Problem 101 Translate each phrase; then simp... [FREE SOLUTION]

Chapter 2: Problem 101

Translate each phrase; then simplify. See Example 17. Find the product of -42 and -6 .

Short Answer

Expert verified

The product of -42 and -6 is 252.

Step by step solution

Translate the Phrase to a Mathematical Expression

The phrase 'Find the product of -42 and -6' means we need to multiply the two numbers together. In mathematical terms, this is written as \(-42 \times -6\).

Multiply the Negative Numbers

To find the product of two negative numbers, multiply them as if they were positive: \(42 \times 6 = 252\).

Apply the Rule of Signs

Since both numbers are negative, multiplying two negative numbers results in a positive product. Therefore, the product is \(+252\).

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Key Concepts

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

Multiplication of Negative Numbers

When you multiply numbers, it's essential to understand what to do when those numbers include negatives. Multiplying negative numbers can sometimes be confusing, but it's quite straightforward once you grasp the basics.

Here's a simple guide:

If both numbers you're multiplying are negative, the result will be positive.
If one number is negative and the other is positive, the result will be negative.

For instance, in the exercise, you're multiplying (-42) by (-6). Both numbers are negative, so according to the rules, the result is positive.

The process itself works just like regular multiplication. Just ignore the negative signs at first, multiply the absolute values, and then apply the sign rule to determine the final result.

Mathematical Expressions

Mathematical expressions are a way to represent operations, numbers, and their relationships using symbols and formulae. Translating a word problem into a mathematical expression is often the first step in solving it.

For example, the phrase "Find the product of -42 and -6" is translated into a mathematical expression as \(-42 \times -6\). Here, the term 'product' indicates multiplication. Thus, expressions are crucial for understanding and solving problems.

Let's break it down further:

Operators: These are symbols like \(+\), \(-\), \(\times\), and \(\div\) that represent mathematical operations.
Operands: These are the numbers on which operations are performed. In this case, -42 and -6.

Understanding how to translate words into expressions is key to solving any mathematical word problem.

Rule of Signs

The rule of signs is a critical concept in arithmetic that helps determine the sign of a product or quotient. When you're multiplying or dividing numbers, you can use these simple rules:

Two negative numbers: Multiplying or dividing them always results in a positive number. Example: \(-42 \times -6 = +252\).
One negative and one positive number: The result will always be negative. Example: \(-42 \times 6 = -252\).
Two positive numbers: The result is positive, naturally.

These rules provide an easy and systematic way to determine the sign of your answer without complex calculations.

Remembering these rules can simplify your calculations and reduce errors when handling negative numbers. Once you get these basics, dealing with multiplication or division of negative numbers becomes much less daunting.

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91影视

Translate each phrase; then simplify. See Example 17. Find the product of -42 and -6 .

Short Answer

Step by step solution

Translate the Phrase to a Mathematical Expression

Multiply the Negative Numbers

Apply the Rule of Signs

Key Concepts

Multiplication of Negative Numbers

Mathematical Expressions

Rule of Signs

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