Multiplication of Integers: Rules
Multiplication Rule	Examples
(-) × (-) = (+)	(-3) × (-5) = 15
(-) × (+) = (-)	(-3) × (5) = -15
(+) × (+) = (+)	3 × 5 = 15
(+) × (-) = (-)	3 × (-5) = -15

Multiplication of Decimals

Decimals can be easily multiplied by following the steps added below,

Step 1: Note the digits after the decimal in the number of the multiplication.

Step 2: Multiply both the numbers without worrying about decimals.

Step 3: Now put the decimal in the place after counting the same from the right side.

This is explained by the example added below,

Example: Find the product of 2.34 and 1.2

Solution:

For 2.34 × 1.2

Here we have total 3 digits after decimal from both the numbers.

Multiplying the same without worrying about decimal, we get 2808.

Thus, putting decimal at third place from the right,

We get, 2.808

Multiplication of 2 Digits

Multiplication of two digits number can be easily achieved by the following steps:

Step 1: Multiply the ones digit of the second number by the first number and write down the result.

Step 2: Multiply the tens digit of the second number by the first number and write down the result shifted one position to the left.

Step 3: Add the two partial products from steps 1 and 2 to obtain the final result.

Let’s see following illustration, where 23 and 17 are multiplied together to get the result of 391.

Multiplication of 3 Digits

Multiplication of three digits number can be easily achieved using the following steps:

Step 1: Multiply the ones digit of the second number by the first number and write down the result.

Step 2: Multiply the tens digit of the second number by the first number and write down the result shifted one position to the left.

Step 3: Multiply the hundreds digit of the second number by the first number and write down the result shifted two positions to the left.

Step 4: Add the three partial products from steps 1, 2, and 3 to obtain the final result.

Let’s see following illustration, where 234 and 114 are multiplied together to get the result of 26676.

Multiplication Real life Applications

Here are some real-life applications of multiplication.

• Area Calculation: When measuring the area of a rectangular room, you multiply the length by the width (length × width) to find the total square footage.
• Volume Calculation: To determine the volume of a box or container, you multiply the length, width, and height (length × width × height).
• Time and Distance: When calculating speed, you multiply the rate (e.g., miles per hour) by the time (hours) to find the distance travelled.
• Cooking: Recipes often require multiplying ingredients. For example, if a recipe calls for doubling the ingredients, you multiply each quantity by 2.
• Shopping: When buying multiple items with the same price, you multiply the price by the quantity to find the total cost.
• Salary Calculation: Monthly or annual salaries are often calculated by multiplying the hourly wage or the daily rate by the number of hours worked or days worked.

Fast Multiplication Tricks and Tips

Use the following Multiplication tips and tricks to calculate product of numbers fast:

Finger Multiplication

1. Assign each finger a number from 6 to 10.
2. To multiply, touch the corresponding fingers and count the touches to get the result.

Multiplying by 9

1. For multiplying any number by 9, use the “finger trick”.
2. For example, to multiply 7 by 9, fold down the 7th finger from the left. The result is 63.

Multiplying by 11

1. For two-digit numbers, add the digits together and place the sum in the middle.
2. For example, 23 multiplied by 11 becomes 2 (2+3) 3, so the result is 253.

Distributive Property

1. Break down multiplication into simpler parts.
2. For example, to multiply 6 by 17, you can break it down into (6 x 10) + (6 x 7).

Multiplying by 5

1. To multiply any number by 5, simply divide the number by 2 and add a zero.
2. For example, 8 multiplied by 5 is (8 / 2) with a zero, giving 40.

Squaring Numbers Ending in 5

1. To square a number ending in 5, take the digit before 5, multiply it by the next number, and append 25.
2. For example, 75 squared is (7 x 8) with 25, resulting in 5625.

Cross Multiplication

1. Useful for multiplying numbers with two digits.
2. Multiply the tens and units separately and add them together.
3. For example, 23 multiplied by 34 is (20 x 30) + (20 x 4) + (3 x 30) + (3 x 4).

Zero Property

1. Any number multiplied by zero is zero.

Using Powers of 10

1. To multiply by powers of 10, add the number of zeros to the original number.
2. For example, 6 multiplied by 100 is 600.

Breaking Down Large Numbers

1. Break down large numbers into more manageable parts for easier multiplication.

Multiplication Word Problems

We have provided you with some solved word problems on multiplication.

Multiplication Problem 1: If a box of pencils has 12 pencils. Then 5 boxes has how many pencils.

Solution:

No. of pencils in one box = 12

Total box = 5

Total pencils in 5 boxes = 12 × 5 = 60

Thus, 5 box has a total of 60 pencils.

Multiplication Problem 2: A class has 50 students and in school, there are 8 classes with an equal number of students. Now find the total number of students in the school.

Solution:

Number of Students in a Class = 50

Number of classes in the School = 8

Total Number of Students in School = 50 × 8 = 400

Thus, there are a total of 500 students in the school.

Multiplication Problem 3: A farmer has 7 baskets of apples, and each basket contains 5 apples. How many apples does the farmer have in total?

Solution:

Number of apples in a basket = 5

Number of basket = 7

Total Apples = 5 × 7 = 35

Thus, there are a total of 35 apples

Multiplication Practice Questions

Here are a few more solved examples on multiplication.

Multiplication Example 1: Isha wants to make 4 sets of bracelets, and each set requires 6 beads. How many beads does Emma need in total?

