Multiplication
In math, multiplication is the method of calculating the product between two or more numbers. It is a primary arithmetic operation. We use multiplication more often in real life. When few groups of equal sizes are combined we perform multiplication there.
What is Multiplication?
Multiplication is an operation used in math to multiply different types of numbers. The obtained result after multiplication is known as a product. For example, you bought 9 cupcakes for your birthday party and your friends bought 9 cupcakes more. Now to find the total number of cupcakes we will use multiplication here i.e., 2 times 9 is 18. This can be written in a mathematical form of multiplication expression as 2 × 9 = 18. Please note that the same calculation can also be done using addition operation as, 9 + 9 = 18 cupcakes. That is why we say that multiplication is nothing but repeated addition.
Multiplication Symbol (×)
In mathematics, we have different symbols. The multiplication symbol is one of the majorly used math symbols we use while performing multiplication. In the above section, we read about multiplication of two numbers 2 and 9. If we observe the pattern of multiplication (2 × 9 = 18), the symbol (×) is connecting the two numbers and completes the given expression. Multiplication is denoted by three symbols the cross symbol ×, by the midline dot operator (⋅), and by asterisk *.
Multiplication Formula
While performing multiplication we use some terms which are:
 Multiplicand: Total number of items in each group is called multiplicand.
 Multiplier: The number of equal groups is called multiplier.
 Product: The final result after multiplying multiplicand and multiplier is a product.
 Multiplication symbol: Cross × (which connects the entire expression.)
The multiplication formula is given as Multiplier × Multiplicand = Product
Let us understand the multiplication formula with the help of the mathematical expression.
7(multiplier) × 5 (multiplicand) = 35 (product)
Now with this basic concept of multiplication let us learn how to solve the multiplication problems.
How to Solve Multiplication Problems?
While solving multiplication problems, onedigit numbers can be multiplied in a simple way by using multiplication tables, but for larger numbers, we split the numbers into columns using their respective place values, like ones, tens, hundreds, thousands, and so on. There are two types of problems which we solve:
 Multiplication without regrouping
 Multiplication with regrouping
Let us understand the two cases with help of examples.
Multiplication Without Regrouping
Multiplication of two numbers without regrouping involves smaller numbers with the singledigit product. There is no need to take a carryover to the next higher place value in this multiplication. It is the basic level that could help a learner understand the basics of multiplication before moving on to the higher level of problems including regrouping. Let us understand this with the help of the example given below.
Example: Help James in multiplying 2022 by 4.
Solution: Follow the given steps.
Step 1: Start with ones place digits. (4 × 2 = 8)
Step 2: Multiply tens place digits. (4 × 2 = 8)
Step 3: Now multiply the digit of hundreds place. (4 × 0 = 0)
Step 4: Now multiply digits of thousands place. (4 × 2 = 8)
Step 5: 2022 × 4 = 8088.
Th H T O
2 0 2 2
× 4
8 0 8 8
Multiplication With Regrouping
Multiplication of more than two numbers with regrouping involves numbers with the 2digit product. In this type of multiplication, we need to take a carryover to the next higher place value. Let us understand this with the help of the example given below.
Example: Help Jack in multiplying 2468 with 8
Solution: Follow the given steps and try to relate them with the image given after the steps.
2468 × 8
Step 1: Start with ones place digits, multiply 8 × 8 = 64 ones which means 6 tens 4 ones. Now carry 6 tens to tens column.
Step 2: Multiply tens. 6 × 8 = 48 tens. 48 tens + 6 tens (carry from step 1) = 54 tens = 50 hundreds 4 tens. Carry 5 hundreds to hundreds column.
Step 3: Multiply hundreds. 4 × 8 = 32 hundreds. 32 hundreds + 5 hundreds (carry from step 2) = 37 hundreds = 3 thousands 7 hundreds. Carry 3 thousands to thousands column.
Step 4: Multiply thousands. 2 × 8 = 16 thousands. 16 thousand + 3 thousands (carry from step 3) = 19 thousands.
Step 5: 2468 × 8 = 19744.
Multiplication Using Number Line
A number line is a visual aid for you to understand multiplication because it allows you to jump backward and forward on each number. Let's explore multiplication using a number line. Observe the direction of arrows in the below number line image, it is towards the right side. For multiplication, we move towards the right side of the number line as while multiplying we increase the value of a number to the given number of times.
The above number line shows 3 times 6 is 18. The representation can also be written as 6 + 6 + 6 = 18. The multiplication statement can be written as, 3 × 6 = 18.
Real Life Multiplication Word Problems
The concept of multiplication is often used in our daytoday activities. We should carefully observe the situation and identify the solution using the tips and tricks that follows multiplication. Let us understand the theory behind the reallife multiplication word problems with the help of an interesting example.
Example: A box contains 245 fruits. Find the number of fruits in 4 such boxes using the multiplication formula.
Solution: To solve such multiplication word problems the easiest way is to note down the given parameters and then solve.
Given:
The total number of fruits in one box = 245
The number of boxes = 4
Total number of fruits in 4 such boxes = 245 × 4.
Step 1: Start with ones place digits, multiply 4 × 5 = 20 ones which can be written as 2 tens 0 ones. Now carry 2 tens to the tens column.
