Concept: Regrouping Products
Regrouping Products is a Grade 5 math concept from Illustrative Mathematics Chapter 4 (Wrapping Up Multiplication and Division with Multi-Digit Numbers) that explains why and how we carry digits during multiplication. When the result of multiplying within one place value is 10 or more, we regroup the excess into the next higher place value — the key idea behind carrying in the standard multiplication algorithm.
Key Concepts
When the result of multiplying in one place value is 10 or more, we regroup it into groups of the next higher place value. For example, a product of 35 ones is regrouped as 3 tens and 5 ones.
$$35 \text{ ones} = 3 \text{ tens} + 5 \text{ ones}$$.
Common Questions
What is regrouping in multiplication?
Regrouping in multiplication means converting 10 or more units of one place value into 1 unit of the next higher place. For example, a product of 32 ones is regrouped as 3 tens and 2 ones. This is the carry step in the standard algorithm.
How does regrouping work in multi-digit multiplication?
When multiplying digits gives a two-digit result (10 or more), write the ones digit in the current column and carry the tens digit to the next column. For example, 4 × 8 = 32: write 2, carry 3.
What chapter covers regrouping products in Illustrative Mathematics Grade 5?
Concept: Regrouping Products is covered in Chapter 4 of Illustrative Mathematics Grade 5, titled Wrapping Up Multiplication and Division with Multi-Digit Numbers.
Why do we carry in multiplication?
Carrying (regrouping) in multiplication is necessary because each place value column can only hold single digits (0-9). When a column's product reaches 10 or more, the overflow is moved to the next column as a new, larger unit.
What is an example of regrouping in multiplication?
Product 4 × 8 = 32: regroup as 3 tens and 2 ones. Write 2 in the ones column and carry 3 to the tens column. Product 6 × 7 = 42: write 2 in the current column and carry 4.