Solution:

Number of beads required for one bracelet = 6 beads

Number of bracelet to be made = 4

Total beads required = 6 × 4 = 24 beads

Thus, a total of 24 beads are required to make 4 bracelets.

Multiplication Example 2: A garden has 5 rows of sunflowers, with 9 sunflowers in each row. How many sunflowers are there in the garden?

Solution:

Number of Sunflowers in each row = 9

Number of Rows = 5

Total Number of Sunflower in the Garden = 9 × 5 = 45

Thus, there are a total of 45 sunflowers in the garden.

Multiplication Example 3: Find the product of 232 × 24

Solution:

232 × 24

= 232 × 20 + 232 × 4

= 4640 + 928

= 5568

Multiplication Example 4: Find the product of 123 × 45

Solution:

123 × 45

= 123 × 40 + 123 × 5

= 4920 + 655

= 5575

Practice Problems on Multiplication

Following are some practice problems on Multiplication for you to solve.

Problem 1: Multiply the following:

• 23 × 17 = ?
• 46 × 29 = ?
• 87 × 63 = ?
• 124 × 58 = ?
• 315 × 42 = ?

Problem 2: Sarah bought 5 crates of apples, with each crate containing 24 apples. How many apples did she buy in total?

Problem 3: A library has 8 rows of bookshelves, and each row has 32 bookshelves. How many bookshelves are there in total?

Problem 4: A sports store sells soccer balls in packs of 6. If a school buys 9 packs of soccer balls, how many soccer balls do they get?

Problem 5: Emily has a garden with 6 rows of sunflowers, and each row has 7 sunflowers. How many sunflowers are there in her garden?

Multiplication Practice Questions

Answer the following MCQs (Here only one answer is correct)

1. What is the product of 8 multiplied by 9?

1. 72
2. 64
3. 81
4. 17

2. If you multiply 6 by 7, what is the result?

1. 49
2. 42
3. 36
4. 14

3. What is the product of 5 multiplied by 3?

1. 8
2. 15
3. 18
4. 23

4. If you have 4 groups of 6, what is the total?

1. 12
2. 24
3. 30
4. 36

5. Calculate the product of 9 multiplied by 4.

1. 27
2. 36
3. 45
4. 54

6. How much is 7 times 8?

1. 56
2. 64
3. 72
4. 80

7. If you multiply 11 by 3, what is the result?

1. 33
2. 22
3. 44
4. 5

8. What is the product of 2 multiplied by 10?

1. 12
2. 15
3. 20
4. 25

9. If you have 3 groups of 7, what is the total?

1. 10
2. 17
3. 21
4. 24

10. Calculate the product of 12 multiplied by 5.

1. 48
2. 60
3. 72
4. 84

Multiplication in Summary

Here are some key notes on Multiplication in Maths:

1. Definition: Multiplication is a fundamental arithmetic operation.
2. Symbol: Denoted by “X” or “*”.
3. Result: The outcome of multiplying two or more numbers is called the product.
4. Commutative: Order of numbers doesn’t affect the result [Tex](a \times b = b \times a) [/Tex].
5. Associative: Grouping of numbers doesn’t affect the result [Tex](a \times b) \times c = a \times (b \times c) [/Tex]
6. Example: [Tex]3 \times 4 = 12 [/Tex]

Articles Related to Multiplication:

• Mathematical Concepts for Beginners
• Basic Arithmetic Operations
• Distributive Property

Multiplication – FAQs

What is Multiplication in Maths?

Multiplication is the fundamental operation of mathematics that is equal to the repetitive addition of any number. Suppose if we have to find the sum of 7 added to itself 5 times then we simply find the product of 7 × 5 and that gives the required answer.

What is the Symbol of Multiplication?

The symbol used to represent multiplication in mathematics is the cross (×) symbol. Sometimes we also use an asterisk (*) or a dot(.) to represent multiplication operations.

What are the terms involved in Multiplication?

In a multiplication equation (a × b), “a” and “b” are called the factors. “a” is the multiplicand, and “b” is the multiplier. The result is called the product.

What are properties of Multiplication?

Various properties of the multiplication operation are,

• Multiplication of any number with zero is always zero.
• Multiplication of any number with one is always the number itself.
• Multiplication of either two positive numbers or two negative numbers is always positive.
• Multiplication of a positive and a negative number is always a negative number, etc.

How is multiplication represented?

Multiplication is often represented using the “×” symbol or an asterisk “*”, as well as in mathematical notation, like “2 × 3” or “2 * 3”, which means multiplying 2 by 3.

What is relation between Multiplication and Addition?

Multiplication is called the process of repetitive addition. Suppose we have to find the sum of a number added to itself multiple times. Then this is easily achieved by taking the product of the number with how many times it is repeated.

How do I Multiply 2 Numbers?

To multiply any 2 numbers, we can take any number and start multiplying its one’s digit and write in the first row, and then with ten’s digit but shifted one place away from the decimal position. This proceeds until all the numbers are used. Then finally add all the rows, to get the desired result.

How do you Multiply a number by 0?

When any number is multiplied by 0, the result is always 0. This is known as the zero property of multiplication.

Can you Multiply Negative Numbers?

Yes, we can multiply negative numbers. When we multiply two negative numbers, the result is positive and when you multiply a positive number by a negative number (or vice versa), the result is negative.

What is the Multiplication Identity?

Multiplication identity is a number multiplied by any number, resulting in the original number and multiplication identity is 1.

How is Multiplication related to Exponential Notation?

Exponential notation is a shorthand for writing repeated multiplications. For example, 2³ means 2 × 2 × 2.