Placing Real Numbers on the Number Line: An Easy Guide

Feb 07, 2023

A real number is any number that can be found on the number line, including both positive and negative numbers, whole numbers, and decimal numbers. Simply put, real numbers are all the numbers that exist in the mathematical universe, including the rational and irrational numbers.

I. Placing real numbers in the number line

  • Real numbers are numbers that can be placed on a number line. A number line is a line where every point on the line corresponds to a real number and every real number corresponds to a point on the line.
  • The real numbers include all rational numbers (such as integers, fractions, and decimals) and irrational numbers (such as √2, π, etc.).
  • Real numbers can be positive, negative, or zero, and can be represented on the number line with arrows pointing to the right for positive numbers and to the left for negative numbers, with zero at the origin.

II. Addition, Subtraction, Multiplication, Division of Real Numbers

  • Addition of real numbers is straightforward and follows the commutative, associative, and distributive properties. For example, if a and b are real numbers, then (a + b) + c = a + (b + c) and a + b = b + a.
  • Subtraction of real numbers is defined as the addition of the opposite. If a and b are real numbers, then a - b = a + (-b), where -b is the opposite of b.
  • Multiplication of real numbers is also straightforward and follows the commutative, associative, and distributive properties. For example, if a, b, and c are real numbers, then \((a \times b) \times c = a \times (b \times c)\) and \(a \times b = b \times a\).
  • Division of real numbers is defined as the multiplication of the numerator by the reciprocal of the denominator. If a and b are real numbers and b ≠ 0, then a/b = \(a \times (1/b)\), where 1/b is the reciprocal of b.

Examples:

Which of the following numbers are real numbers: √2, π, 3.14, -4?
Answer: All of them are real numbers.

Where would you place the number -5 on the number line?
Ans: -5 would be placed to the left of the origin (0) on the number line.

Which real number is represented by the point exactly in the middle of 2 and 4 on the number line?
Answer: The real number represented by the point exactly in the middle of 2 and 4 on the number line is 3.

Which real number is represented by the point that is twice as far from 0 as 2 is on the number line?
Answer: The real number represented by the point that is twice as far from 0 as 2 is on the number line is 4

Simplify the expression 2 + (-3).
Answer: 2 + (-3) = -1

Multiply -5 and 3.
Answer: \(-5 \times 3 = -15\)

Evaluate \((2 + 3) \times 4\).
Answer: \((2 + 3) \times 4 = 5 \times 4 = 20\)

Subtract 7 from -2.
Answer: -2 - 7 = -9

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Article Posted in: Maths

John Horton

John Horton is a highly respected mathematician who has made significant contributions to the field of mathematics through his research and writing. He is known for his innovative and playful approach to mathematical concepts, making them accessible and enjoyable to a wide range of readers. With several books published on mathematics and science, he has become a popular author in the field of popular mathematics.His writing style is clear, concise, and filled with humor, making complex mathematical ideas easy to understand. He has received many accolades for his work, and is widely regarded as a gifted educator and communicator of mathematics.

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