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Chapter 2: Problem 9

Multiply the integers. $$-3(5)$$

Short Answer

Expert verified
The product is \(-15\).

Step by step solution

01

Determine the Sign of the Product

When multiplying two numbers, first determine the sign of the product. The rule is: multiplying two numbers with different signs results in a negative product.
02

Multiply the Absolute Values

After determining the sign, multiply the absolute values of the numbers. The absolute value of \(-3\) is \(3\), and the absolute value of \(5\) is \(5\). Multiply these together: \(3 \times 5 = 15\).
03

Apply the Sign to the Product

Since we determined the product is negative in the first step, apply the negative sign to the result from the second step. Thus, the final product is \(-15\).

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Key Concepts

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

headline of the respective core concept
Multiplying integers involves simple rules that help determine both the magnitude and the sign of the result. Let's understand this concept deeply by using the exercise as an example. Consider the problem: Multiply \(-3\) and \(5\). Here鈥檚 how we can break it down.
headline of the respective core concept
When we talk about integer multiplication, it is fundamentally the repeated addition of a number. For instance, multiplying \(-3\) by \(5\) means adding \(-3\) to itself five times. However, to simplify things, we use some rules. Multiply the absolute values first and then apply the sign rules.\
\
Multiplying absolute values is the same as normal multiplication. In our example, the absolute values of \(-3\) and \(5\) are \3\ and \5\, respectively. Multiply these numbers together and get \3 \times 5 = 15\.
headline of the respective core concept
To find the absolute value of an integer, ignore the sign and consider only the number itself. The absolute value of a positive number is the number itself. The absolute value of a negative number is the number without the negative sign. For example: \
    \
  • The absolute value of \3\ is \3\.\
  • The absolute value of \(-3\) is also \3\.\
      \
      In the exercise, both numbers have different signs. One is negative (\

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Most popular questions from this chapter

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

Divide the real numbers, if possible. $$\frac{30}{-6}$$

Rank the numbers from least to greatest. $$-|-46|,-(-24),-60,5^{2},|-12|$$

Translate the English phrase to a mathematical expression. Then simplify. \(-15\) divided into \(-45\)

Temperatures on the moon range from \(-184^{\circ} \mathrm{C}\) during its night to \(214^{\circ} \mathrm{C}\) during its day. Find the difference between the highest temperature on the moon and the lowest temperature.
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