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Chapter 1: Problem 26

Multiply. $$ (-7)(-7) $$

Short Answer

Expert verified
The product is 49.

Step by step solution

01

Understand the Problem

The task is to multiply two negative numbers: \(-7\) \(\times\) \(-7\). It's important to know that multiplying two negative numbers will result in a positive product.
02

Calculate the Product

Multiply the absolute values of the numbers. Since both numbers are \(-7\), their absolute value is \(7\). Calculate: \(7 \times 7 = 49\).
03

Determine the Sign

Since both factors are negative, the product will be positive. Therefore, \((-7) \times (-7) = 49\).

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Key Concepts

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

Understanding Absolute Value
Absolute value is a key concept in mathematics, especially when dealing with negative numbers. The absolute value of a number is its distance from zero on a number line, regardless of direction.
- For example, both \(-7\) and \(7\) have an absolute value of \(7\). This is because they are both exactly seven units away from zero.
- When you see vertical bars around a number, like \(|-7|\) or \(|7|\), it indicates the absolute value.
Understanding absolute values is crucial when multiplying negative numbers, as you first consider their absolute values before applying the sign rules.
Resulting in a Positive Product
Multiplying two negative numbers might seem tricky, but it always results in a positive product.
Here's why: When you multiply one negative number by another, the negatives "cancel out."
Think of it like turning a double negative into a positive in language. For instance: - \(-7 \times -7\): Calculate the absolute value to get \(7 \times 7\), which equals \(49\).
Knowing this product is positive is essential. It's like subtracting a debt, which increases value.
Remember these are rules of arithmetic operations that help in smoothly handling any equations with negative numbers.
Role of Negative Factors in Multiplication
Negative factors in multiplication are important to understand as they affect the outcome or sign of the product.
- A factor is simply a number multiplied by another number. When factors are negative, different multiplication rules apply.
- Multiplying a positive factor by a negative one results in a negative product, e.g., \( 7 \times -7 = -49 \).
- Multiplying two negative factors results in a positive product, as seen in the original exercise where \(-7 \times -7 = 49\).
By understanding these rules, you can accurately navigate problems involving both positive and negative numbers.

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Most popular questions from this chapter

The expression \(\frac{d}{t}\) represents the average speed \(r\) in miles per hour if a distance of \(d\) miles is traveled in \(t\) hours. Find the rate to the nearest whole number if the distance between Dallas, Texas, and Kaw City, Oklahoma, is 432 miles, and it takes Peter Callac 8.5 hours to drive the distance.

Write each sentence as an equation or inequality. Use \(x\) to represent any unknown number. The sum of 8 and twice a number is 42

Perform the following operations. Write answers in lowest terms. $$ \frac{7}{18} \div \frac{14}{36} $$

Insert parentheses so that the following expression simplifies to 28. $$2 \cdot 5+3^{2}$$

Perform the following operations. Write answers in lowest terms. $$ \frac{5}{12}+\frac{4}{12} $$
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