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Chapter 1: Problem 18

Find each product. $$ 3(-15) $$

Short Answer

Expert verified
-45

Step by step solution

01

Identify the Numbers

We need to find the product of 3 and -15.
02

Recognize the Multiplication Operation

The exercise indicates multiplication, so we use the multiplication symbol.
03

Apply the Multiplication Rule

Multiplying a positive number by a negative number results in a negative product. Hence, 3 times -15 will be negative.
04

Multiply the Absolute Values

Ignore the signs and multiply the absolute values of the numbers: 3 脳 15.
05

Compute the Product

The product of 3 and 15 is 45. Since one of the numbers is negative, the final product will be -45.

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Key Concepts

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

Product of Positive and Negative Numbers
When multiplying integers, it's essential to understand how the signs of the numbers affect the product.
In the given exercise, we are multiplying a positive number (3) by a negative number (-15).
According to the multiplication rule, the product of a positive and negative number is always negative.
Think of it like this: if you have a positive and you multiply it by something that takes away (negative), overall, you are left with less or a negative.
Absolute Value
When dealing with integers, absolute value helps simplify the multiplication process.
The absolute value of a number is its distance from zero on a number line, regardless of direction (ignoring the sign).
For example, the absolute value of both 3 and -3 is 3, and for -15, it is 15.
When multiplying 3 and -15, first find the absolute values (3 and 15), then multiply them.
After multiplying the absolute values, apply the rule for the signs to determine the final result.
Multiplication Rules
Understanding multiplication rules for integers is crucial.
Here are the basic rules:
  • When you multiply two positive numbers, the product is positive.
  • When you multiply two negative numbers, the product is also positive.
  • However, when you multiply a positive number by a negative number, the product is negative.

In our example, we multiplied 3 by -15.
According to the rules, a positive times a negative equals a negative, leading to a final product of -45.

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Most popular questions from this chapter

Write each sentence as an equation, using \(x\) as the variable. Then find the solution from the set of integers between \(-12\) and \(12,\) inclusive. When 5 is added to a number, the result is \(-5\)

Translate each phrase into a mathematical expression. Use \(x\) as the variable. Combine like terms when possible. Six times a number, added to the sum of the number and six

Simplify each expression. $$ -5(8 x+2)-(5 x-3)-3 x+17 $$

Write each sentence as an equation, using \(x\) as the variable. Then find the solution from the set of integers between \(-12\) and \(12,\) inclusive. When 6 is added to a number, the result is \(-3\)

Write a numerical expression for each phrase and simplify. Twice the product of \(-8\) and \(2,\) subtracted from \(-1\)
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