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Number lines are used to visually represent various relationships between integers, fractions, and decimals. They illustrate how mathematical operations work in these relationships, such as how adding or subtracting different numbers will move you in different directions. Some number lines are shown with arrows pointing in opposite directions on either end of the line to designate a continuity of numbers in positive and negative directions: The number line is shown as a line with equally spaced "tick marks" along the whole line. Some ticks may purposely be left out or left blank so that you have to find solutions for the missing values. Numbers to the left of zero are negative, with the (‐) sign always shown, and numbers to the right of zero are positive, but the (+) sign is usually not shown. If you move to the right on the number line, the numbers always increase in size, and if you move to the left on the number line, the numbers always decrease in size. Remember, this means that when it comes to negative numbers, -3 < -2 < -1, the closer a negative number is to zero, the greater it is. However, the closer a positive number is to zero, the smaller it is. Be careful with this concept, since it is very easy to miss a question because of this! Unless specifically noted, number lines are generally drawn to scale, which will enable you to make accurate estimations of distances and positions of points on a number line. Not all numbers will always be explicitly shown. Some problems may deal exclusively with the multiples of a number, as shown below. Example Number Line Problems Solve for the blank values: Did you get -6 and 2 for the missing numbers? This number line has evenly spaced tickets, which are 2 apart. It is possible that some problems include number lines that are not drawn to scale, but require you to solve equations and understand the relative order of numbers. Work through the following example to solidify your understanding. Solution Fractions in a Number Line Solution Please note that the possible values listed above are not the only solutions to the question! Be aware as you approach all of the number line questions that you are being asked to relate numbers positionally and that negative numbers such as -1 are greater than -5, since they are closer to 0! Practice Problems Answers to Practice Problems -1 15 C 2 A < C < B
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