How to do Calculations with a Number line

In math Calculations, a number line can be defined as a straight with numbers placed at equal or segments along its length.

A number line can be extended infinitely in any direction and is usually represented horizontally. A knowledge of the properties of numbers is fundamental to the study of mathematics. Students who possess this knowledge will be well-prepared for the study of all aspect of mathematical Calculations.

A number line can also be used to represent both positive and negative integers as well.

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Writing numbers on a number line makes comparing numbers easier. Numbers on the left are smaller than the numbers on the right of the number line.

A number line can also be used to carry out addition, subtraction and multiplication. We always move right to , move left to  and skip count to . Much of the terminology used in this post can be most easily illustrated by applying it to numbers. For this reasons we strongly recommend that you work through this fundamental concept even though it is familiar. Let us start with number line that we learnt in secondary school, a useful way of picturing numbers is to use a number line. Here positive numbers are represented on the right-hand side of this line, negative numbers on the left-hand side. Any whole or fractional number can be represented by a point on this line which is also called the real number line, or simply the real line.

Note that a minus sign is always used to indicate that a number is negative, whereas the use of a plus sign is optional when describing positive numbers. The line extends indefinitely both to the left and to the right. Mathematically we say that the line extends from minus infinity to plus infinity. The symbol for infinity is ∞. The symbol > means ‘greater than’; example 12 > 9. Given any number, all numbers to the right of it on the number line are greater than the given number. The symbol < means ‘less than’; for example −6 < 13. We also use the symbols ≥ meaning ‘greater than or equal to’ and ≤ meaning ‘less than or equal to’. For example, 5 ≤ 10 and 5 ≤ 5 are both

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true statements. Sometimes we are interested in only a small section, or interval, of the real line. The writing [1,4] means all the real numbers between 1 and 4 inclusive, that is 1 and 4 are included in the interval. So therefore the interval [1,4] comprises of all real numbers x, such that 1 ≤ x ≤ 4. The square brackets, [,] mean that the end-points are included in the interval and such an interval is said to be closed. We write (1,4) to represent all real numbers between 1 and 4, but not including the end-points. Thus (1,4) means all real numbers x such that 1 < x < 4, and such an interval is said to be open. An interval may be closed at one end and open at the other. For example, (1,4] consists of all numbers x such that 1 < x ≤ 4. Intervals can be represented on a number line. A closed end-point is denoted by •; an open end point is denoted by ◦.