Multiplication

In math, multiplication is the method of finding the product of two or more numbers. It is a primary arithmetic operation that is used quite often in real life. Multiplication is used when we need to combine groups of equal sizes. Let us learn more about multiplication in this page.

Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers. Multiplication is used to simplify the task of repeated addition of the same number.

Example: If there are 6 boxes of cupcakes and each box has 9 cupcakes, find the total number of cupcakes.

Solution: We can solve this question by addition but it would take longer to add these to get the answer. That is, 9 + 9 + 9 + 9 + 9 + 9 = 54 cupcakes. In other words, when we have larger numbers to work upon, then multiplication is useful.

Now, let us use multiplication to solve this problem. We will multiply the number of boxes with the number of cupcakes in each box. If we multiply 6 × 9, we will get the total number of cupcakes, which is 6 × 9 = 54 cupcakes. Thus, we can see that we get the same result in a shorter period of time. This is the reason why multiplication is also termed as repeated addition.

Multiplication Symbol (×)

In mathematics, we have different symbols. The multiplication symbol is one of the commonly used math symbols. In the example given above, we learnt about the multiplication of two numbers 6 and 9. If we observe the expression of multiplication (6 × 9 = 54), we can see that the symbol (×) connects the two numbers and completes the given expression. Apart from the cross symbol (×), multiplication is also denoted by the mid-line dot operator (⋅), and by the asterisk sign (*).

The multiplication formula is expressed as, Multiplicand × Multiplier = Product; where:

• Multiplicand: The first number (factor).
• Multiplier: The second number (factor).
• Product: The final result after multiplying the multiplicand and multiplier.
• Multiplication symbol: '×' (which connects the entire expression)

Let us understand the multiplication formula with the help of the following expression.

7(multiplicand) × 5 (multiplier) = 35 (product)

Using this basic concept of multiplication let us learn how to solve multiplication problems.

While solving multiplication problems, one-digit numbers can be multiplied in a simple way by using the 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 multiplication problems:

• Multiplication without regrouping
• Multiplication with regrouping

Let us understand the two cases with the help of examples.

Multiplication Without Regrouping

Multiplication of two numbers without regrouping involves smaller numbers where there is no need to take a carry-over to the next higher place value. 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: Multiply 3014 by 2.

Solution:

• Step 1: Start with the digit in ones place. (2 × 4 = 8)
• Step 2: Multiply 2 with the digit in tens place. (2 × 1 = 2)
• Step 3: Now, multiply 2 with the digit in hundreds place. (2 × 0 = 0)
• Step 4: Now multiply 2 with the digit in thousands place. (2 × 3 = 6)
• Step 5: 3014 × 2 = 6028.

Th H T O
3 0 1 4
× 2
6 0 2 8

Multiplication With Regrouping

Multiplication of more than two numbers with regrouping involves numbers with a 2-digit product. In this type of multiplication, we need to take a carry-over to the next higher place value. Let us understand this with the help of the example given below.

Example: Multiply 2468 with 8

Solution: Let us multiply 2468 × 8 using the steps given below and try to relate them with the figure given after the steps.

• Step 1: Start with the digit in ones place, that is, 8 × 8 = 64 ones which means 6 tens 4 ones. Now, carry 6 tens to the tens column.
• Step 2: Multiply 8 with the digit in the tens place, that is, 8 × 6 = 48 tens. Now, we will add this to the carry-over. This means, 48 + 6 (carry-over from step 1) = 54. Carry 5 to the hundreds column.
• Step 3: Multiply 8 with the digit in the hundreds place, that is, 8 × 4 = 32 hundreds. Now, let us add this to the carry-over from the previous step. This means, 32 + 5 (carry-over from step 2) = 37. We will again carry 3 to thousands column.
• Step 4: Multiply 8 with the digit in the thousands place, that is, 8 × 2 = 16 thousands. So, let us again add this to the carry-over, that is, 16 + 3 (carry-over from step 3) = 19
• Step 5: Therefore, the product of 2468 × 8 = 19744.

Multiplication on a number line means to apply the multiplication operation on a given set of numbers through a number line. A number line is a visual representation of numbers on a straight line. We know that multiplication is also known as repeated addition. So, to perform multiplication on a number line, we start from zero and move towards the right side of the number line for the given number of times.

Example: Multiply 3 × 5 using a number line.

Solution: Observe the following number line to see the working of 3 × 5 = 15. We will start from 0 and move towards the right of the number line We will form 3 groups of 5 equal intervals. This will take us to 15.

The above number line shows 3 times 5 is 15. The representation can also be written as 5 + 5 + 5 = 15. The multiplication statement is expressed as, 3 × 5 = 15.

Multiplication word problems can be easily solved by carefully observing the situation and identifying the solution. Let us understand the theory behind the real-life 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 the digit in ones place. Multiply 4 × 5 = 20. Now carry 2 to the tens column.
Step 2: Multiply 4 with the digit in tens place, that is, 4 × 4 = 16. Now, add this to the carry-over from the previous step. 16 + 2 (carry-over from step 1) = 18. From this, carry 1 to the hundreds column.
Step 3: Multiply 4 with the digit in hundreds place, 4 × 2 = 8 hundreds. 8 + 1 (carry-over from step 2) = 9.
Step 4: Therefore, the product of 245 × 4 = 980.

