Question

List five multiples of each number. $$14$$

Short answer

The multiples of 14 are 14, 28, 42, 56, 70.

Step-by-step solution

Understand Multiples

A multiple of a number is the product of that number and an integer. For example, multiples of 14 are found by multiplying 14 by integers such as 1, 2, 3, etc.

Calculate the First Multiple

Multiply 14 by 1. \( 14 \times 1 = 14 \)

Calculate the Second Multiple

Multiply 14 by 2. \( 14 \times 2 = 28 \)

Calculate the Third Multiple

Multiply 14 by 3. \( 14 \times 3 = 42 \)

Calculate the Fourth Multiple

Multiply 14 by 4. \( 14 \times 4 = 56 \)

Calculate the Fifth Multiple

Multiply 14 by 5. \( 14 \times 5 = 70 \)

List All Multiples

Combine all the results: 14, 28, 42, 56, 70.

Key concepts

Product of Integers

Understanding the product of integers is essential in mathematics. The product is what you get when you multiply two or more numbers together. For instance, if you multiply 14 by 3, you get 42.
In general, the product of two numbers, say, \(a\) and \(b\), is written mathematically as \(a \times b\). Here, \(a\) and \(b\) are the integers, and the result of \(a \times b\) is their product.
Key Points:

• Product represents repeated addition: For example, \( 3 \times 4 \) is the same as adding 3 four times, resulting in 12.
• Commutative property: The product does not change regardless of the order of multiplication. For example, \( 3 \times 4 = 4 \times 3 \).

Remember, understanding the product of integers helps in solving many mathematical problems involving multiplication and finding multiples.

Multiplication

Multiplication is a fundamental mathematical operation that combines groups of numbers. It is represented by the symbol \( \times\). In the process, you take one number (the multiplicand) and add it to itself a certain number of times, as determined by the other number (the multiplier).
For example, if you want to find the multiples of 14, you continuously multiply 14 by consecutive natural numbers:

• 14 times 1 is \( 14 \)
• 14 times 2 is \( 28 \)
• 14 times 3 is \( 42 \)

More than just a basic operation, multiplication is integral in many areas of science, economics, and everyday life.
Some important properties of multiplication include:

• Commutative property: \( a \times b = b \times a \)
• Associative property: \((a \times b) \times c = a \times (b \times c)\)
• Distributive property: \(a \times (b + c) = (a \times b) + (a \times c)\)

Mathematical Operations

Mathematical operations are procedures or functions that take one or more values and produce another value. These operations include addition, subtraction, multiplication, and division. Each serves a different purpose and is used in various contexts.
Here’s a brief overview of these operations:

• **Addition**: Combining numbers to get a sum. For example, \(2 + 3 = 5\).
• **Subtraction**: Taking away one number from another to get the difference. For example, \(5 - 2 = 3\).
• **Multiplication**: Combining groups of equal size. For example, \(4 \times 3 = 12\).
• **Division**: Splitting a number into equal parts. For example, \(12 \text{ divided by } 3 = 4\).

Understanding these operations and how they relate to each other is crucial in mathematics. They form the foundation for more advanced mathematical concepts and problem-solving techniques. Always take time to practice and get comfortable with these basics, as they will be useful throughout your learning journey.