Breaking Apart and Rearranging Factors

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.