Evaluate The Expression: ${ 3 \frac{2}{3} + 2 \frac{1}{4} }$

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Introduction

When dealing with fractions, it's essential to understand how to add and subtract them correctly. In this article, we will evaluate the expression 3 2/3 + 2 1/4, which involves adding two mixed numbers. We will break down the process step by step, using the correct techniques to simplify the expression.

Understanding Mixed Numbers

Before we begin, let's review what mixed numbers are. A mixed number is a combination of a whole number and a fraction. It's written in the form a b/c, where a is the whole number, b is the numerator, and c is the denominator. In the given expression, 3 2/3 and 2 1/4 are both mixed numbers.

Converting Mixed Numbers to Improper Fractions

To add mixed numbers, we need to convert them to improper fractions first. An improper fraction is a fraction where the numerator is greater than or equal to the denominator. To convert a mixed number to an improper fraction, we multiply the whole number by the denominator and add the numerator. Then, we write the result as a fraction with the original denominator.

Let's convert 3 2/3 to an improper fraction:

3 2/3 = (3 × 3) + 2/3 = 9 + 2/3 = 29/3

Similarly, let's convert 2 1/4 to an improper fraction:

2 1/4 = (2 × 4) + 1/4 = 8 + 1/4 = 33/4

Adding Improper Fractions

Now that we have both mixed numbers converted to improper fractions, we can add them. However, we need to find a common denominator first. The least common multiple (LCM) of 3 and 4 is 12. We can rewrite both fractions with a denominator of 12:

29/3 = (29 × 4) / (3 × 4) = 116/12

33/4 = (33 × 3) / (4 × 3) = 99/12

Now that we have a common denominator, we can add the fractions:

116/12 + 99/12 = (116 + 99) / 12 = 215/12

Converting the Result Back to a Mixed Number

The result of the addition is an improper fraction. To convert it back to a mixed number, we divide the numerator by the denominator:

215 ÷ 12 = 17 with a remainder of 11

So, the result of the expression 3 2/3 + 2 1/4 is 17 11/12.

Conclusion

Evaluating the expression 3 2/3 + 2 1/4 involves converting mixed numbers to improper fractions, finding a common denominator, adding the fractions, and finally converting the result back to a mixed number. By following these steps, we can simplify the expression and find the correct result.

Tips and Tricks

  • When adding mixed numbers, it's essential to convert them to improper fractions first.
  • Finding a common denominator is crucial when adding fractions.
  • Converting the result back to a mixed number can help make the answer more understandable.

Frequently Asked Questions

  • Q: What is the result of the expression 3 2/3 + 2 1/4? A: The result is 17 11/12.
  • Q: How do I convert a mixed number to an improper fraction? A: Multiply the whole number by the denominator and add the numerator. Then, write the result as a fraction with the original denominator.
  • Q: What is the least common multiple (LCM) of 3 and 4? A: The LCM of 3 and 4 is 12.

Further Reading

  • Adding and Subtracting Fractions: A Comprehensive Guide
  • Mixed Numbers: Understanding and Simplifying
  • Improper Fractions: Converting and Simplifying

Introduction

In our previous article, we evaluated the expression 3 2/3 + 2 1/4, which involved adding two mixed numbers. We broke down the process step by step, using the correct techniques to simplify the expression. In this article, we will answer some frequently asked questions related to evaluating expressions with mixed numbers.

Q&A

Q: What is the difference between a mixed number and an improper fraction?

A: A mixed number is a combination of a whole number and a fraction, written in the form a b/c. An improper fraction is a fraction where the numerator is greater than or equal to the denominator, written in the form a/b.

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

A: To convert a mixed number to an improper fraction, multiply the whole number by the denominator and add the numerator. Then, write the result as a fraction with the original denominator.

Q: What is the least common multiple (LCM) of 3 and 4?

A: The LCM of 3 and 4 is 12.

Q: How do I add mixed numbers?

A: To add mixed numbers, convert them to improper fractions first. Then, find a common denominator and add the fractions. Finally, convert the result back to a mixed number.

Q: What is the result of the expression 2 1/4 + 1 3/4?

A: To evaluate this expression, convert the mixed numbers to improper fractions:

2 1/4 = (2 × 4) + 1/4 = 8 + 1/4 = 33/4

1 3/4 = (1 × 4) + 3/4 = 4 + 3/4 = 19/4

Now, find a common denominator (which is 4) and add the fractions:

33/4 + 19/4 = (33 + 19) / 4 = 52/4 = 13

So, the result of the expression 2 1/4 + 1 3/4 is 13.

Q: What is the result of the expression 5 2/3 + 3 1/6?

A: To evaluate this expression, convert the mixed numbers to improper fractions:

5 2/3 = (5 × 3) + 2/3 = 15 + 2/3 = 47/3

3 1/6 = (3 × 6) + 1/6 = 18 + 1/6 = 109/6

Now, find a common denominator (which is 6) and add the fractions:

47/3 = (47 × 2) / (3 × 2) = 94/6

109/6 + 94/6 = (109 + 94) / 6 = 203/6

So, the result of the expression 5 2/3 + 3 1/6 is 33 5/6.

Q: How do I subtract mixed numbers?

A: To subtract mixed numbers, convert them to improper fractions first. Then, find a common denominator and subtract the fractions. Finally, convert the result back to a mixed number.

Q: What is the result of the expression 7 3/4 - 2 1/4?

A: To evaluate this expression, convert the mixed numbers to improper fractions:

7 3/4 = (7 × 4) + 3/4 = 28 + 3/4 = 119/4

2 1/4 = (2 × 4) + 1/4 = 8 + 1/4 = 33/4

Now, find a common denominator (which is 4) and subtract the fractions:

119/4 - 33/4 = (119 - 33) / 4 = 86/4 = 21 2/4

So, the result of the expression 7 3/4 - 2 1/4 is 21 2/4.

Conclusion

Evaluating expressions with mixed numbers can be challenging, but with the right techniques and practice, you can become proficient in simplifying these expressions. Remember to convert mixed numbers to improper fractions, find a common denominator, and add or subtract the fractions as needed. Finally, convert the result back to a mixed number to make the answer more understandable.

Tips and Tricks

  • When adding or subtracting mixed numbers, it's essential to convert them to improper fractions first.
  • Finding a common denominator is crucial when adding or subtracting fractions.
  • Converting the result back to a mixed number can help make the answer more understandable.

Further Reading

  • Adding and Subtracting Fractions: A Comprehensive Guide
  • Mixed Numbers: Understanding and Simplifying
  • Improper Fractions: Converting and Simplifying