Multiplication

By Alex David

March 28, 2025

Adding the same number repeatedly can be time-consuming. What if you could multiply instead? Multiplication makes calculations faster and easier, helping you solve problems in seconds!

It is one of the most important operators in mathematics. But when you learn about multiplication in context to mental approach, this will boost your confidence and provide leisure to you.

What is Multiplication?

Here is the simple definition:

“Multiplication is the repeated addition of equal-sized groups.”

It is among the four basic arithmetic operators, along with addition, subtraction, and division.

Example:

Take two baskets of apples; each basket contains a total of four apples; now we have to calculate the total number of apples.

Make this basic problem more simple and easy. Let’s make this problem easier for mental calculations. We have to multiply 2 by 4 — 2 * 4.

Parts of Multiplication:

It is an operator; surely it works with operands. In this way, a simple problem has different parts. Sometimes, people use three or four parts of multiplication.

For better understanding, we take the above example and clear our concepts. We have two baskets, and each has four apples. In this problem, baskets are equal-size groups. So, here is the first part is multiplier. It is simply defined as:

“The number of equal-size groups is called multiplier.”

The number of apples in each basket is the second part—multiplicand.

“The number of objects in a group is called multiplicand.”

The third one is the multiplication sign itself: “” and the last and most important part is product. It is defined as:

“The final result is called the product.”

In the above example, the final result—8 is called the product.

This image is showing parts of multiplication.

Symbol of Multiplication:

It is represented by different signs according to the environment in which we are working. In math, we use minus sign “ × ” but in computer, we mostly use asterisk sign “ * ” and dot sign “ . ” which is usually used in physics and for other calculations

Example

4 × 5 = 20

4 . 5 = 20

4 * 5 = 20

Position in PEMDAS:

PEMDAS is an acronym that helps us remember the order of operations in mathematics, ensuring calculations are done correctly and consistently. PEMDAS stands for:

P: Parentheses (solve expressions inside parentheses first)

E: Exponents (evaluate powers and roots next)

MD: Multiplication and Division (work from left to right)

AS: Addition and Subtraction (work from left to right)

If division and multiplication appear simultaneously in the question, then the left-to-right rule is applicable.

Multiplication of Different Number:

Multiplying Integers

For multiplying integers, we just look at the sign of integers. And remember the following scenarios.

Multiplication of two Positive Integers

The final result (product) of two positive integers is always a positive integer. Like

4 × 5 = 20.

Multiplication of two Negative Integers

When two negative integers get multiplied, the product is always a positive integer.

e.g. (−4) × ( −5) = 20

For Knowledge: Usually, we use parenthesis in the case of a negative integer.

Multiplication of one Positive and one Negative Integer

When either of the integers is negative, the product is always negative.

Example:

-3 × 2 = – 6

2 × (- 4) = – 8

Apply Mental Math Tricks

Here you remember all this by using mental math ability for multiplication. Just remember two lines:

When both integers have the same sign, the product is always a positive number.
When any one of the integers among the both has a negative sign, the product is always a negative number.

Multiplying Fractions

In case of multiplying the fraction, just remember one line in your mind—use mental math.

“Multiply the numenator with numenator and denominator with denominator.”

General Form:

ab × cd = a x cb x d

Example

45 × 23 = 4 × 25 × 3 = 815

This image is showing the multiplication of fraction.

Multiplying Decimals

Multiplication of decimals looks hard but use mental tricks and make this super-easy.

Example of Decimal:

Let’s say you have to calculate multiplication of 15.3 and 2.4. Treat them as integers and get the solution.

153 × 24 = 3672

Now put the decimal point, Keep this: “the product of the two decimal numbers will have decimal up to two positions from right to left,” and same for other decimal numbers

Not need to practice this again and again; just remember one line:

“Multiply decimals like integers and place the decimal point.”

Multiplying Numbers with Powers

In math, the power of a number is a way to describe how many times a number (called the base) is multiplied by itself. It is written using an exponent, which shows the number of times the multiplication happens.

When the bases are same but the powers are different

Mentally goes through this scenario by calling to mind this:

“When bases are the same, then add the powers.”

For Example

53 × 54 = 53 + 4 57

57 = 5 × 5 × 5 × 5 × 5 × 5 × 5

53 × 54 = 78,125

When the bases are different but the powers are the same

Handle this scenario with great confidence by just remembering the mental trick:

“When bases are different but exponents are the same, multiply the bases first, then take the power of the product.”

For Example

43 × 23 = (4 × 2)3 83

83 = 8 × 8 × 8 = 512

When the bases and powers are different

If the bases and powers are different, then take this situation as a simple multiplication scenario—simply solve as an individual and then multiply them. Like 23 × 32

Simple solve 23 and 32 first, this situation will become 8 × 9 = 72. ‘

This image is showing the tip of multiplication.

Useful Tips:

Use of tables: One of the best multiplication tips and tricks is the use of tables. Usually multiplication revolves around the tables; start to memorize the tables as much as you can. This will help to solve many problems in a few seconds.
Use Mental Math Concepts: Here in this article, I used mental tricks. Gradually remember them to tackle basic problems and then move on to solve complex ones.

Some Facts:

Identity Element: Identity is the vital property of multiplication. When you multiply any number by 1, you will get the same number again. In this way, digit 1 becomes the identity element.
Effect of Zero: If you multiply any number by zero, the product is always zero.

Conclusion

Multiplication is the essential operator of mathematical calculation. It is important to learn about it from basic to advanced. For this, we have to know about its definition, parts, symbols, and some basic rules, like how to deal with integers, fractions, and decimals.

Frequently Asked Questions (FAQs)

Q # 1: Why is multiplication called “repeated addition”?

It simplifies the process of adding the same number multiple times. Instead of adding 9 + 9 + 9 + 9, you can write it as 9 × 4 for a faster calculation.

Q # 2: What is the difference between multiplication and exponentiation?

It repeatedly adds a number, while exponentiation repeatedly multiplies a number by itself. Example:

Multiplication: 3 × 3 = 9 (adding three twice)
Exponentiation: 3³ = 3 × 3 × 3 = 27 (multiplying three three times)

Q # 3: How is multiplication used in everyday life?

It is used in budgeting, cooking (scaling recipes), calculating wages (hours × rate), traveling (speed × time), and business profit calculations.

Q # 4: What is the lattice method for multiplication?

The lattice method is a visual multiplication technique where numbers are placed in a grid and multiplied systematically, making it easier for large numbers.