The Ultimate Guide to Multiplication for Beginners: Definition, Tables and Examples

Multiplication is one of the most important math skills children need to master in early education. It is the foundation for more advanced math concepts such as division, fractions, and algebra. Learning multiplication also improves problem-solving skills and helps children understand everyday math applications such as counting money, telling time, or measuring ingredients in recipes.

This article will introduce multiplication in a fun and effective way. Whether you are looking for simple explanations for beginners, fun multiplication examples, or printable multiplication tables for PDF download, this article will provide you with everything you need to make learning multiplication easy and enjoyable.

What is Multiplication?

Multiplication is an operation that represents the basic idea of adding the same numbers repeatedly. The numbers being multiplied are called factors and the result obtained by multiplying two or more numbers is called the product of these numbers. Multiplication is used to simplify the task of adding the same numbers over and over again.

This may seem like a big concept for kids, but with simple explanations and examples, it will become easier to understand. Essentially, multiplication is a faster way to add the same number multiple times. For example, instead of saying 3 + 3 + 3, we can simply say 3 × 3, which equals 9.

Here’s another example to help you better understand the definition of multiplication:

Examples: If there are 7 cartons of eggs and each carton contains 9 eggs, find the total number of eggs.

Solution: First of all, we can solve this problem by adding, but it will take longer to add these up. In other words, 9 + 9 + 9 + 9 + 9 + 9 + 9 = 63 eggs. Using addition in this case would be tedious. In other words, multiplication is easier when we have larger numbers to calculate.

Now, let’s use multiplication to solve this problem. We will multiply the total number of boxes by the number of eggs in each box. If we multiply 7 × 9, we get the total number of eggs, which is 7 × 9 = 63 eggs. It can be seen that by using multiplication for arithmetic we can get the same result in less time. This is why multiplication is also known as repeated addition.

Multiplication Chart & Table

A multiplication table is a table that represents the product of two numbers. Having a multiplication table saves a lot of time and effort in calculations.

We will also provide printable multiplication tables from 1 to 20 download:

Multiplication Chart 1 to 10

Times table chart 1 to 10 consists of the numbers written from 1 to 10 on the top-most row of the grid as well as on the left-most column of the grid. Here’s a multiplication table 1 to 10:

Multiplication Chart 1 to 20

The charts list multiples of 1 to 20. These tables are very useful in solving math problems and calculations.

Importance of multiplication tables for students

Multiplication tables, also known as math multiplication tables, are a fundamental part of arithmetic calculations. Children have a much stronger memory than adults. What we learn at an early age has a strong impact on the brain and is retained throughout life.

Math multiplication tables are very useful and some of the uses of these math tables are given below:

• Math tables help students in learning math.
• Makes it easier for students to solve math problems.
• Makes students memorize the knowledge about multiplication firmly.

Multiplication Formula

The multiplication formula is expressed as: multiplicand × multiplier = product

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

For example, 4 (multiplicand) x 6 (multiplier) = 24 (final product). Using this basic concept of multiplication, you can then learn how to solve multiplication problems.

Multiplication Tricks

Multiplying single-digit numbers is a simple task. However, multiplying two or more digits is a difficult and time-consuming task. Here are some multiplication mnemonics that students can memorize as they work out the product.

• Multiplication of numbers can be done in any order. (5 x 4 = 4 x 5)
• When multiplying a number by a multiple of 10, simply add a 0 equal to the multiple of 10 next to the multiplier.(e.g. 7 x 100 = 700)
• If multiplying by three numbers, multiply by the smaller number first for quicker calculations, then multiply by the third number.
• If the multiplication includes two- or three-digit numbers, write the expansion of those numbers before multiplying. (Example: 45 x 9 = (40 + 5) x 9 = 40 x 9 + 5 x 9 = 360 + 45 = 405)

How to Solve Multiplication Problems?

When solving multiplication problems, one-digit numbers can be multiplied simply by using the multiplication table, but for larger numbers, such as values in the hundreds and thousands, we have to use their respective place value and group the numbers into columns to multiply them.

Besides, there are two types of multiplication problems: multiplication without grouping and multiplication with regrouping. Let’s understand both with the help of examples.

Multiplication without regrouping

Multiplication of two numbers without regrouping involves smaller numbers that do not require rounding to the next higher place value. This basic level helps learners understand the fundamentals of multiplication before moving on to higher level problems. Let’s understand this through the following example.

Example: Multiply 4013 by 2.

Solution:

• Step 1: Start with the digits in the first digit. (2 × 3 = 6)
• Step 2: Multiply 2 by the number in the tens place.(2 × 1 = 2)
• Step 3: Now, multiply 2 by the number in the hundreds place. (2 × 0 = 0)
• Step 4: Finally, multiply 2 by the number in the thousands place. (2 × 4 = 8)
• Step 5: 4013 × 2 = 8026

Multiplication with regrouping

Multiplication with regrouping over two digits is a multiplication where the product is two digits. In this multiplication operation, we need to round the multiplier to the next higher place value. Let us understand this with the help of the following example.

