Problem 91 - Elementary Algebra

Question

Add or subtract and reduce to lowest terms. $$ 12+13+16 $$

Step-by-Step Solution

Answer

41

Step 1: Identify the Operation

Before solving the problem, identify the operation that needs to be performed. In this case, we need to add the numbers 12, 13, and 16.

Step 2: Add the Numbers

Add the numbers together one by one. Start by adding 12 and 13.

Step 3: Compute 12 + 13

Calculate the sum: \[ 12 + 13 = 25 \]

Step 4: Add the Result to 16

Take the sum from Step 3 and add it to 16: \[ 25 + 16 = 41 \]

Step 5: Simplify the Result

Now, check if the final result, 41, can be reduced to the lowest terms. Since 41 is already a whole number and is a prime number, it cannot be simplified further.

Key Concepts

Addition

Addition is a basic arithmetic operation that involves combining numbers to get a total sum. It's one of the four fundamental operations and is essential for more complex mathematical concepts. When you add numbers, you combine their values to find out how much they total up to.
For instance, when you are given the numbers 12, 13, and 16, the task is to find their sum. Here’s how you can do this effectively:

• Start with the first two numbers: 12 and 13.
• Add them together: \(12 + 13 = 25\).
• Next, take the sum (25) and add the last number: 16.
• Calculate: \(25 + 16 = 41\).

This step-by-step process helps to manage simpler additions as part of the total calculation. As you practice, you will learn to do this faster and with larger numbers. Remember, **addition** is all about combining numbers to see the total you get when you join them together.

Prime Numbers

Prime numbers are special numbers greater than 1, that only have two divisors: 1 and themselves. They can't be divided evenly by any other numbers. Recognizing prime numbers is important in various number operations, such as simplifying or factoring numbers.
In our previous addition, the result was 41. To determine if this can be simplified, one step is to check whether it's a prime number. Here's how to do that:

• Verify if there's any whole number, other than 1 and 41, that divides 41.
• You will find that no such number exists, confirming 41 is indeed a prime number.

Being prime means it can't be reduced into factors. Prime numbers often appear in mathematics and are foundational to various theories and applications. Thus, knowing how to identify them is a useful skill.

Number Operations

Number operations include the basic arithmetic tasks we perform with numbers: addition, subtraction, multiplication, and division. Understanding these is key to solving virtually any math problem. Let’s delve into why these operations matter:

• **Addition** combines numbers to calculate a sum, like \(12 + 13 + 16 = 41\).
• **Subtraction** determines the difference between numbers, checking how much less one number is than another.
• **Multiplication** finds the total when you have a certain number of groups of the same size.
• **Division** splits numbers into equal parts or finds out how many times one number fits into another.

These operations serve as the building blocks for more complex equations in science, engineering, and everyday scenarios. Grasping them firmly ensures that more advanced concepts are much easier to tackle. Whether adding up shopping bills or calculating probabilities, these foundational skills are invaluable.