Placing Real Numbers on the Number Line: An Easy Guide

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

Are you having trouble understanding real numbers? Look no further! LearnPick is here to help. Our platform connects students with experienced and knowledgeable tutors who specialize in teaching real numbers and other mathematical concepts. Our tutors are available to work with you one-on-one, helping you to build a strong foundation in real numbers and to achieve your academic goals. So why wait? Sign up today and find the right tutor for you.