What is multiplication? Isn’t it simply a faster method of addition? So, when you are multiplying a number by another number, you will add a number the same amount of times as the other number calls. Multiplication can be made easier than ever if you learn array multiplication. They are useful representations of multiplication concepts. Chairs arranged evenly in an auditorium or a marching troop depict arrays. You can easily calculate the participating members if you visualize them in rows and columns. So, what is an array in multiplication? How can arrays help solve multiplication problems faster? Learn all about array multiplication in the article below.
Here is what we’ll cover:
- What is an array in multiplication?
- How to write an array multiplication equation?
- How to perform array multiplication with skip counting?
- What are the benefits of array model multiplication?
- Real-life examples of array multiplication
What is an array in multiplication?
Visually seeing things can help develop a concrete understanding of important math concepts. Array employs visualizing multiplication members in rows and columns. An array is an arrangement of numbers, objects, or pictures in the form of rows and columns. A row is horizontal (from left to right), while a column (up and down) is vertical.
Each column must contain the same number of objects in an array, and the same applies to each row. They must have the same number of objects as the other rows.
How to write an array multiplication equation?
To write an array multiplication equation, you first consider the number of rows and then the number of columns. Let us look at a few examples below to understand array multiplication.
In the following figure, the array has 2 rows and 4 columns of smileys. It can also be described as a 2 by 4 array. The word “by” can be represented with a multiplication cross.
Hence, mathematically, you write an array as 2 × 4. And two times four equals eight, so the equation will be: 2 × 4 = 8
This array has 3 rows and 4 columns. It is a 3 by 4 array, and you can write it as 3 × 4. The multiplication equation will be: 3 × 4 = 12
So, you can see from the above examples that the first number represents the number of rows, and the second number represents the number of columns. So, the second array is 3 × 4, not 4 × 3, even though the calculated product, i.e. 12, will be the same either way.
How to perform array multiplication with skip counting?
What is skip counting? Skip counting is a method of counting forward by numbers other than 1. So, if you have to skip-count by a number, you will keep adding the same number in every step to the previously obtained number. It is just like repeated addition. Suppose you have to skip count by 2, so your answers will be 4, 6, 8, 10, 12, 14, and so on. So, every time you add 2 to the previous number, i.e. add 2 to 4 to get 6, add 2 to 6 to get 8, and so on.
Let us take the following donuts array example to understand how to skip count for array multiplication.
The above array has three rows, and each row has five donuts. So, there are five columns of donuts. To calculate the total number of donuts, you can simply count them. But employing skip counting speeds up the process and makes it much easier.
Here, you can skip count by 5 for every row to calculate the number of donuts. The first row has five donuts, so when you skip count by 5, the end of the second row amounts to ten, and that of the third row will give fifteen, which is your answer. It is the same as 3 × 5 =15
In the above image, you can also skip count column-wise. You will have to skip count by three as each column has three donuts. So, for five columns, the skip counting by three would go like 3, 6, 9, 12, and 15.
So, interestingly one array can have two equations: one for columns and the other for rows. In the above example, the multiplication equations are:
For rows: 3 × 5 = 15
For columns: 5 × 3 = 15
What are the benefits of array model multiplication?
Array multiplication has several benefits in understanding and solving mathematical problems. Not just Math, computer languages such as Python use NumPy array multiplication to multiply an array. Some of the key benefits of array model multiplication in mathematics are as follows:
1. Array multiplication makes it easy to visualize problems
It can be a great way to introduce multiplication with hands-on objects, but it can be tedious when working with larger numbers or doing several problems. You can use a paper dot array to slide an L-shaped cover over the top of the array. This way, you can show any multiplication fact you want. The following image represents the dot array and L-cover.
You can use the dot array and L-cover as follows. Suppose you want to explain what 6 × 8 looks like, i.e. 6 groups of 8. Slide the L-cover on the dot array as shown below.
Now, there are six rows, and each row has eight dots. You can easily calculate the total number of dots in the array by 6 × 8 = 48.
2. Array multiplication allows the use of strategies instead of rote memorization
Let us take the example of 6 × 7 to understand this. It gets tough for students to memorize answers for multiplications like this one, but they find it easier when they use 5 × 7 as a stepping stone. Students are mostly familiar with multiples of five from an early age. So, it gets much simpler when they see 6 × 7 as just one more group of 7 than 5 × 7. They will just have to add 35 + 7 to find the answer: 6 × 7 = 42.
3. Array multiplication allows students to see the commutative property in action
According to the commutative property, you will get the same answer on multiplying the same numbers in any order. For instance, whether you multiply 4 × 7 or 7 × 4, both equal the same answer: 28.
Using dot array multiplication, you can explain the multiplication facts. To explain the commutative property, turn the array 90 degrees. The dot array will show the multiplication fact, and the total number of dots won’t change.
A multiplication sentence has several numbers, and each has a special name. The numbers that you multiply are called factors. The answer obtained by multiplying the factors is called the product.
6 × 7 = 42
Here, 6 is a factor that represents the number of rows, factor 7 represents objects in each row, and product 42 represents the total number of objects.
When the array is turned on its side, things change as follows.
7 × 6 = 42
Here, factor 7 represents the number of rows, factor 6 represents objects in each row, and the product 42 is the total number of objects.
The order of the factors changes, but the product stays the same, exhibiting a mathematical property known as the Commutative Property of Multiplication.
4. Using arrays for large numbers
Using arrays, students can easily explore calculations on large numbers such as 12 x 5. The array can be split into useful chunks. For instance, 12 x 5 can be broken down to work out calculations.
12 x 5 = (10 x 5) + (2 x 5).
Although drawing dots is a good technique for beginners, it can get tedious. The blank array method helps solve complex multiplications by adopting an informal way. They teach students how to adopt other strategies, such as compensating, for the process of multiplication.
The following example shows the blank array method for multiplication. Here, for calculating 34 x 9, the student decided to do 34 x 10. Next, he takes off the 34 x 1, simplifying the process.
So, 34 x 10 = 340
340 – 34 = 306
You can also break down 34 as 30 and 4. Then, you will subtract 30 from 340, followed by 4 from the 310.
5. Multiplication arrays worksheets allow students to practice equations
Multiplication array worksheets are a great way to practice equations. Students are generally given to complete the equation to describe the array, as shown in the image below.
Real-life examples of Array multiplication
You can practice array multiplication whenever and wherever you come across arrays. They are present all around you. Following are some common real-life examples of arrays for multiplication:
- A tray of eggs
- A muffin baking tin
- A chocolate box
- Blister packs of medicines
- Water bottles in cartons
- Matrices are also arrays
- Contacts on a cell phone
- A restaurant menu
- A question paper is an array of numbered questions, where each question is assigned some marks.