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The Arithmetic Expressions Calculator will calculate:
Arithmetic Expressions Calculator Parameters: The numbers used are integers. For exponents (ie 43) enter 4^3 [the ^ symbol is avilable on most keyboards by holding Ctrl and pressing the number 6]. Note that the calculator computes the math within the brackets in the following order (), [], {} so { 2+1 [ 4 * (4 ÷ 6) + 2 ] - 2 }
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Numbers have been used since antiquity to represent or compare various amounts of items. We can combine numbers in various ways, where the most important combination is through the four basic operations: addition, subtraction, multiplication and division.
Addition occurs when the total of two different amount is to be found. The participants in addition are called addends and the result of addition (i.e. the total) is called sum. In symbols, addition is written as
where a and b are the addends and c is the sum. For example, in the addition 3 + 4 = 7, 3 and 4 are addends and 7 is the sum.
Subtraction is the inverse operation of addition. It occurs when we remove an amount from a total, to (usually) obtain a smaller amount. The biggest number is called minuend, the smaller number subtracted from the biggest is called subtrahend and the result of subtraction is called difference. In symbols, subtraction is written as
where a is the minuend, b is the subtrahend and c is the difference. For example, in the subtraction 9 - 5 = 4, 9 is the minuend, 5 is the subtrahend and 4 is the difference.
Multiplication is a shorter way to find the sum of a repeated addition of the same addends. Thus, instead of writing n times the addition a + a + a + + a, we simply write n × a.
The numbers involved in multiplication are called factors and the result of multiplication is called product. Thus, in the operation
n and a are factors and b is the product. For example, in the multiplication 7 × 3 = 21, 7 and 3 are factors and 21 is the product.
Division is the inverse operation of multiplication. It occurs when an item a is divided into n equal parts. The number representing the item is called dividend, the number that shows in how many parts the whole is divided is called divisor and the result of division is called quotient. We write
where a is the dividend, n is the divisor and b is the quotient. For example, in the division 28 ÷ 4 = 7, 28 is the dividend, 4 is the divisor and 7 is the quotient.
Another common operation is raising a number in a certain power. This means multiplying n times a number a by itself. In other words, power is a recurrent multiplication by the same factor. Thus, instead of multiplying n times the number a by itself, i.e. b = a × a × a × (n times), we write
where a is called base, n is called exponent and b is called power. For example, in the operation 25 = 32, 2 is the base, 5 is the exponent and 32 is the power (you can test examples of this using the exponents calculator.
If all operations are involved in an arithmetic expression, then there is a hierarchy of operations, i.e. some operations have a higher order of priority than the others, and therefore, they are done first. The rule concerning this order of operation is known as the PEMDAS Rule, which is an acronym for Parenthesis - Exponents - Multiplication - Division - Addition - Subtraction and shows the order of operations in an arithmetic expression. According to PEMDASS Rule, we must begin from the part of the expression inside parenthesis (if any) where exponents are calculated first, then we do multiplications and divisions from left to right as they have the same order of priority, and at the end, after finishing with all the above operations, we conclude with addition and subtraction from left to right (they also have the same order of priority).
Another thing to point out here is the various types of parenthesis (otherwise known as brackets). Thus, if different types of brackets are used in an arithmetic expression, we begin with the expression inside the round brackets, as they are the innermost ones, then with the square brackets which include the round ones, and then with the curled brackets (which include the other two types).
This calculator is different from the other Math calculators on iCalculator™ as there is not a specific number of inputs which are combined in an expression that potentially contains:
When solving an arithmetic expression, the following must be considered:
The following Math tutorials are provided within the Arithmetic section of our Free Math Tutorials. Each Arithmetic tutorial includes detailed Arithmetic formula and example of how to calculate and resolve specific Arithmetic questions and problems. At the end of each Arithmetic tutorial you will find Arithmetic revision questions with a hidden answer that reveal when clicked. This allows you to learn about Arithmetic and test your knowledge of Math by answering the revision questions on Arithmetic.