Calculate The Sum:$\[ 1 \frac{1}{2} + 33 \\]

Introduction

In mathematics, calculating the sum of fractions and whole numbers is a fundamental operation that is essential for solving various mathematical problems. In this article, we will focus on calculating the sum of a mixed number and a whole number, specifically the expression $1 \frac{1}{2} + 33$. We will break down the problem into smaller steps and provide a clear explanation of each step.

Understanding Mixed Numbers

A mixed number is a combination of a whole number and a fraction. In the expression $1 \frac{1}{2}$, the whole number part is 1 and the fraction part is $\frac{1}{2}$. To add a mixed number and a whole number, we need to first convert the mixed number to an improper fraction.

Converting Mixed Numbers to Improper Fractions

To convert a mixed number to an improper fraction, we multiply the whole number part by the denominator and add the numerator. In this case, we have:

$$1 \frac{1}{2} = \frac{(1 \times 2) + 1}{2} = \frac{3}{2}$$

Adding the Improper Fraction and the Whole Number

Now that we have converted the mixed number to an improper fraction, we can add it to the whole number. To add an improper fraction and a whole number, we need to first convert the whole number to an improper fraction with the same denominator as the improper fraction.

In this case, we have:

$$33 = \frac{33 \times 2}{2} = \frac{66}{2}$$

Now we can add the two improper fractions:

$$\frac{3}{2} + \frac{66}{2} = \frac{69}{2}$$

Simplifying the Result

The result of the addition is an improper fraction. To simplify the result, we can divide the numerator by the denominator:

$$\frac{69}{2} = 34 \frac{1}{2}$$

Conclusion

In this article, we have calculated the sum of a mixed number and a whole number, specifically the expression $1 \frac{1}{2} + 33$. We have broken down the problem into smaller steps and provided a clear explanation of each step. We have converted the mixed number to an improper fraction, added the improper fraction and the whole number, and simplified the result.

Key Takeaways

• To add a mixed number and a whole number, we need to first convert the mixed number to an improper fraction.
• To add an improper fraction and a whole number, we need to first convert the whole number to an improper fraction with the same denominator as the improper fraction.
• The result of the addition may be an improper fraction, which can be simplified by dividing the numerator by the denominator.

Practice Problems

1. Calculate the sum of $2 \frac{1}{3} + 25$.
2. Calculate the sum of $3 \frac{2}{5} + 12$.
3. Calculate the sum of $4 \frac{3}{4} + 18$.

Answer Key

1. $27 \frac{2}{3}$
2. $15 \frac{2}{5}$
3. $22 \frac{3}{4}$
   Calculating the Sum: A Q&A Guide =====================================

Introduction

In our previous article, we discussed how to calculate the sum of a mixed number and a whole number. In this article, we will provide a Q&A guide to help you understand the concept better. We will answer some common questions related to calculating the sum of mixed numbers and whole numbers.

Q: What is a mixed number?

A: A mixed number is a combination of a whole number and a fraction. For example, $1 \frac{1}{2}$ is a mixed number where the whole number part is 1 and the fraction part is $\frac{1}{2}$.

Q: How do I convert a mixed number to an improper fraction?

A: To convert a mixed number to an improper fraction, you need to multiply the whole number part by the denominator and add the numerator. For example, to convert $1 \frac{1}{2}$ to an improper fraction, you would multiply 1 by 2 and add 1, resulting in $\frac{3}{2}$.

Q: How do I add an improper fraction and a whole number?

A: To add an improper fraction and a whole number, you need to first convert the whole number to an improper fraction with the same denominator as the improper fraction. Then, you can add the two improper fractions.

Q: What is the difference between adding a mixed number and a whole number and adding two mixed numbers?

A: When adding a mixed number and a whole number, you need to convert the mixed number to an improper fraction and then add it to the whole number. When adding two mixed numbers, you need to convert both mixed numbers to improper fractions and then add them.

Q: Can I simplify the result of adding a mixed number and a whole number?

A: Yes, you can simplify the result of adding a mixed number and a whole number by dividing the numerator by the denominator.

Q: What are some common mistakes to avoid when calculating the sum of mixed numbers and whole numbers?

A: Some common mistakes to avoid when calculating the sum of mixed numbers and whole numbers include:

• Not converting the mixed number to an improper fraction before adding it to the whole number
• Not converting the whole number to an improper fraction with the same denominator as the improper fraction
• Not simplifying the result of the addition

Q: How can I practice calculating the sum of mixed numbers and whole numbers?

A: You can practice calculating the sum of mixed numbers and whole numbers by working through examples and exercises. You can also use online resources and calculators to help you practice.

Q: What are some real-world applications of calculating the sum of mixed numbers and whole numbers?

A: Calculating the sum of mixed numbers and whole numbers has many real-world applications, including:

• Cooking and recipe measurement
• Building and construction
• Finance and accounting
• Science and engineering

Conclusion

In this article, we have provided a Q&A guide to help you understand the concept of calculating the sum of mixed numbers and whole numbers. We have answered some common questions related to the topic and provided tips and examples to help you practice.

Key Takeaways

• A mixed number is a combination of a whole number and a fraction.
• To convert a mixed number to an improper fraction, multiply the whole number part by the denominator and add the numerator.
• To add an improper fraction and a whole number, convert the whole number to an improper fraction with the same denominator as the improper fraction.
• The result of adding a mixed number and a whole number can be simplified by dividing the numerator by the denominator.

Practice Problems

1. Calculate the sum of $2 \frac{1}{3} + 25$.
2. Calculate the sum of $3 \frac{2}{5} + 12$.
3. Calculate the sum of $4 \frac{3}{4} + 18$.

Answer Key

1. $27 \frac{2}{3}$
2. $15 \frac{2}{5}$
3. $22 \frac{3}{4}$