Problem 18 - Basic College Mathematics

Question

Multiply by \(1,2,3,\) and so on, to find ten multiples of each number. $$ 11 $$

Step-by-Step Solution

Answer

The first ten multiples of 11 are 11, 22, 33, 44, 55, 66, 77, 88, 99, and 110.

Step 1 - Identify the first multiple

Multiply 11 by 1 to get the first multiple. \(11 \times 1 = 11\)

Step 2 - Identify the second multiple

Multiply 11 by 2 to get the second multiple. \(11 \times 2 = 22\)

Step 3 - Identify the third multiple

Multiply 11 by 3 to get the third multiple. \(11 \times 3 = 33\)

Step 4 - Identify the fourth multiple

Multiply 11 by 4 to get the fourth multiple. \(11 \times 4 = 44\)

Step 5 - Identify the fifth multiple

Multiply 11 by 5 to get the fifth multiple. \(11 \times 5 = 55\)

Step 6 - Identify the sixth multiple

Multiply 11 by 6 to get the sixth multiple. \(11 \times 6 = 66\)

Step 7 - Identify the seventh multiple

Multiply 11 by 7 to get the seventh multiple. \(11 \times 7 = 77\)

Step 8 - Identify the eighth multiple

Multiply 11 by 8 to get the eighth multiple. \(11 \times 8 = 88\)

Step 9 - Identify the ninth multiple

Multiply 11 by 9 to get the ninth multiple. \(11 \times 9 = 99\)

Step 10 - Identify the tenth multiple

Multiply 11 by 10 to get the tenth multiple. \(11 \times 10 = 110\)

Key Concepts

Multiples

Understanding multiples is key to mastering multiplication tables. A multiple of a number is the product of that number and any integer. For example, the multiples of 11 are results you get when you multiply 11 by integers like 1, 2, 3, and so on.
Multiples are usually found by this pattern: 11, 22, 33, and so forth. They follow a regular sequence, which makes them easier to identify and memorize.
Let's look into it:

• 11 multiplied by 1 equals 11, so 11 is the first multiple of 11.
• 11 multiplied by 2 equals 22, so 22 is the second multiple of 11.
• Continuing this pattern, 11 multiplied by 3 gives us 33, which is the third multiple of 11.
• By following this simple pattern, you can find any multiple by multiplying 11 with any whole number.

This regular pattern is what makes multiplication tables a vital part of basic arithmetic.

Basic Arithmetic

Basic arithmetic consists of fundamental mathematical operations: addition, subtraction, multiplication, and division.
Multiplication is particularly important when dealing with multiplication tables. It repeatedly adds a number a certain number of times. For example, multiplying 11 by 2 means adding 11 twice, which equals 22.
Let's break down multiplication:

• Multiplication is a shortcut for repeated addition.
• If you multiply 11 by 3, you are essentially adding 11 three times: 11 + 11 + 11 = 33.
• This concept works for any combination of numbers.

Understanding these simple yet essential rules will help you solve more complex problems later on. Remember, knowing the basics will also help you understand and memorize the multiplication tables better.
The first steps in arithmetic set the foundation for more advanced math topics.

Step-by-Step Solution

Breaking down problems into smaller, manageable steps makes math easier. Here’s a step-by-step guide on finding multiples of 11:

• Step 1: Multiply 11 by 1 to get 11, which is our first multiple.
• Step 2: Multiply 11 by 2 to get 22, the second multiple.
• Step 3: Continue by multiplying 11 by 3 to get 33, the third multiple.
• Step 4: Repeat the process for the subsequent multiples (11 × 4 = 44, 11 × 5 = 55, and so on).

By following these steps, you get a clear roadmap to solve the problem.
Using systematic steps can help better understand and solve math problems. Whether you are working with multiplication tables or any other type of problem, a step-by-step approach can make complex concepts simpler.
Practicing regularly using this step-by-step method will improve your mathematical skills and boost your confidence in solving arithmetic problems.