(-18),-|20|, 4^{2},|-3|^{2}$$

Fill in the blank with \(<,>,\) or \(=\) $$-|32| \square|0|$$

Translate each English phrase to a mathematical expression. Then simplify. Subtract 24 from \(-35\)

Assume \(a>0\) (this means that \(a\) is positive) and \(b<0\) (this means that \(b\) is negative). Find the sign of each expression. $$|a| \div b$$

Assume \(a>0\) (this means that \(a\) is positive) and \(b<0\) (this means that \(b\) is negative). Find the sign of each expression. $$-(b)$$
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