Signed numbers are a set of numbers that include both positive and negative values, represented by a sign (+ or -) in front of the number. They are used to describe quantities that have direction or can be above or below a reference point.
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Signed numbers can be used to represent quantities that have direction, such as temperature above or below freezing, elevation above or below sea level, and financial gains or losses.
The absolute value of a signed number is the distance of the number from zero on the number line, regardless of its sign.
When adding or subtracting signed numbers, the signs of the numbers determine the direction of the result.
Multiplying or dividing signed numbers follows specific rules, where the sign of the result depends on the signs of the factors.
Signed numbers are essential in many mathematical operations, such as solving equations, graphing functions, and understanding concepts like vectors and complex numbers.
Review Questions
Explain how signed numbers are used to represent quantities with direction or reference points.
Signed numbers are used to represent quantities that have a direction or are measured in relation to a reference point. For example, temperature can be represented using signed numbers, with positive values indicating temperatures above a reference point (such as freezing) and negative values indicating temperatures below that reference point. Similarly, elevation can be represented using signed numbers, with positive values indicating heights above sea level and negative values indicating depths below sea level. Signed numbers allow for the clear representation of these types of directional or relative quantities.
Describe the relationship between signed numbers and the number line.
The number line is a visual representation of the set of real numbers, with positive numbers to the right of zero and negative numbers to the left. Signed numbers are directly related to the number line, as they indicate the position of a number on the line. The absolute value of a signed number represents the distance of that number from zero on the number line, regardless of its sign. Understanding the number line and how signed numbers are positioned on it is crucial for performing operations with signed numbers, such as adding, subtracting, multiplying, and dividing.
Analyze the rules for performing operations with signed numbers and explain how they are applied in various mathematical contexts.
The rules for performing operations with signed numbers are essential for understanding and applying them in various mathematical contexts. When adding or subtracting signed numbers, the signs of the numbers determine the direction of the result. For example, adding a positive number and a negative number is equivalent to subtracting the absolute value of the negative number. When multiplying or dividing signed numbers, the sign of the result depends on the signs of the factors, with a positive and a negative resulting in a negative, and two negatives resulting in a positive. These rules allow for the efficient manipulation of signed numbers in equations, graphing functions, and working with concepts like vectors and complex numbers. Understanding and applying these rules is crucial for success in pre-algebra and beyond.