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Chapter 1: Problem 42

For each of the following, indicate if the answer has a positive or negative sign: \((1.4)\) a. A negative number is divided by a positive number. b. Two negative numbers are added.

Short Answer

Expert verified
a. Negative b. Negative

Step by step solution

01

Understanding Division of Different Signs

When a negative number is divided by a positive number, the result is always negative because the signs differ.
02

Understanding Addition of Negative Numbers

When two negative numbers are added, the result is always negative because you are adding two quantities that are both less than zero.
03

Applying the Rules

Based on the rules of signs: a. Negative divided by positive equals negative. b. Negative plus negative equals negative.

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Key Concepts

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

positive and negative numbers
Understanding how positive and negative numbers work is crucial in math. Numbers can either be positive or negative.
Positive numbers are greater than zero. Examples include 1, 2, 3, etc.
Negative numbers are less than zero. Examples include -1, -2, -3, etc.
When working with these types of numbers, always pay attention to their signs, as this affects the outcome of basic operations like addition and division.
division rules
When dividing numbers, the signs of the numbers being divided affect the result.
Here are some simple rules to remember:
  • If you divide a positive number by a positive number, the result is positive.
  • If you divide a negative number by a positive number, the result is negative.
  • If you divide a positive number by a negative number, the result is negative.
  • If you divide a negative number by a negative number, the result is positive.

For example, if -10 is divided by 2, the result is -5 because a negative divided by a positive gives a negative result.
Consistently applying these rules will help you solve division problems with ease.
addition rules
Adding numbers also follows specific rules based on their signs.
Here are the key rules for addition:
  • When adding two positive numbers, the result is positive. For example: 3 + 4 = 7.
  • When adding two negative numbers, the result is negative. For example: -3 + -4 = -7.
  • When adding a positive number and a negative number, subtract the smaller absolute value from the larger absolute value and keep the sign of the number with the larger absolute value. For example: -3 + 5 = 2 (positive) and 5 + (-3) = 2 (positive).

These rules help manage signs and ensure accurate results when performing addition.

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Most popular questions from this chapter

Select the correct phrase(s) to complete the following statement: A hypothesis is confirmed when: (1.2) a. one experiment proves the hypothesis b. many experiments validate the hypothesis c. you think your hypothesis is correct

Write each of the following as a standard number: a. \(1.2 \times 10^{4}\) b. \(8.25 \times 10^{-2}\) c. \(4 \times 10^{6}\) d. \(5.8 \times 10^{-3}\)

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Which number in each of the following pairs is larger? a. \(7.2 \times 10^{3}\) or \(8.2 \times 10^{2}\) b. \(4.5 \times 10^{-4}\) or \(3.2 \times 10^{-2}\) c. \(1 \times 10^{4}\) or \(1 \times 10^{-4}\) d. \(0.00052\) or \(6.8 \times 10^{-2}\)

Classify each of the following statements as an observation (O) or a hypothesis ( \(\mathrm{H}\) ): \((1.2)\) a. Analysis of a sample of 100 toys indicated that 5\% contained lead. b. Reduced \(\mathrm{CO}_{2}\) emission can help reduce global warming. c. A child with fever higher than \(40^{\circ} \mathrm{C}\) is likely to suffer damage to brain function.
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