H T O
1 2
2 4 5
× 4
9 8 0

Therefore, the total number of fruits in 4 such boxes = 245 × 4 = 980.

Tips and Tricks on Multiplication:

Here is a list of a few tips and tricks that can be used while performing multiplication.

• In multiplication, the order of numbers does not matter. So choose the order that you are more comfortable with. When using the 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, multiplying 5 × 17 × 2 will be difficult if we try to multiply 5 × 17 first. Instead of this, multiplying 5 and 2 gives 10 which can be easily multiplied by 17 to get 170.
• When multiplying a 2-digit number with a one-digit number, it sometimes helps to break the two-digit 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 solve mentally.
• Even if you do not remember the multiplication fact, it can be easily mentally figured out. For example, 17 × 9 is difficult to remember. But this can be restructured mentally as 17 × (10 - 1). So, the answer will be 170 - 17 = 153.

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What Does Multiplication Mean?

Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers. Multiplication is used to simplify the task of repeated addition of the same number. It is used when we need to combine groups of equal sizes. For example, if 5 baskets contain 4 apples each, then to find the total number of apples we can use multiplication and solve it as 5 × 4 = 20 apples.

Which Formula is Used to Perform Multiplication?

The formula that we use to perform multiplication is 'Multiplicand × Multiplier = Product'. For example, 9 (multiplicand) × 5 (multiplier) = 45 (product)

What are the Properties of Multiplication?

The different properties of multiplication are given below.

• Commutative property of multiplication: The product of two numbers does not change if we change the order of the 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.
• Associative property of multiplication: The product of three or more 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.
• Identity property of multiplication: If any number is multiplied by 1, the product is the number itself. For example, 12 × 1 = 12. Here, 1 is the identity element of multiplication.
• Zero property of multiplication: If any number is multiplied by 0, the product is always zero. This is the zero property of multiplication. For example, 12 × 0 = 0.
• Distributive property of multiplication: As per the distributive property of multiplication, when we multiply a number with the sum of two or more addends, we get a result that is equal to the result that is obtained when we multiply each addend separately by the number. This property is also applicable to subtraction and is represented as A × (B + C) = AB + AC, or A × (B - C) = AB - AC. For example, 12 × (13 + 5) = (12 × 13) + (12 × 5) = 216.

What is the Multiplication Symbol?

While performing multiplication, we use a cross (×) symbol which connects the entire expression, this (×) symbol is known as the multiplication symbol. For example, 7 times 4 is 28 can be represented as 7 × 4 = 28.

What are the Parts of Multiplication?

The different parts of multiplication are expressed as follows. Let us understand this with an example: 6 × 4 = 24.

• Multiplicand (Factor): Multiplicand is the first number. In this case, 6 is the multiplicand.
• Multiplier (Factor): Multiplier is the second number. In this case, 4 is the multiplier.
• Product: The final result after multiplying the multiplicand and multiplier. In this example, 24 is the product.
• Multiplication symbol: '×' (which connects the entire expression)

Give an Example of a Multiplication Sentence.

In order to solve a multiplication problem, we need to write it in the form of a multiplication sentence. For example, what is 36 times 9? We know that 36 times 9 is written in the form of a multiplication sentence as 36 × 9 = 324. Here, 36 and 9 are the factors and 324 is the product. So, 36 times 9 is 324.

How is Multiplication Related to Addition?

Multiplication represents the basic idea of repeated addition of the same number. It simplifies the task of repeated addition. For example, if there are 3 packs of pencils and each pack has 6 pencils, let us find the total number of pencils. We can solve this question by addition, that is, 6 + 6 + 6 = 18 pencils. However, when we have larger numbers to deal with, then multiplication is useful. Now, if we use multiplication to solve this problem, we need to multiply the number of packs with the number of pencils in each pack. This means, 3 × 6 = 18 pencils. Thus, we get the same result easily. Hence, multiplication is also termed as repeated addition.

What is the Difference Between Multiplication and Division?

In multiplication, we combine groups of equal sizes, while in division, we split or separate the given number into equal groups. Multiplication is the product of two or more numbers where the numbers that are multiplied are the factors and the result is termed as the product. In division, the number that is divided is called the dividend, the number which divides the dividend is called the divisor and the result is the quotient.

How is Multiplication Used in Everyday Life?

Multiplication is commonly used in our everyday lives. For example, we can calculate the price of the items according to the rate per quantity, we can find the correct quantity of the ingredient to be used in cooking, we can calculate the value of multiple items when the value of 1 item is known, and so on.

What are the Multiplication Strategies?

Multiplication strategies are different ways in which multiplication can be learned. For example, multiplication using a number line, multiplication with the help of a place value chart, separating the Tens and Ones and then multiplying them separately, and so on. These strategies help learners to understand the multiplication concept with a broader perspective.