Order of Factors
Order of Factors is a Grade 4 math skill in enVision Mathematics, Chapter 7: Factors and Multiples. Students learn that the order of factors does not change the product, known as the commutative property of multiplication, which helps find all factor pairs of a number more efficiently.
Key Concepts
Property The order of factors does not change the product. This is known as the commutative property of multiplication. $$a \times b = b \times a$$.
Examples For the number 16, the factor pairs (1, 16) and (16, 1) both result in the product 16: $1 \times 16 = 16$ and $16 \times 1 = 16$. For the number 12, the factor pairs (3, 4) and (4, 3) both result in the product 12: $3 \times 4 = 12$ and $4 \times 3 = 12$.
Explanation The commutative property of multiplication states that you can multiply numbers in any order and the result will be the same. This means that if you find one factor pair for a number, like (2, 9) for 18, you can switch the order to find another, (9, 2). This is useful because once you find one factor pair, you automatically know a second one just by swapping the numbers. This can make finding all the factors of a number faster.
Common Questions
What is the order of factors property?
The commutative property of multiplication states that you can multiply numbers in any order and get the same product. For example, 3 times 4 equals 12 and 4 times 3 also equals 12.
How does the commutative property help find factor pairs?
If you find one factor pair like (2, 9) for 18, you automatically know the reverse pair (9, 2) exists without additional calculation, making it faster to list all factor pairs.
What are factor pairs?
Factor pairs are two numbers that multiply together to make a given product. For example, (3, 4) and (4, 3) are both factor pairs of 12.
Why is the order of factors important in Grade 4 math?
Understanding that order does not affect the product allows students to work more efficiently when finding all factors of a number by recognizing that each pair includes its reverse.
What chapter covers order of factors in enVision Mathematics Grade 4?
Order of factors and the commutative property are covered in Chapter 7: Factors and Multiples in enVision Mathematics Grade 4.