Multiplication is an interesting way to calculate the product between two values. It is a way of calculating the product of two or more numbers in mathematics. It is a simple mathematical operation that we employ daily. Multiplication tables are the most common and popular application.
Multiplication of two numbers is considered to be the repeated addition of one number concerning another in mathematics. Whole numbers, natural numbers, integers, fractions, and other types of numbers can be used. When a is multiplied by b, it signifies that m is multiplied by itself ‘b’ times.
Aside from addition, subtraction, and division, Multiplication (denoted by ×) is a mathematical operation. In primary school, students learn the four basic arithmetic operations on their own.
What is Multiplication?
Multiplication is an arithmetic operation that is used to simplify various numeric expressions. The arithmetic process of calculating the product of two or more numeric values is known as Multiplication. Multiplication of two numbers, such as ‘a’ and ‘b,’ is expressed as ‘a’ multiplied by ‘b.’
In other words, Multiplication can be defined as the process of repeatedly adding a number to another number in mathematics. It gives the result as the multiplied product of that number.
When you multiply 5 by 3, for example, you are adding 3 to itself five times, resulting in 3 + 3 + 3 + 3 + 3 = 15. It is a straightforward method for any individual to multiply numbers and calculate multiplication products.
What are some of the examples of Multiplication?
Arithmetic operations such as the simplification of polynomials or algebraic equations contain the arithmetic operator of Multiplication (×).
Can be countless examples of the Multiplication of numbers. Following are some of them for a better understanding.
- Multiply 2 and 4 = 2 × 4 = 8
- Multiply 3 by 3 = 3 × 3 = 9
- Multiplication of 6 by 2 = 6 × 2 = 12
- Multiply 7 by 9 = 7 × 9 = 63
- Multiplication of 7 by 7 = 7 × 7 = 49
- The product of 1 × 1 = 1
What are the different symbols for Multiplication?
Have you wondered which symbol comes in between the two values that are supposed to be multiplied? The most common sign that denotes the Multiplication of two values is ×.
This particular sign helps a person understand the arithmetic operation to be used in the given numeric expression. It means if you see an expression like 4 × 3, it is easy to understand that this particular numeric value is to be multiplied.
For example 4 × 3, 6 × 2, 5 × 5, and so on.
Even though the cross sign (×) is a popular method of devoting Multiplication, a dot (.) is also used sometimes.
For example: (4).(3) = 12, (3).(5) = 15, and so on.
What is the formula used for Multiplication?
Although Multiplication is a common numerical operation, it has a specific formula. The formula for Multiplication is given by:
Multiplier × Multiplicand = Product.
For example: In the expression of 2 × 3 = 6
2 is multiplier
3 is multiplicand
6 is the product of multiplier and multiplicand
Some facts regarding the formula of Multiplication are:
- The total number of objects in a group is called the multiplicand
- The multiplier denotes the total number of equal groups
- The result of an arithmetic operation between a multiplier and a multiplicand is known as the product
Some properties of Multiplication
Multiplication is an effective method to understand various numeric formulas. Nevertheless, this particular operation includes multiple properties that help in the simplification of arithmetic operations. Multiplication properties are as follows:
- Distributive property
- Commutative property
- Zero property
- Closure property
- Associative property
- Identity property
What are the different steps to solve multiplication problems?
One-digit integers may be multiplied easily using multiplication tables, but bigger numbers are split into columns using their appropriate place values. One should start from ones, tens, hundreds, and thousands and move on to the bigger numbers.
Multiplication difficulties can be divided into two categories:
- Multiplication without regrouping
- Multiplication with regrouping
What are the facts regarding the Multiplication without regrouping?
When multiplying two integers without regrouping, one is dealing with smaller numbers that do not require a carry-over to its next higher place value.
It is the entry-level method that can assist a student grasp the fundamentals of Multiplication before moving on to more advanced difficulties like regrouping. Let us look at an example to help you comprehend what the method is all about.
