A number line is a visual representation of numbers on a straight line. This line is used to compare numbers that are placed at equal intervals on an infinite line that extends on both sides, horizontally or vertically. As we move towards the right side of a horizontal number line, the numbers increase; as we move towards the left, the numbers decrease. Show
What is a Number Line?A visual representation of numbers on a straight line drawn either horizontally or vertically is known as a number line. Writing down numbers on a number line makes it easy for us to compare them and to perform basic arithmetic operations on them. Zero (0) is considered to be the origin of a number line. The numbers to the left of 0 are negative numbers and the numbers to the right of 0 are all positive numbers. So, we can say that on a number line, as we move towards the right, the value of numbers increases. This means that the numbers present on the right are larger than the numbers on the left. For example, 3 comes to the right of 1, so 3 > 1. Observe the vertical and horizontal number lines given below. How to Draw a Number Line?In order to draw a number line or to plot a number on it, we use the following steps.
Negative and Positive Number LineAs we discussed above, a number line has positive and negative numbers. The section of the number line to the left side of zero forms a negative number line. While, the section on the right side of zero contains all positive numbers, and it forms a positive number line. It can be extended to infinity from both ends (right and left). The parts of a number line and some of its properties are given below. Parts of a Number LineObserve the parts of a number line given below to relate to the following features of a number line.
Number Line with DecimalsWe can represent various types of numbers on a number line, such as whole numbers, fractions, decimals, integers, rational numbers, and even irrational numbers. Now, let us learn how to draw a number line with decimals. For example, let us represent 2.4 on a number line using the steps given below:
This is how we draw a number line with decimals. Inequalities on a Number LineInequality is a mathematical statement used for the comparison of quantities. We can graph inequalities on a number line by marking the part that the inequality represents. Graphing Inequalities on a Number LineLet us learn how to graph inequalities on a number line. Observe the figure given below that represents the following inequalities on a number line: x ≥ 5, x > 5, x ≤ 5, and x < 5. Example 1: Represent x ≥ 5 on a number line. Solution: In order to represent x ≥ 5 on a number line, we can follow the steps given below:
Note: It is to be noted that if the inequality says that the number is included, then we mark a filled circle on the particular number, whereas, if the inequality says that the number is not included then we mark an empty circle on the number. In the above case, it says that x is greater than or equal to 5, so we will mark a filled circle on 5. Example 2: Represent x > 5 on a number line. Solution: In order to represent x > 5 on a number line, we will follow the steps given below:
Example 3: Represent x ≤ 5 on a number line. Solution: In order to represent x ≤ 5 on a number line, we will follow the steps given below:
Example 4: Represent x < 5 on a number line. Solution: In order to represent x < 5 on a number line, we will follow the steps given below.
Tips and Tricks on Number line
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FAQs on Number LineWhat is a Number Line in Math?A number line is a visual representation of numbers on a straight line. This line is used to compare numbers that are placed at equal intervals on an infinite line that extends on both sides, horizontally or vertically. What is a Number Line Model?A number line model is a representation of numbers plotted on an infinite line that extends at both ends. What all Operations can be Performed Using Number Line?The four basic arithmetic operations of addition, subtraction, multiplication, and division can be easily performed using a number line. For addition and multiplication, we move towards the right side and for subtraction, we move towards the left side of the number line. What all Numbers can be Represented on a Number Line?We can represent real numbers on the number line. It includes the set of whole numbers, integers, fractions, decimals, rational and irrational numbers. How to Perform Addition Using Number Line?When we perform addition on a number line, we count by moving one interval at a time towards the right side. For example, if we need to solve 4 + 5, we start by marking the number 4 on the number line. Since we are adding 4 and 5, we will move 5 steps to the right. This brings us to 9. Hence, 4 + 5 = 9. How to Graph an Inequality on a Number Line?We can easily graph inequalities on a number line. For this, we just need to circle the value and shade the appropriate region on the number line. For example, let us represent x > 7 on the number line using the following steps:
(For more details, read the section 'Inequalities on a Number Line' on this page.) How to Represent Fractions on a Number Line?In order to represent fractions on a number line, we find two whole numbers between which the fraction lies. Then, we make equal intervals between those two whole numbers and appropriately mark the given fraction. How to Represent Rational Numbers on Number Line?In order to represent rational numbers on the number line, we locate two integers between which the number is lying. Then we mark the point by making equal intervals between those two points. If the rational number is in the form of an integer, then we can simply locate the point with respect to the origin and mark it. What is an Open Number Line?An open number line is an empty number line in which the numbers are not marked. It is used to create a visual model according to our requirement and convenience so that we can perform different arithmetic operations like addition and subtraction on a number line. What is a Double Number Line?Double number lines consist of 2 number lines that have corresponding pairs of values marked on them. Double number lines are commonly used to compare 2 quantities or ratios which represent a relationship. For example, the scale on a map is a double number line that shows the distance given in centimeters and the corresponding distance in kilometers. Why are Number Lines Important?Number lines are important because they make us visualize the position and order of all real numbers including positive numbers and negative numbers. They also help in understanding the basics of addition and subtraction. What does ≥ mean in an inequality?a ≥ b means that a is greater than or equal to b.
How do you use ≥?greater than or equal (≥). For example, if 6≥3, we will read it as “6 is greater than or equal to 3′. less than or equal to (≤). For example, if 6≤3, we will read it as “6 is less than or equal to 3′.
What is the boundary line for ≥ or ≤?If the original inequality is < or >, the boundary line is drawn as a dashed line, since the points on the line do not make the original sentence true. If the original inequality is ≤ or ≥, the boundary line is drawn as a solid line, since the points on the line will make the original inequality true.
What does this inequality mean ≤?Inequality. Inequality. An inequality is a mathematical relationship between two expressions and is represented using one of the following: ≤: "less than or equal to"
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