

We have recently expanded the step-by-step solutions for polynomial multiplication and division problems. In particular, polynomial multiplication and division are critical skills for upper-level high-school and college math classes. Polynomials can be added, subtracted, multiplied and divided using methods analogous to numeric arithmetic. Polynomials are sums of terms that include variables and exponents, such as 3 x 2 + 4 x – 5. In high school, students extend long arithmetic with numbers to apply to mathematical expressions called polynomials. We look forward to expanding our step-by-step support for long division to include decimals in the near future.

Presently, Wolfram|Alpha only returns step-by-step long division solutions for integers, not for decimal numbers. Step-by-Step Problem Solving Long Addition If it seems to you like every generation learns a new long arithmetic method, that may not be your faulty memory! In fact, there are many variations of the long arithmetic algorithm, and which one you learn in school can depend on a variety of factors, from geographical region to teacher preference to curriculum updates. Moreover, since there is a variety of long arithmetic methods, it can be challenging for parents to help their students. Long arithmetic can be challenging for students seeing it for the first time. While the long arithmetic algorithms can be carried out without fully thinking through the place value reasoning each time, it can be conceptually useful for students to understand the process of, for example, multiplying the ones, multiplying the tens and multiplying the hundreds, then combining those results to get the final result. 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.
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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.”
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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.