Example: Multiply 2468 by 8.

Solution:

• Step 1: Start with the digit in ones place, that is, 8 × 8 = 64 ones which means 6 tens 4 ones. So, carry 6 tens to the tens column.
• Step 2: Multiply 8 with the digit in the tens place, that is, 8 × 6 = 48 tens. We’ll 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, 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. Then, 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: The final product of 2468 × 8 = 19744.

Multiplication Examples

See a few more examples of multiplication here:

• Multiplication of 3 and 3 = 3 x 3 = 9
• Multiplication of 4 by 7 = 4 x 7 = 28
• Multiplication of 5 by 5 = 5 + 5 + 5 + 5 + 5 = 25; 5 x 5 = 25
• Multiplication of 10 x 10 = 100
• Multiplication of 7 by 8 = 7 x 8 = 56

Properties of Multiplication

The properties of multiplication are:

• Closure Property
• Commutative property
• Associative property
• Distributive property
• Identity property
• Zero property

Closure property of multiplication

The product of two integers is an integer (5 x 3 = 15). The product of two fractions is either a fraction or an integer (1/2 x 2 = 1)

Commutative property of multiplication

The commutative property of multiplication states that if A and B are any two integers, then:

A x B = B x A

For example, 2 x 8 = 8 x 2 = 16

Associative property of multiplication

As per the associative property of multiplication, if A, B, and C are any three integers, then:

A × (B × C) = (A × B) × C

For example, 2 × (3 × 4) = (2 × 3) × 4 = 24

Distributive property of multiplication

According to the distributive property of multiplication, if A, B, and C are any three integers, then:

A × (B + C) = (A × B) + (A × C)

For example: 4 × (2 + 3) = 4 × 2 + 4 × 3 = 20

Identity property of multiplication

If we multiply any value by 1, its value remains the same:

A x 1 = A

For example, 3 x 1 = 3

Zero property of multiplication

The zero property of multiplication states that any number multiplied by 0 is equal to zero only. Where A is any integer:

A x 0 = 0

For example: 7 x 0 = 0

Multiplication sign

When multiplying two or more numbers, if the symbols (+ and -) are different, the output results will be different, the specific symbol rules are as follows:

Operation	Result
(+ve) × (+ve)	+ve
(+ve) × (-ve)	-ve
(-ve) × (+ve)	-ve
(-ve) × (-ve)	+ve

Note: When two positive integers are multiplied together, the result is positive; when a positive integer is multiplied by a negative integer or vice versa, the result is negative; when two negative integers are multiplied together, the result is a positive integer.

Multiplication Using Number Line

Multiplication on a number line is the operation of multiplying a given set of numbers by 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. Therefore, to multiply on a number line, we start from zero and move to the right of the number line a given number of times.

For example, multiply 3 x 5 on a number line. Observe the number line below to see how 3 × 5 = 15 works. We will start at zero and move to the right of the number line. This will give us 15.

Word Problems on Multiplication

Multiplication word problems can be easily solved by looking at the situation carefully and finding a solution. In addition, let us understand the theory behind multiplication word problems in real life with the help of interesting examples.

Q.1: If Jane has 11 baskets with 5 apples in each basket, how many apples does Jane have in total?

Solution:

• Number of baskets Jane has = 11
• Number of apples in each basket = 5
• Total number of apples = (number of baskets) × (number of apples in each basket)
  

  = 11 × 5 = 55

• Therefore, Jane has 55 apples.

Q.2: Harry bought 3 boxes of chocolates from the market. If each box has 50 chocolates, how many chocolates does he have in total?

Solution:

• No. of boxes = 3 No. of boxes = 3
• Number of chocolates per box = 50
• Total number of chocolates = 3 x 50 = 150
• Hence, Harry has 150 chocolates.

Q.3: Find the product of 13.99 × 10000.

Solution:

• 13.99 × 10000
  

  = 139900.00= 139900

FAQs on Multiplication

1. What are the rules of multiplication?

The main rules of multiplication are:

1. When two integers are multiplied together, the result is an integer value
2. When a value is multiplied by 0, the result is 0
3. When a value is multiplied by 1, the result is the same
4. The order in which two or more numbers are multiplied does not matter

2. What is a multiplication fact?

A multiplication fact is the product of two specific numbers. The order in which the numbers are arranged does not change the product. For example, 2 x 3 = 6 and 3 x 2 = 6.

Conclusion

By using the resources and math tips shared in this guide, you can make the process of learning math enjoyable and effective for your child.

Remember, the goal is not just to memorize the basics like the multiplication tables, but to help your child truly understand and apply multiplication in a meaningful way. With continued practice and encouragement, children will not only master basic math skills but also develop a lifelong love of learning math.