Paul Said, I Walked $2 \frac{1}{2}$ Miles On Saturday And $2 \frac{3}{4}$ Miles On Sunday. How Many Miles Is That In All?

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Introduction

In mathematics, mixed numbers are a combination of a whole number and a fraction. When we add mixed numbers, we need to follow a specific procedure to get the correct result. In this article, we will learn how to add mixed numbers with different denominators.

What are Mixed Numbers?

A mixed number is a combination of a whole number and a fraction. It is written in the form of a whole number followed by a fraction. For example, 2122 \frac{1}{2} is a mixed number where 2 is the whole number and 12\frac{1}{2} is the fraction.

Adding Mixed Numbers: A Step-by-Step Guide

To add mixed numbers, we need to follow these steps:

Step 1: Add the Whole Numbers

The first step is to add the whole numbers. In the given problem, we have 2122 \frac{1}{2} miles on Saturday and 2342 \frac{3}{4} miles on Sunday. We need to add the whole numbers, which are 2 and 2.

2 + 2 = 4

Step 2: Add the Fractions

The next step is to add the fractions. We need to find a common denominator for the fractions 12\frac{1}{2} and 34\frac{3}{4}. The least common multiple (LCM) of 2 and 4 is 4.

$\frac{1}{2}$ = $\frac{2}{4}$
$\frac{3}{4}$ = $\frac{3}{4}$

Now, we can add the fractions:

$\frac{2}{4}$ + $\frac{3}{4}$ = $\frac{5}{4}$

Step 3: Combine the Whole Number and the Fraction

Now, we need to combine the whole number and the fraction. We have a whole number 4 and a fraction 54\frac{5}{4}.

4 + $\frac{5}{4}$ = 4 + 1 $\frac{1}{4}$ = 5 $\frac{1}{4}$

Conclusion

In this article, we learned how to add mixed numbers with different denominators. We followed a step-by-step guide to add the whole numbers and the fractions, and then combined the whole number and the fraction to get the final result.

Example Problems

Here are some example problems to practice adding mixed numbers:

  • 3133 \frac{1}{3} + 2232 \frac{2}{3} = ?
  • 4144 \frac{1}{4} + 3343 \frac{3}{4} = ?
  • 5125 \frac{1}{2} + 4124 \frac{1}{2} = ?

Tips and Tricks

Here are some tips and tricks to help you add mixed numbers:

  • Make sure to find a common denominator for the fractions.
  • Add the fractions first, and then add the whole numbers.
  • Combine the whole number and the fraction to get the final result.

Real-World Applications

Adding mixed numbers has many real-world applications. For example, you can use it to calculate the total distance traveled in a trip, the total cost of an item, or the total amount of time spent on a task.

Final Thoughts

In conclusion, adding mixed numbers is a simple yet important math concept. By following the step-by-step guide and practicing with example problems, you can become proficient in adding mixed numbers. Remember to find a common denominator, add the fractions first, and combine the whole number and the fraction to get the final result.

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Introduction

Adding mixed numbers can be a challenging task, especially for students who are new to math. In this article, we will answer some frequently asked questions about adding mixed numbers.

Q&A

Q: What is a mixed number?

A: A mixed number is a combination of a whole number and a fraction. It is written in the form of a whole number followed by a fraction. For example, 2122 \frac{1}{2} is a mixed number where 2 is the whole number and 12\frac{1}{2} is the fraction.

Q: How do I add mixed numbers with different denominators?

A: To add mixed numbers with different denominators, you need to follow these steps:

  1. Add the whole numbers.
  2. Find a common denominator for the fractions.
  3. Add the fractions.
  4. Combine the whole number and the fraction to get the final result.

Q: What is the least common multiple (LCM)?

A: The least common multiple (LCM) is the smallest number that is a multiple of two or more numbers. For example, the LCM of 2 and 4 is 4.

Q: How do I find the LCM of two numbers?

A: To find the LCM of two numbers, you can list the multiples of each number and find the smallest number that is common to both lists. Alternatively, you can use the following formula:

LCM(a, b) = (a × b) / GCD(a, b)

where GCD(a, b) is the greatest common divisor of a and b.

Q: What is the greatest common divisor (GCD)?

A: The greatest common divisor (GCD) is the largest number that divides two or more numbers without leaving a remainder. For example, the GCD of 12 and 18 is 6.

Q: How do I add fractions with different denominators?

A: To add fractions with different denominators, you need to find a common denominator and then add the fractions. For example, to add 12\frac{1}{2} and 34\frac{3}{4}, you need to find a common denominator, which is 4. Then, you can add the fractions:

12\frac{1}{2} = 24\frac{2}{4} 34\frac{3}{4} = 34\frac{3}{4} 24\frac{2}{4} + 34\frac{3}{4} = 54\frac{5}{4}

Q: Can I add mixed numbers with unlike denominators?

A: Yes, you can add mixed numbers with unlike denominators. However, you need to follow the steps outlined above to add the fractions and then combine the whole number and the fraction to get the final result.

Q: What are some real-world applications of adding mixed numbers?

A: Adding mixed numbers has many real-world applications, such as calculating the total distance traveled in a trip, the total cost of an item, or the total amount of time spent on a task.

Conclusion

In this article, we answered some frequently asked questions about adding mixed numbers. We hope that this article has helped you to understand the concept of adding mixed numbers and how to apply it in real-world situations.

Example Problems

Here are some example problems to practice adding mixed numbers:

  • 3133 \frac{1}{3} + 2232 \frac{2}{3} = ?
  • 4144 \frac{1}{4} + 3343 \frac{3}{4} = ?
  • 5125 \frac{1}{2} + 4124 \frac{1}{2} = ?

Tips and Tricks

Here are some tips and tricks to help you add mixed numbers:

  • Make sure to find a common denominator for the fractions.
  • Add the fractions first, and then add the whole numbers.
  • Combine the whole number and the fraction to get the final result.

Final Thoughts

In conclusion, adding mixed numbers is a simple yet important math concept. By following the steps outlined in this article and practicing with example problems, you can become proficient in adding mixed numbers. Remember to find a common denominator, add the fractions first, and combine the whole number and the fraction to get the final result.