For example: if 2015 is multiplied by 3, then the steps for the solution are:
- First, multiply the digit in the one place, 3 × 5 =15
- The value 15 is written by writing down 5 in the product space, and 1 is carried over to the next digit in the tens place.
- Then, multiply 3 with the value in the tens place, 3 × 1 + 1 (carried value) = 4
- After this, multiply the digit 2 by the value given in the hundreds place, 2 × 0 = 0
- Finally, multiply 3 (in the thousands place) by 2, 2 × 3 = 6
- The answer is: 6045
Facts about Multiplication with regrouping
The product is two digits when multiplying more than two numeric values with regrouping. One must carry over to the next digit place of higher value in this type of Multiplication. Let us consider an example to understand and comprehend what Multiplication with regrouping is about.
For example, multiply 2423 by 5
The steps for the solution are:
- Always start with the one’s place.
- The first step should be to multiply 3 × 5 = 15
- As the product of 3 and 5 is 15, 1 is carried to the digit in the tens place.
- The next step is to multiply 5 by 2 = 10 + 1 (carried value) = 11
- The same happens in this step, i.e., 1 is carried to the hundreds of place
- Now, multiply 4 by 5 and add the carried value of the previous digit. 4 × 5 + 1 = 21
- From the value of 21, 2 is carried to the number in the thousands place.
- Finally, multiply 5 by 2 and add the carried value is 2 from the previous Multiplication. 5 × 2 + 2 = 12
- The final answer is: 12115
What are the other facts related to Multiplication?
- The term “multiply” comes from the Latin multus, which means “many,” and plex, which comes from the Proto-Indo-European plek, which indicates “to plait.”
- Multiplication is another approach to adding a number again and again. It is, in other words, repeated addition.
- The 10s and 1s digits in answer to a 9’s Multiplication fact always add up to 9. 9×4=36, for example, therefore 3+6=9.
- Multiplication has the commutative property, which indicates that the sequence of the numbers in an equation is irrelevant.
- Multiplication has the associative property, which implies it doesn’t matter how the numbers are organized or which numbers are evaluated first. Subtraction and division are not covered by associative legislation.
- “Math” comes from the Proto-Indo-European term *me, which means “to chop grass” and is connected to “mow.”
- When it comes to Multiplication, the zero (0) property states that the answer is zero wherever there is a zero in a problem.
- Gottfried Wilhelm Leibniz (1647–1716) was indeed a worldwide genius who utilized both the cap symbol (^) and the dot symbol (.) to represent Multiplication. While the dot is still occasionally used to signify intersection in set theory, the cap symbol is currently the most common.
- The division is the inverse of Multiplication.
- Multiplication is one of the four fundamental mathematical operations, alongside addition, subtraction, and division.
- When an even number is multiplied by 6, the result has the same number as the even number. 6×2=12, 6×4=24, and 6×6=36, for example.
- The multiplier and multiplicand are the numbers that will be multiplied, and they are often referred to as “factors.” A “product” is the result of Multiplication.
- Over 4,000 years ago, the Babylonians were among the first to employ multiplication tables, although their tables were established on base 60.
- Multiplication tables are also known as the “Table of Pythagoras,” after the legendary Ionian Greek philosopher and scholar Pythagoras of Samos.
- Leibniz was the first person to invent a mechanism that could perform Multiplication.
- Around the year 1200, Arabic numbers were introduced in Europe, simplifying Multiplication and allowing for more sophisticated calculations.
- St. Andrew’s Cross is an alternate name for the multiplication sign “x.”
- When you multiply 1,089 by 9, you get the absolute opposite: 9,801
Multiplication is a fascinating yet easy-to-understand arithmetic operation. The various methods used for multiplying different types of numbers are mentioned above. While Multiplication is a major application of mathematics, it is applicable in daily life also. This particular arithmetic operation provides convenience while solving advanced numeric problems.