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Chapter 1: Problem 20

Multiply or divide as indicated. See Examples 4 and 5 . $$ -5 \cdot 0 $$

Short Answer

Expert verified
The result is 0.

Step by step solution

01

Identify the Operation

The expression given is \(-5 \cdot 0\). This tells us to multiply -5 by 0. The operation to be performed here is multiplication.
02

Apply the Multiplication Property of Zero

According to the multiplication property of zero, any number multiplied by zero equals zero. Therefore, \(-5 \cdot 0 = 0\).
03

Confirm the Sign

When zero is involved in a multiplication, the sign of the other number doesn't affect the result as the product is zero. Therefore, the result is 0, and there is no need to consider a negative sign.

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Key Concepts

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

Multiplication
Multiplication is a fundamental arithmetic operation that involves combining equal groups. To multiply two numbers means you'll combine these groups to form a total. Multiplication is often referred to as repeated addition. For example, if you have 3 sets of 2 apples, multiplying 3 by 2 will give you 6 apples in total. When you see the multiplication symbol (\( \cdot \) or \( \times \)), it means you should perform this operation.
For instance, when we multiply \(-5 \cdot 0\), we use the multiplication operation to combine -5 groups of zero. However, when multiplying by zero, the result is not the typical addition of groups, as zero means there are actually no groups to count!
Negative Numbers
Negative numbers are numbers less than zero and are represented by a minus sign (-) before them. They are found below zero on the number line and are used to represent opposite values, like debts or temperatures below freezing.
When multiplying negative numbers with other numbers, two main rules apply:
  • Multiplying two negative numbers results in a positive number. For example, \(-3 \times -2 = 6\).
  • Multiplying a positive number by a negative number results in a negative number. For example, \(3 \times -2 = -6\).
However, in our original exercise, the presence of zero in the multiplication overrides these rules, leading to a product of zero regardless of the negative sign.
Zero in Arithmetic
Zero is a unique and essential number in arithmetic. It acts as a placeholder in our number system and represents a null or void quantity. One of the most important properties of zero is its behavior in multiplication.
According to the multiplication property of zero:
  • Any number multiplied by zero results in zero.
  • This applies no matter whether the number is positive, negative, or itself zero.
Therefore, in the exercise \(-5 \cdot 0\), the multiplication property of zero dictates the answer is zero, illustrating that 0 removes any quantity, regardless of the other number's value or sign.

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Most popular questions from this chapter

Simplify each expression. See Examples \(11,14,\) and \(15 .\) $$ 5 k-(3 k-10) $$

Translating Write each phrase as an algebraic expression. Use the variable \(x\) to represent each unknown number. See Example 8 . Twice the sum of a number and three.

In your own words, explain why the empty set is a subset of every set.

Complete the statement to illustrate the given property. \(7 \cdot 1=\quad\)_____Multiplicative identity property.

Simplify each expression. See Examples \(11,14,\) and \(15 .\) $$ 1.5 x+2.3-0.7 x-5.9 $$
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