Step 2: Multiply tens, 4 × 4 = 16 tens. 16 tens + 2 tens (carry from step 1) = 18 tens = 1 hundreds 8 tens. Carry 1 hundreds to hundreds column.
Step 3: Multiply hundreds, 4 × 2 = 8 hundreds. 8 hundreds + 1 hundreds (carry from step 2) = 9 hundreds.
Step 4: 245 × 4 = 980.
H T O
1 2
2 4 5
× 4
9 8 0
Total number of fruits in 4 such boxes = 245 × 4 = 980.
Tips and Tricks on Multiplication:
Below are a few tips and tricks that you can follow while performing multiplication in your everyday life.
 In multiplication, the order of numbers does not matter. So choose the order that you are more comfortable with. When relying on memory of multiplication tables, compared to 9 × 4, students may remember 4×9 more easily.
 When multiplying three numbers, choose the two numbers that can be multiplied easily. For example, 5×17×2 will be difficult if we try to multiply 5×17 first. Instead, multiplying 5 and 2 gives 10 which is easily multiplied by 17 to get 170.
 When multiplying a 2digit number with a onedigit number, it sometimes helps to break the twodigit number as per the place values. Then multiply each part and add. For example, 37×4 can be solved mentally by breaking 37 as 30+7. Then 30×4=120 and 7×4=28. So the final answer is 120+28=148. While this may seem more tedious when written down, it is much easier to do mentally.
 Even if you don’t remember the multiplication fact, it can be easily mentally figured out. For example, 17×9 is difficult to remember. But restructure this mentally as 17×(10−1). So the answer will be 170−17=153.
Topics Related to Multiplication
Check out these interesting articles to know about multiplication and its related topics.
Multiplication Examples

Example 1: Use multiplication tricks to solve the following multiplication word problem.
The price of a book is $48. Find the price of 500 such books.Solution:
Price of one book = $48
Price of 500 books = 500 × 48H T O
5 0 0
× 4 8
4 0 0 0
+2 0 0 0 x
2 4 0 0 0The price of such 500 books is $24000.
The other way to solve this question is to simply multiply 48 by 5 and attach two zeros with the final answer. So, by multiplying 48 × 5, we get 240. But the given value is 500, so our final product will be $24000.

Example 2: Solve the following multiplication word problem.
What is 784 times 44?Solution:
Using multiplication formula, 784 times 44 = 784 × 44
Therefore, 784 times 44 is 34496.
FAQs on Multiplication
What does Multiplication Mean?
In math, the addition of equal size groups is known as multiplication. It is also called repeated addition. For example, 2 times 2 times 2 times 2 can be written as 2 × 2 × 2 × 2 = 16. Similarly, if 4 baskets contain 4 apples each, then to find the total number of apples we can write the expression in repeated addition form i.e., 4 + 4 + 4 + 4 = 16 or 4 times 4 is 16 (4 × 4 = 16).
Which Formula is Used to Perform Multiplication?
The formula we use to perform multiplication is 'Multiplier × Multiplicand = Product'. For example, 9(multiplier) × 5 (multiplicand) = 45 (product)
What Are Multiplication Strategies?
Multiplication strategies are different ways in which Multiplication can be learned. For example, using a number line, with the help of a Place Value Chart, separating the Tens and Ones and then multiplying them separately, and many others. These strategies help learners to understand the multiplication concept with a broader perspective.
What is a Multiplication Symbol?
While performing multiplication a cross (x) symbol connects the entire expression, this (x) symbol is known as the multiplication symbol. For example, 7 times 4 is 28 can be represented as 7 × 4 = 28.
What Are The Three Main Parts of Multiplication?
The 3 parts of multiplication are:
 Multiplicand: In the multiplication process, we perform multiplication using a total number of objects in each group this part is called multiplicand.
 Multiplier: In multiplication total number of such equal groups is called the multiplier.
 Product: The final result obtained after performing multiplication is known as the product.
What is an example of a Multiplication Sentence?
If we are given a statement word problem of multiplication, then first we need to write it in a number form. For example:
Statement word problem: What is 36 times 9?
Solution: 36 times 9 = 36 × 9 = 324
The 36 times 9 is 324.
What are the Properties of Multiplication?
There are various properties of multiplication that we need to keep in mind while performing multiplication. Below mentioned are few properties of multiplication with respective illustrations.
 The product of two numbers does not change when we change the order of the respective numbers. This property of multiplication is known as the commutative property of multiplication which is represented as A × B = B × A. For example, 12 × 13 = 13 × 12 = 156.
 The product of three numbers does not change when we change the grouping of the numbers. This property of multiplication is known as the associative property of multiplication which is represented as A × (B × C) = (A × B) × C = B × (A × C). For example, 12 × (13 × 5) = (12 × 13) × 5 = 13 × (12 × 5) = 780.
 The product of any number by 1 is the number itself. For example, 12 × 1 = 12. 1 is the identity element of multiplication.
 The product of zero and a number is always zero. For example, 0 × 12 = 0.
 The product of a number by the sum or difference of two numbers is the same as the sum or difference of the products of that number by the two numbers separately. This property of multiplication is known as the distributive property of multiplication which is represented as A × (B + C) = AB + AC, or A × (B  C) = AB  AC. For example, 12 × (13 + 5) = 12 × 13 + 12 × 5 = 216.