Regrouping Decimal Factors
Regrouping decimal factors is a Grade 5 math skill in enVision Mathematics, Chapter 4: Use Models and Strategies to Multiply Decimals. After decomposing decimals, students apply the Commutative and Associative Properties to regroup whole number parts together and decimal unit parts together, making multiplication simpler: (a x 0.1) x (b x 0.1) = (a x b) x (0.1 x 0.1).
Key Concepts
After decomposing decimals, you can use the Commutative and Associative Properties to regroup the factors. This allows you to group the whole numbers together and the decimal units together.
$$(a \times 0.1) \times (b \times 0.1) = (a \times b) \times (0.1 \times 0.1)$$.
Common Questions
How do you regroup decimal factors to simplify multiplication?
Decompose each decimal, then use the Commutative and Associative Properties to group whole number parts together and decimal unit parts together before multiplying.
How does regrouping help with decimal multiplication?
Grouping whole numbers together and decimal units together creates simpler multiplications, like (4 x 3) x (0.1 x 0.1) = 12 x 0.01 = 0.12.
What properties allow regrouping of decimal factors?
The Commutative Property (order does not matter) and the Associative Property (grouping does not matter) allow any rearrangement of factors.
Where is regrouping decimal factors taught in enVision Grade 5?
Chapter 4: Use Models and Strategies to Multiply Decimals in enVision Mathematics, Grade 5.
Why is regrouping decimal factors useful for mental math?
By separating the whole number calculation from the decimal unit calculation, students can handle each part mentally and combine for the final product.