Breaking Apart and Rearranging Factors
Breaking Apart and Rearranging Factors is a skill on Pengi from Lesson 6: Mental Math Strategies for Multiplication in enVision, Mathematics, Grade 4.
Key Concepts
Property To multiply mentally, you can break a factor into its own factors and then use the Commutative and Associative Properties to rearrange the multiplication into an easier problem. $a \times (b \times c) = (a \times b) \times c$.
Examples To solve $25 \times 8$, break apart $8$ into $4 \times 2$. The problem becomes $25 \times 4 \times 2$. Rearrange to get $(25 \times 4) \times 2$, which simplifies to $100 \times 2 = 200$. To solve $5 \times 28$, break apart $28$ into $2 \times 14$. The problem becomes $5 \times 2 \times 14$. Rearrange to get $(5 \times 2) \times 14$, which simplifies to $10 \times 14 = 140$. To solve $5 \times 48$, break apart $48$ into $4 \times 12$. The problem becomes $5 \times 4 \times 12$. Rearrange to get $(5 \times 4) \times 12$, which simplifies to $20 \times 12 = 240$.
Explanation This mental math strategy involves breaking one of the numbers in a multiplication problem into its factors. Then, you can rearrange the factors to create an easier multiplication, often by making a multiple of 10 or 100. This uses the Associative Property of Multiplication, which allows you to group and multiply factors in any order. The goal is to transform a difficult problem into a series of simpler calculations.
Common Questions
What is Breaking Apart and Rearranging Factors?
Breaking Apart and Rearranging Factors is a skill on Pengi from Lesson 6: Mental Math Strategies for Multiplication in enVision, Mathematics, Grade 4.
What grade level is Breaking Apart and Rearranging Factors for?
Breaking Apart and Rearranging Factors is part of the Grade 4 Math curriculum, covered in enVision, Mathematics, Grade 4. It is designed for students studying Math at the Grade 4 level.
How can I learn Breaking Apart and Rearranging Factors?
Pengi offers an AI-guided lesson for Breaking Apart and Rearranging Factors that walks you through the key concepts step by step. The lesson is aligned to enVision, Mathematics, Grade 4 so the content matches what you see in class.
How do I practice Breaking Apart and Rearranging Factors?
After learning the concept, use the Practice mode to work through targeted exercises on Breaking Apart and Rearranging Factors. The AI adapts to your level and gives feedback on each answer so you can identify and fix mistakes.
Which textbook covers Breaking Apart and Rearranging Factors?
Breaking Apart and Rearranging Factors is covered in enVision, Mathematics, Grade 4, specifically in Chapter 3: Use Strategies and Properties to Multiply by 1-Digit Numbers under Lesson 6: Mental Math Strategies for Multiplication. Pengi's lesson is aligned directly to this textbook so you can follow along with your class.
Is Breaking Apart and Rearranging Factors free to study on Pengi?
Yes, the core Learn and Practice modes for Breaking Apart and Rearranging Factors are available for free on Pengi. No credit card is required to start studying.