Write Two Multiplication Sentences for an Array
Write Two Multiplication Sentences for an Array is a Grade 3 math skill from Eureka Math directly connecting arrays to the Commutative Property. An array with a rows and b columns generates two multiplication sentences: a × b and b × a. Both equal the same product. For example, a 4 × 7 array produces 4 × 7 = 28 and 7 × 4 = 28. Writing both sentences from one array reinforces that order of factors does not affect the product and that every array simultaneously represents two multiplication facts.
Key Concepts
Property An array with $a$ rows and $b$ columns can be described by two multiplication sentences: $a \times b$ and $b \times a$. Both sentences result in the same total.
Examples An array with 3 rows of 5 stars can be described by $3 \times 5 = 15$. After rotation, it has 5 rows of 3 stars, described by $5 \times 3 = 15$. An array with 3 rows of 6 dots can be described by $3 \times 6 = 18$. After rotation, it has 6 rows of 3 dots, described by $6 \times 3 = 18$.
Explanation An array can be viewed in two ways depending on how you group the objects. You can count the number of rows and the items in each row, or you can rotate the array and count the new rows and items. This shows that the order of the numbers (factors) in a multiplication problem can be swapped without changing the total (product). This is known as the commutative property of multiplication.
Common Questions
How many multiplication sentences can you write for one array?
Two. An array with a rows and b columns gives: a × b = product and b × a = product. Both equations describe the same array.
Write two multiplication sentences for an array with 3 rows and 8 columns.
3 × 8 = 24 and 8 × 3 = 24.
What property explains why both multiplication sentences for an array are true?
The Commutative Property of Multiplication: a × b = b × a. The array can be read by rows or by columns, giving the same total either way.
Why does writing two sentences for an array help with learning multiplication facts?
It shows that knowing one fact (e.g., 5 × 9 = 45) automatically gives you another (9 × 5 = 45). This halves the number of unique facts to learn.
In which textbook is Write Two Multiplication Sentences for an Array taught?
This skill is taught in Eureka Math, Grade 3.