Aligning numbers based on their digits amounts to lining up the digits with the same place values.

For example, a three-digit number with no decimal uses three place values: the hundreds, tens and ones. In our base-10 number system, each digit represents a count of a certain value associated with its place in the number. The long arithmetic algorithms are rooted in the concept of place value. Long arithmetic is used to solve addition, subtraction, multiplication and division problems in writing, often by organizing numbers one on top of the other, with digits aligned in columns. We have also developed detailed step-by-step solutions for long division of whole numbers and negative numbers as well as-for the high-school level-multiplication and division of polynomials. Now, Wolfram|Alpha Pro returns step-by-step solutions for long addition, subtraction, multiplication and division problems, including ones involving decimals or negative numbers.

A fifth grader will not only be expected to “fluently multiply multi-digit whole numbers using the standard algorithm,” but also “add, subtract, multiply, and divide decimals.” The Common Core State Standards for mathematics indicate that first-grade students should learn how to add “a two-digit number and a one-digit number.” By second grade, students “add and subtract within 1000” and, in particular, “relate the strategy to a written method.” In third grade, multiplication by powers of 10 is introduced, and by fourth grade students are tasked to “use place value understanding and properties of operations to perform multi-digit arithmetic,” including multiplication and division. In the past several decades in the United States, long arithmetic has traditionally been introduced between first and fifth grade, and remains crucial for students of all ages. In grade school, long arithmetic is considered a foundational math skill.

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