Multiplication sentence

A multiplication sentence is a number sentence used to express multiplication. It is a type of equation that is limited to the operation of multiplication. Multiplication sentences are made up of at least three terms: two factors and a product, as shown in the figure below.

In a multiplication sentence, the second factor is referred to as the multiplicand. It is the number that is multiplied by the first factor, referred to as the multiplier. However, since multiplication exhibits the commutative property, which means that the position of either of the two factors in a multiplication problem can be switched, the terms multiplicand and multiplier can be ambiguous. As such, most texts simply refer to both terms as factors rather than using the terms "multiplicand" and "multiplier." In either case, the solution to a multiplication problem is referred to as its product. The symbol "·" is also used to denote multiplication; it means the same thing as "×."

Practicing multiplication with multiplication sentences

There are a variety of ways to practice multiplication using multiplication sentences such as filling in missing parts of the multiplication sentence or generating multiplication sentences based on an array.


Complete the following multiplication sentences

1. 6 × 6 = ?

6 × 6 = 36

2. ? × 4 = 28

7 × 4 = 28

3. 4 × ? = 28

4 × 7 = 28

Notice that in the last 2 examples, the positions of the factors are changed, but the product is the same. This is because multiplication, like addition, exhibits the commutative property.

Another way to practice multiplication involves using arrays. An array is an arrangement of objects, typically using rows and columns, that can very effectively represent multiplication. Having students write multiplication sentences to represent a given array can help test and improve their grasp of the concept of multiplication.


Express the number of objects in the following array as a multiplication sentence.

There are 3 rows and 4 columns in the above array, so the array can be referred to as a "three by four array." This tells us what we are multiplying, so all we need to do to write the multiplication sentence is determine the product:

3 × 4 = 12

Using arrays is a very common method for teaching multiplication since it allows for visualization of the multiplication problem as well as confirmation (through counting/addition) of the solution. It also demonstrates the value of multiplication over addition, in terms of efficiency, in cases where multiplication is applicable.