Adding Numbers And Problem Solving Math Exercises

by Scholario Team 50 views

Hey guys! Let's dive into some math problems today that involve adding numbers and creating our own word problems. We're going to tackle two interesting exercises that will put our math skills to the test. So, grab your pencils and let's get started!

4. Adding Even Numbers and the Smallest Six-Digit Odd Number

In this first problem, we're asked to add the smallest six-digit odd number to the sum of even numbers within a specific range. Sounds like a fun challenge, right? Let's break it down step by step.

Identifying the Even Numbers

First, we need to figure out the even numbers between 299,995 and 300,003. Remember, even numbers are those that can be divided by 2 without leaving a remainder. So, looking at the numbers in that range, the even numbers are:

  • 299,996
  • 299,998
  • 300,000
  • 300,002

Summing the Even Numbers

Now that we've identified the even numbers, let's add them up. We can do this manually, or if you're feeling fancy, use a calculator. Either way, the sum is:

299,996 + 299,998 + 300,000 + 300,002 = 1,200,000 - 4 = 1,199,996

Finding the Smallest Six-Digit Odd Number

Next up, we need to find the smallest six-digit odd number. Think about it – the smallest six-digit number is 100,000. But that's an even number. To get the smallest odd number, we simply add 1. So, the smallest six-digit odd number is:

100,001

Adding it All Together

Alright, we're in the home stretch! Now we just need to add the smallest six-digit odd number (100,001) to the sum of the even numbers (1,199,996). Let's do it:

1,199,996 + 100,001 = 1,299,997

Verifying with a Calculator

To be absolutely sure we've got the right answer, it's always a good idea to verify our result using a calculator. Go ahead, punch those numbers in and double-check! You should get the same answer: 1,299,997.

So, the final answer to the first problem is 1,299,997. Great job, guys! You've successfully added even numbers and found the smallest six-digit odd number, and verified the result.

5. Creating and Solving a Word Problem

Now, let's switch gears and tackle the second part of our challenge: creating and solving a word problem. We're given the expression 120,567 + (34,020 + 100,112), and our mission is to come up with a story problem that fits this equation.

Brainstorming a Scenario

The key to creating a good word problem is to think of a real-life situation where addition makes sense. Let's consider some possibilities. This expression involves adding three numbers together, so let's brainstorm a scenario: We need a context where three quantities are combined.

For example, we could think about:

  • Money earned or saved
  • Items collected
  • Distances traveled
  • Number of people

Let’s go with a money scenario. Imagine someone is saving up for a big purchase and has different sources of income.

Crafting the Word Problem

Now, let's turn our scenario into a clear and engaging word problem. Here’s an example:

“Sarah is saving money to buy a car. She has $120,567 in her savings account. She also receives a bonus of $34,020 from her job and wins $100,112 in the lottery. How much money does Sarah have in total?”

Solving the Problem

Now that we have our word problem, let's solve it! We'll use the given expression: 120,567 + (34,020 + 100,112).

First, we need to solve the addition inside the parentheses: 34,020 + 100,112 = 134,132

Next, we add that result to the first number: 120,567 + 134,132 = 254,699

So, Sarah has a total of $254,699.

Checking Our Work

It's always a good idea to check our work, especially with word problems. Does our answer make sense in the context of the problem? Well, Sarah started with a significant amount of money and then added two more large sums. So, an answer in the hundreds of thousands seems reasonable.

Alternative Word Problem Examples

To give you more ideas, let’s consider a couple of alternative word problems we could have created using the same expression:

  • Items Collected: “A museum has 120,567 artifacts in its main collection. It receives a donation of 34,020 ancient coins and an additional collection of 100,112 historical documents. How many items does the museum have in total?”

  • Distances Traveled: “A delivery truck travels 120,567 miles in the first year. In the second year, it travels 34,020 miles for local deliveries and 100,112 miles for long-distance deliveries. What is the total distance the truck travels in two years?”

Each of these problems uses the same numbers but places them in different contexts, showing the versatility of addition in real-world situations.

Key Steps in Creating a Word Problem

To recap, here are the key steps to keep in mind when creating your own word problems:

  1. Understand the Expression: First, make sure you understand the mathematical expression you’re working with. Identify the operations involved (addition, subtraction, multiplication, division) and the numbers you need to include.

  2. Choose a Context: Select a scenario or context that makes sense for the operation. Think about real-life situations where the numbers could be used.

  3. Craft the Narrative: Write a clear and engaging narrative that tells a story. Include the necessary information and a question that needs to be answered.

  4. Solve the Problem: Work through the problem yourself to ensure that it is solvable and that the answer makes sense in the context of the problem.

  5. Check for Clarity: Read the word problem carefully to make sure it is clear, concise, and easy to understand.

By following these steps, you can create your own challenging and interesting word problems!

Final Thoughts

So, guys, we've successfully tackled two different types of math problems today! We added even numbers and the smallest six-digit odd number, and we created and solved our own word problem. Remember, math can be fun and creative, and with a little practice, you can become a math whiz!

Keep practicing, keep exploring, and most importantly, keep having fun with math! You've got this!