A. On a number line, numbers lie to the right of zero and...

a. On a number line, ______numbers lie to the right of zero and______ numbers lie to the left of zero. b. The numbers $\ldots-3,-2,-1,0,1,2,3, \ldots$ are called _______. c. The distance between a number and zero on the number line is called its ______ value. d. Two numbers that are the same distance from zero on the number line, but on opposite sides of zero are called ______.

a. On a number line, ______numbers lie to the right of zero and______ numbers lie to the left of zero.
b. The numbers $\ldots-3,-2,-1,0,1,2,3, \ldots$ are called _______.
c. The distance between a number and zero on the number line is called its ______ value.
d. Two numbers that are the same distance from zero on the number line, but on opposite sides of zero are called ______.

Key Concepts

Absolute Value

Absolute value is a concept that measures the distance of a number from zero on the number line, without considering direction. It is always a non-negative number, reflecting the magnitude of a number irrespective of its sign. This concept is fundamental in mathematics, particularly in solving equations and inequalities that involve distance or magnitude.

Integers

Integers include the entire set of whole numbers along with their negative counterparts and zero. They form a number system that does not include fractions or decimals and are commonly used in various mathematical operations. This system is essential for understanding number comparisons, sequences, and properties affected by sign and magnitude.

Opposites/ Additive Inverses

Opposites, or additive inverses, are pairs of numbers that have the same absolute value but are on opposite sides of zero. When added together, they sum to zero. This concept is pivotal in understanding the balancing of equations and the properties of numbers within the additive number system, where every number has a unique counterpart that cancels it out.

Positive Numbers

Positive numbers are the set of numbers that are greater than zero. These numbers lie to the right of zero on the number line and represent quantities or values that indicate an increase or a gain. They are used in various branches of mathematics to show addition, growth, or any measurement that is above the baseline of zero.

Negative Numbers

Negative numbers are the numbers that are less than zero. They appear to the left of zero on the number line and are often used to represent a loss, a decrease, or values below a designated neutral point. In many contexts, such as temperature or debt, negative numbers help illustrate values that fall below an established baseline.

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