Adding Big Numbers: Regrouping Made Easy

What You'll Learn

• Always start adding from the ones column (right side), then move left to tens, then hundreds.
• When a column adds up to 10 or more, you regroup (carry) to the next column on the left.
• Regrouping is just trading 10 ones for 1 ten, or 10 tens for 1 hundred.
• The word "regroup" means to reorganize into new groups.
• You can check your work by adding again in a different order.

Words to Know

Regroup

To trade 10 of one kind for 1 of the next bigger kind

10 ones get regrouped into 1 ten when a column is too full

Place Value

What a digit is worth based on where it sits in a number

In 47, the 4 is worth 40 because it's in the tens place

Carry

Moving the extra value to the next column when a column overflows

When 7 + 6 = 13, you carry 1 to the tens column

Column

A vertical line of digits you add together

The ones column has the 7 and the 6 in it

Sum

The total answer when you add numbers together

The sum of 47 and 36 is 83

Algorithm

A step-by-step set of rules for solving a problem

The regrouping steps are an algorithm for adding big numbers

Check What You Learned

Fun Facts

• When adding multi-digit numbers, you must align them by place value — ones under ones, tens under tens, hundreds under hundreds.

  Source: Common Core State Standards Initiative, CCSS.MATH.CONTENT.3.NBT.A.2

• You should always begin adding from the rightmost column (ones) and move left toward larger place values.

  Source: Khan Academy, "Adding multi-digit numbers"

• When a column's sum reaches 10 or more, you regroup (carry) by writing the ones digit in that column and carrying the tens digit to the next column on the left.

  Source: Khan Academy, "Addition with regrouping"

• Regrouping is the process of trading 10 ones for 1 ten, or 10 tens for 1 hundred — it is a reorganization, not a creation of new value.

  Source: Khan Academy, "Regrouping whole numbers"

• The word "regroup" means to reorganize or form into new groups.

  Source: Merriam-Webster Dictionary

• The abacus, used by ancient civilizations for thousands of years, relies on the same principle of trading groups of ten.

  Source: Britannica, "Abacus"