Problem 45 - Beginning and Intermediate Algebra

Question

Find each sum or product. $$ 1999+2+1+8 $$

Step-by-Step Solution

Answer

The sum is 2010.

Step 1 - Identify the problem

The task requires finding the sum of the numbers 1999, 2, 1, and 8.

Step 2 - Add the first two numbers

First, add 1999 and 2. 1999 + 2 = 2001.

Step 3 - Add the next number

Next, add 1 to the result of the previous step. 2001 + 1 = 2002.

Step 4 - Add the final number

Finally, add 8 to the result obtained from the previous step. 2002 + 8 = 2010.

Key Concepts

step by step addition

Let's break down the problem by tackling each part individually. This method, known as step by step addition, makes it easier to handle large numbers by dividing the problem into manageable chunks. Here's how to do it:

First, identify the problem. We need to find the sum of these numbers: 1999, 2, 1, and 8.

Next, add the first two numbers.

• 1999 + 2 = 2001

Now, add the next number to the result from the previous step.

• 2001 + 1 = 2002

Lastly, add the final number to the result.

• 2002 + 8 = 2010

So, by using a step by step addition method, we find that the sum is 2010. This process helps ensure accuracy and makes it easier to solve complex addition problems.

basic arithmetic operations

Addition is one of the basic arithmetic operations, which also includes subtraction, multiplication, and division. Understanding and mastering these operations is fundamental for problem-solving in algebra and beyond.

Addition brings two or more numbers together to make a larger number. For example, in our problem, we combined 1999, 2, 1, and 8. Writing each step can ensure no mistakes are made. Here are some important points to remember:

• Always start by lining up numbers by their place value.
• Begin adding from the rightmost digits (ones place).
• Carry over any value more than 9 to the next higher place value.

Using these tips, you'll be equipped to handle even more complex addition problems accurately.

problem-solving in algebra

Aside from basic arithmetic, problem-solving in algebra often involves identifying the correct operations to apply and the order in which to apply them. This step-by-step approach helps develop critical thinking and analytical skills that are necessary for more advanced mathematical concepts.

When dealing with algebraic problems:

• Break down the problem into smaller parts.
• Identify which operations are needed, starting with addition if it's indicated.
• Follow the correct order of operations (remember PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

Practicing this approach with basic arithmetic problems makes tackling larger and more complex algebraic equations less intimidating. You’ll gain confidence in your ability to solve problems systematically and efficiently.