Operations with Real Numbers
1. Addition of Real Numbers
Addition of real numbers involves combining two or more numbers to find their sum. The result of adding any two real numbers is always a real number.
Example:
\[ 3.5 + 2.7 = 6.2 \]
Here, both 3.5 and 2.7 are real numbers, and their sum, 6.2, is also a real number.
2. Subtraction of Real Numbers
Subtraction of real numbers involves finding the difference between two numbers. The result of subtracting any two real numbers is always a real number.
Example:
\[ 8.9 - 4.3 = 4.6 \]
Here, both 8.9 and 4.3 are real numbers, and their difference, 4.6, is also a real number.
3. Multiplication of Real Numbers
Multiplication of real numbers involves finding the product of two or more numbers. The result of multiplying any two real numbers is always a real number.
Example:
\[ 2.5 \times 3.2 = 8 \]
Here, both 2.5 and 3.2 are real numbers, and their product, 8, is also a real number.
4. Division of Real Numbers
Division of real numbers involves finding the quotient of two numbers. The result of dividing any two real numbers (where the divisor is not zero) is always a real number.
Example:
\[ 10.5 \div 2.5 = 4.2 \]
Here, both 10.5 and 2.5 are real numbers, and their quotient, 4.2, is also a real number.
Practical Applications
Understanding operations with real numbers is crucial for solving real-world problems. For instance, calculating the total cost of items, determining the speed of a vehicle, or finding the area of a shape all involve operations with real numbers.
Example:
If you buy 3 items each costing $4.50, you can find the total cost by multiplying: \( 3 \times 4.50 = 13.50 \). The total cost, $13.50, is a real number.