Problem 44 - Beginning and Intermediate Algebra

Question

Find each sum or product. $$ 49+199+1+1 $$

Step-by-Step Solution

Answer

250

Step 1: Group the Numbers

First, group the numbers together in manageable pairs to simplify the addition. For instance, add 49 and 1 first, then 199 and 1.

Step 2: Add the First Pair

Add the first pair of numbers:49 + 1 = 50

Step 3: Add the Second Pair

Add the second pair of numbers:199 + 1 = 200

Step 4: Add the Results

Finally, add the results from the two pairs together:50 + 200 = 250

Key Concepts

addition

Addition is one of the basic arithmetic operations. It's the process of calculating the total of two or more numbers or amounts. The symbol used for addition is '+'. For example, in the exercise 49 + 199 + 1 + 1, we are trying to find the sum of these numbers. Every addition question involves combining numbers step by step to find the total.

grouping numbers

Grouping numbers helps simplify the addition process, especially when dealing with multiple numbers. Instead of adding them all at once, we split them into smaller, more manageable groups. This approach reduces mistakes and makes calculations easier. For example, in the exercise, we grouped 49 and 1 together and 199 and 1 together. These pairs are easier to add individually before combining the results.

step-by-step solution

Solving a problem step by step is crucial for understanding each part of the process and avoiding errors. Here's a detailed breakdown of the steps from the original solution:

• Step 1: Group the Numbers - Grouping makes calculations manageable. For instance, in our exercise, we grouped 49 + 1 and 199 + 1.
• Step 2: Add the First Pair - We start by adding the first group: 49 + 1 = 50.
• Step 3: Add the Second Pair - Next, we add the second group: 199 + 1 = 200.
• Step 4: Add the Results - Finally, we add the sums from the two pairs together: 50 + 200 = 250.

By completing each step in order, we ensure accuracy and a better understanding of the process.

simplifying addition

Simplifying addition involves breaking down a complex problem into smaller, simpler parts. This helps avoid errors and makes the arithmetic much easier. In our given exercise, instead of adding all four numbers at once, we simplified the process by grouping and summing them step-by-step. This technique is especially useful for beginners, making addition clear and straightforward. Always remember, simplifying complex problems into smaller chunks can make solving them much more manageable.