# Real number calculator

The calculator makes basic and advanced operations with real numbers, natural numbers, integers, rational and irrational numbers. It also shows detailed step-by-step information about calculation procedure. Solve problems with two, three, or more real numbers in one expression. Add, subtract, and multiply real numbers step-by-step. This calculator performs addition, subtraction, multiplication, or division for calculations on positive or negative real numbers. This online real number calculator will help you understand how to add, subtract, multiply, or divide real numbers.

Real numbers are numbers that can be found on the number line. This includes the natural numbers( 1,2,3 ...), integers (-3) rational (fractions) and irrational numbers (like √2 or π). Positive or negative, large or small, whole numbers or decimal numbers are all real numbers. Imaginary numbers and complex numbers cannot be draw in number line, but in complex plane.

#### Examples:

addition of real numbers: -3/2 + pi/2
subtraction of real numbers: 32.14 - 67.32
parenthesis: sin(pi/2) * (1.1+2.2+3.3)
Complex example: Priority of operators and brackets: 3⋅[8−(−1) + (−3)÷(−3)]^2

## Real numbers in word problems:

• Evaluate 18 Evaluate the expression (-4-7i)-(-6-9i) and write the result in the form a+bi (Real + i* Imaginary).
• Complex plane mapping Show that the mapping w = z +c/z, where z = x+iy, w = u+iv and c is a real number, maps the circle |z| = 1 in the z-plane into an ellipse in the (u, v) plane.
• The diameter 2 The diameter of the Earth is 12,756 kilometers. If Mercury's diameter is about 7,876.6 kilometers shorter than that of the Earth, what is the diameter of Mercury?
• Is complex Are these numbers 2i, 4i, 2i + 1, 8i, 2i + 3, 4 + 7i, 8i, 8i + 4, 5i, 6i, 3i complex?
• Is equal Is equal following terms? -9 21 = (-9) 21
• Decimal number I am a decimal number between 0.3 and 0.5 . the digit in my hundredths place is 5 more than the digit in tenth place, off the number in tenth place is 4. what is the number?
• Imaginary numbers Find two imaginary numbers whose sum is a real number. How are the two imaginary numbers related? What is its sum?
• Fruit punch 2 Alberto makes fruit punch with 24.2 ounces of apple juice and 18.4 ounces of pineapple juice. He splits the fruit punch equally into 6 glasses. How much fruit punch is in each glass?
• Write 3 Write a real-world problem involving the multiplication of a fraction and a whole number with a product that is between 8 and 10, then solve the problem.
• Two midpoints Point A is on a number line halfway between -17 and 5 . Point B is halfway between Point A and 0. What integer does Point B represent?
• The sum 15 The sum of the real numbers x and y is 24. Their difference is 12. What is the value of xy?
• On the number line What number is exactly in the middle between 9.8 and -2.4 on the number line?
• Which 8 Which among the following real numbers below is the least? A. 5/8 B. 0.75 C. 7/10 D. 35/99
• Equation with abs value How many solutions has the equation (|x| +x) |x-3| = |x+1| in the real numbers?
• Subtract 4 Subtract the following decimals. a. 0.98 - 0.053 b. 0.67 - 0.4 c. 0.3 - 0.002 d. 3.2 - .789 e. 6.53 - 4.298 f. 6 - 4.32 g. 7 - 3.574 h. 4.83 - 1.8 i. 3.7 - 1.8 j. 16.17 - 11.632
• Logarithmic equation Solve equation: log13(7x + 12) = 0
• Sum and product The sum of the real numbers x and y is 12. Their difference is 8. What is the value of xy?