Question

Find the product of 13 and \(9 .\)

Short answer

Answer: The product of 13 and 9 is 117.

Step-by-step solution

Identify the numbers to be multiplied

In this exercise, we need to multiply 13 by 9. So, we have to multiply these two numbers together to find the product.

Multiply the numbers

To find the product of 13 and 9, we simply need to multiply these two numbers together: \[ 13\times 9 \]

Calculate the product

Now, perform the multiplication: \[ 13\times 9 = 117 \]

Write the final answer

The product of 13 and 9 is 117.

Key concepts

Arithmetic

Arithmetic is all about working with numbers through basic operations such as addition, subtraction, multiplication, and division. When you're asked to find the product of two numbers, like in this exercise where we multiply 13 and 9, you're engaging in a multiplication operation, which is one of the core functions of arithmetic.

Multiplication is essentially repeated addition. For instance, multiplying 13 by 9 is like adding 13, nine times:

• 13 + 13 + 13 + 13 + 13 + 13 + 13 + 13 + 13 = 117

Using multiplication simplifies this process significantly by allowing us to find products quickly and efficiently.

When approaching multiplication:

• Identify each of the numbers you’re working with, which are known as factors.
• Multiply these factors to find the product.
• Ensure accuracy by double-checking your calculations.

Understanding these steps will help you solve many different problems in arithmetic.

Mathematics for Engineers

In the field of engineering, mathematics plays a critical role. It allows engineers to model real-world scenarios and solve practical problems. Basic multiplication, like multiplying 13 by 9, might seem simple, but it's a fundamental skill in more complex calculations.

Engineers apply multiplication in various tasks, such as calculating areas, designing systems, and processing measurements. Consider the following applications:

• Determining the total length of material needed by multiplying the length per piece by the number of pieces.
• Calculating forces in a mechanical structure by using multiplication of known values like pressure and area.
• Estimating costs by multiplying unit costs by quantities.

Basic multiplication is the stepping stone that makes more advanced engineering mathematics accessible. It's essential for anyone wanting to dive into the technical details of engineering fields.

Step-by-step solutions

Step-by-step solutions are incredibly valuable for comprehending how to approach mathematical problems. They break down the problem-solving process into manageable parts, making it easier to follow and replicate with other examples.

Here’s how a step-by-step approach helps:

• **Clarification**: It clearly delineates each phase of the solution process, enhancing understanding.
• **Reinforcement**: It reinforces learning by demonstrating how each step logically leads to the next.
• **Error-checking**: By examining solutions one step at a time, you can quickly spot and correct mistakes.

In the exercise of multiplying 13 and 9, the steps guide you from identifying the factors to calculating the product, ensuring each move is clear and precise. This approach is helpful not just for multiplication but for tackling all sorts of mathematical problems, allowing students to build confidence and problem-solving skills.