Arithmetic Expressions Calculator | iCalculator™ (2024)

The Arithmetic Expressions Calculator will calculate:

  1. The value of an arithmetic expression using the PEMDAS rule.

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 }

Arithmetic Expressions Calculator
Arithmetic Expressions Results (detailed calculations and formula below)
The answer to the Arithmetic Expression is
Arithmetic Expressions calculations
Arithmetic Expressions Calculator Input Values

Theoretical description

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

a + b = c

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

a - b = c

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 × a = b

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

a ÷ n = b

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

b = an

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).

Using the Arithmetic Expressions Calculator

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:

  1. Three types of brackets: round (the innermost), square (that include the round ones); and curled - the outermost (that include the other two types). There may also be some numbers outside the curled brackets.
  2. Five basic operations that include: a) powers (exponents) that are done first; b) division and multiplication that are done simultaneously starting from left to right after having completed the operations with exponents, and c) addition and subtraction that are done simultaneously starting from left to right after having completed divisions and multiplications.

When solving an arithmetic expression, the following must be considered:

  1. Operations start from the part of expression inside the curved brackets; after completing it, we focus on square ones, then the curled ones and finally the rest of operations outside brackets.
  2. Two consecutive operations of the same order (for example one multiplication and one division) must be carried out one by one, while when they have an addition or subtraction in-between, they can be done simultaneously.

Example of math calculations using the PEMDAS rule

18 - 3 × 4 + {20 ÷ [10 + 2 × (3 × 22 - 21 ÷ 3)]} - 3 × 2
= 18 - 3 × 4 + {20 ÷ [10 + 2 × (3 × 4 - 21 ÷ 3)]} - 3 × 2
= 18 - 3 × 4 + {20 ÷ [10 + 2 × (12-7)]} - 3 × 2
= 18 - 3 × 4 + {20 ÷ [10 + 2 × 5]} - 3 × 2
= 18 - 3 × 4 + {20 ÷ [10 + 10]} - 3 × 2
= 18 - 3 × 4 + {20 ÷ 20} - 3 × 2
= 18 - 3 × 4 + 1 - 3 × 2
= 18 - 12 + 1 - 6
= 6 + 1 - 6
= 7 - 6

Arithmetic Math Tutorials associated with the Arithmetic Expressions Calculator

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.

  • 1.1 - Numbering Systems, a Historical View
  • 1.2 - Number Sets, Positive and Negative Numbers and Number Lines
  • 1.3 - Operations with Numbers and Properties of Operations
  • 1.4 - Order of Operations and PEMDAS Rule
  • 1.5 - Multiples, Factors, Prime Numbers and Prime Factorization including LCM and GCF
  • 1.6 - Divisibility Rules
  • 1.7 - Decimal Number System and Other Numbering Systems

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Arithmetic Expressions Calculator | iCalculator™ (2024)


How to find an arithmetic expression? ›

An arithmetic expression is an expression built up using numbers, arithmetic operators (such as +, , -, / and ) and parentheses, "(" and ")". Arithmetic expressions may also make use of exponents, for example, writing 23as an abreviation for ((2 2) 2).

How do you write an arithmetic expression? ›

Arithmetic expressions consist of arithmetic terms that are combined by arithmetic operations. An arithmetic expression consists of arithmetic terms, such as x, x2, xy, or 3xy2, combined by arithmetic operations, such as addition, subtraction, multiplication, and division.

How to do arithmetic calculations? ›

An arithmetic problem should be solved by performing any multiplication or division operation first, moving left to right through the problem. Then we will perform any addition or subtraction operations, again moving left to right through the problem.

What are calculators made for? ›

A calculator is a device that performs arithmetic operations on numbers. Basic calculators can do only addition, subtraction, multiplication and division mathematical calculations.

How do you calculate arithmetic? ›

One method is to calculate the arithmetic mean. To do this, add up all the values and divide the sum by the number of values. For example, if there are a set of “n” numbers, add the numbers together for example: a + b + c + d and so on. Then divide the sum by “n”.

What's arithmetic formula? ›

The arithmetic sequence formula refers to the formula to calculate the general term of an arithmetic sequence and the sum of the n terms of an arithmetic sequence. The general term of an arithmetic sequence is, an = a1 + (n - 1) d. The sum of the first 'n' terms of an arithmetic sequence is, n = (n/2) [2a1 + (n - 1) d]

How do you solve arithmetic terms? ›

Finding the nth term of an arithmetic sequence:

We know the nth term of an arithmetic sequence is given by a n = a + ( n − 1 ) d . Therefore, the 15th term of the given sequence is a 15 = 21 + ( 15 − 1 ) 3 = 21 + 14 ⋅ 3 = 21 + 42 = 63 .

What is an example of arithmetic in math? ›

Addition is among the basic operations in arithmetic. In simple forms, addition combines two or more values into a single term, for example: 2 + 5 = 7, 6 + 2 = 8, where '+' is the addition operator. The procedure of adding more than two values is called summation and involves methods to add n number of values.

What is arithmetic calculator? ›

An electronic calculator is typically a portable electronic device used to perform calculations, ranging from basic arithmetic to complex mathematics. An electronic pocket calculator with a seven-segment liquid-crystal display (LCD) that can perform arithmetic operations A modern scientific calculator with an LCD.

What is basic math called? ›

Arithmetic is the fundamental branch of mathematics that studies numbers and their operations. In particular, it deals with numerical calculations using the arithmetic operations of addition, subtraction, multiplication, and division.

What are the 4 rules of math? ›

The '4 rules' (addition, subtraction, multiplication and division) are at the heart of calculation and problem solving. Over the years a range of teaching methods has been adopted by schools and it is sometimes the case that parents' experiences are not the same as those of their children.

What is a fancy calculator called? ›

A scientific calculator is an electronic calculator, either desktop or handheld, designed to perform calculations using basic (addition, subtraction, multiplication, division) and complex (trigonometric, hyperbolic, etc.) mathematical operations and functions.

How do calculators multiply? ›

Interlocking mechanisms between the numeral wheels automatically provide for carryovers. Multiplication is performed by repeated addition; subtraction is done by an indirect method; and division is done by repeated subtraction.

How to get infinity in calculator? ›

- Look for a key labeled "∞" or a symbols menu where you can select "∞". If you are using a different model of calculator, the process may vary slightly, but it typically involves accessing a secondary function or special symbols menu to find the infinity symbol.

How do you identify an arithmetic sequence? ›

If the sequence has a common difference, it is arithmetic; if it has a common ratio, it is geometric. We can therefore determine whether a sequence is arithmetic or geometric by working out whether adjacent terms differ by a common difference, or a common ratio.

How to evaluate an arithmetic expression? ›

Parentheses may be used in expressions to specify the order of evaluation. Expressions within parentheses are evaluated first. When parentheses are nested, the innermost set of parentheses is evaluated first, and then successively more inclusive parentheses are evaluated.

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