Regrouping in Math

Regrouping is a fundamental concept in math, particularly in arithmetic and place value. It is also known as borrowing or carrying in some contexts. Regrouping involves changing the value of digits within a number when performing operations like addition, subtraction, multiplication, and division.

Regrouping in Addition and Subtraction

When adding or subtracting numbers, regrouping is necessary when the sum or difference of two digits is greater than 9 (or the base of the number system being used, such as 10 in the base-10 system).

For example, when adding 28 + 47:

   28
 + 47
 -----
  75

In this case, regrouping is necessary because 8 + 7 is 15, which is greater than 9. So, we regroup by carrying the 1 to the tens place and writing the 5 in the ones place.

Regrouping in Multiplication and Division

In multiplication, regrouping occurs when multiplying a digit by another digit results in a product greater than 9. For example, in 23 × 7, regrouping is necessary when multiplying 3 by 7, as the product is 21, which is greater than 9. The 2 is carried over to the tens place, and the 1 is written in the ones place.

In division, regrouping occurs when the divisor does not evenly divide the current partial remainder. In this case, a larger part of the dividend is used to form the quotient. This process may be repeated until the division is complete.

Study Guide for Regrouping

When studying regrouping, it's important to understand the place value of digits in a number and how regrouping affects the value of a number. Here are some key points to remember:

Regrouping is also known as borrowing or carrying.
Regrouping is necessary when the result of an operation exceeds the base of the number system being used (e.g., 9 in the base-10 system).
Practice regrouping in addition, subtraction, multiplication, and division to gain proficiency.
Understand the concept of place value and how regrouping affects the value of digits within a number.

By practicing regrouping and understanding its underlying principles, you can become proficient in performing arithmetic operations involving regrouping.

◂Math Worksheets and Study Guides Seventh Grade. Fraction Operations

Create And Print more Fractions worksheets with Comparing Fractions, Equivalent Fractions, and Simplifying Fractions

The resources above cover the following skills:

Number and Operations (NCTM)

Compute fluently and make reasonable estimates.

Develop and analyze algorithms for computing with fractions, decimals, and integers and develop fluency in their use.

Grade 7 Curriculum Focal Points (NCTM)

Number and Operations and Algebra: Developing an understanding of operations on all rational numbers and solving linear equations

Students extend understandings of addition, subtraction, multiplication, and division, together with their properties, to all rational numbers, including negative integers. By applying properties of arithmetic and considering negative numbers in everyday contexts (e.g., situations of owing money or measuring elevations above and below sea level), students explain why the rules for adding, subtracting, multiplying, and dividing with negative numbers make sense. They use the arithmetic of rational numbers as they formulate and solve linear equations in one variable and use these equations to solve problems. Students make strategic choices of procedures to solve linear equations in one variable and implement them efficiently, understanding that when they use the properties of equality to express an equation in a new way, solutions that they obtain for the new equation also solve the original equation.