# Multiplication sentence

A multiplication sentence is a number sentence used to express multiplication.

## What is a multiplication sentence

A multiplication sentence is a type of equation made up of 3 numbers. It represents the operation of multiplication. In the multiplication sentence, the first two numbers are called factors and the last number is called the product. Usually, the multiplication sentence is constructed as follows:

- The first factor is the number of groups of objects.
- The second factor is the number of objects in each group.
- The third number, the product, is the total number of objects.

### Parts of a multiplication sentence

Each part of the multiplication sentence has a specific name, 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 discussed above, the first factor is often presented as the group of objects while the second factor is presented as the number of objects in each group; this can be helpful when first teaching or learning multiplication sentences, but due to the commutative property, this is not something that is typically carried through as a student progresses in their mathematical studies.

Regardless of what order the factors are multiplied in, 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 "×."

### How to write a multiplication sentence

To write a multiplication sentence, use the following steps:

- Determine how many groups of objects you have, and write this as the first factor.
- The first factor is followed by a multiplication sign which is then followed by the second factor, which indicates the number of objects in each group.
- The second factor is followed by an equals sign (=), after which the total number of objects is written, completing the multiplication sentence.

## 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.

Examples

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.

Example

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.