Simplify The Expression: ${ 3 \frac{5}{8} + \frac{7}{8} = }$
Introduction
When dealing with fractions, it's essential to understand how to add and simplify them. In this article, we will focus on simplifying the expression 3 5/8 + 7/8. We will break down the steps involved in adding fractions and provide a clear explanation of the process.
Understanding the Problem
The given expression is 3 5/8 + 7/8. To simplify this expression, we need to add the fractions 5/8 and 7/8. However, before we can add the fractions, we need to convert the mixed number 3 5/8 to an improper fraction.
Converting Mixed Numbers to Improper Fractions
A mixed number is a combination of a whole number and a fraction. To convert a mixed number to an improper fraction, we need to multiply the whole number by the denominator and then add the numerator. The result is then written as an improper fraction with the same denominator.
In this case, the mixed number is 3 5/8. To convert it to an improper fraction, we need to multiply 3 by 8 and then add 5.
3 × 8 = 24 24 + 5 = 29
So, the improper fraction equivalent of 3 5/8 is 29/8.
Adding Fractions with Different Denominators
Now that we have converted the mixed number to an improper fraction, we can add the fractions 29/8 and 7/8. However, the fractions have different denominators, so we need to find a common denominator before we can add them.
The least common multiple (LCM) of 8 and 8 is 8. Since both fractions already have a denominator of 8, we can add them directly.
Adding Fractions with the Same Denominator
Now that we have found a common denominator, we can add the fractions 29/8 and 7/8.
29/8 + 7/8 = (29 + 7)/8 = 36/8
Simplifying the Result
The result of the addition is 36/8. However, we can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD).
The GCD of 36 and 8 is 4.
36 ÷ 4 = 9 8 ÷ 4 = 2
So, the simplified fraction is 9/2.
Conclusion
In this article, we simplified the expression 3 5/8 + 7/8 by converting the mixed number to an improper fraction, adding the fractions with the same denominator, and simplifying the result. We hope that this article has provided a clear explanation of the process involved in simplifying expressions with fractions.
Frequently Asked Questions
- 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, while an improper fraction is a single fraction with a numerator greater than the denominator.
- 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 then add the numerator.
- Q: How do I add fractions with different denominators? A: To add fractions with different denominators, find a common denominator and then add the fractions.
Step-by-Step Guide
- Convert the mixed number to an improper fraction by multiplying the whole number by the denominator and then adding the numerator.
- Find a common denominator for the fractions.
- Add the fractions with the same denominator.
- Simplify the result by dividing both the numerator and the denominator by their greatest common divisor.
Common Mistakes to Avoid
- Not converting the mixed number to an improper fraction before adding the fractions.
- Not finding a common denominator before adding the fractions.
- Not simplifying the result after adding the fractions.
Real-World Applications
- Adding fractions is an essential skill in mathematics, and it has many real-world applications, such as calculating percentages, measuring ingredients for recipes, and determining the cost of items.
- Understanding how to add fractions can also help you to solve problems in science, technology, engineering, and mathematics (STEM) fields.
Conclusion
In conclusion, simplifying the expression 3 5/8 + 7/8 requires converting the mixed number to an improper fraction, adding the fractions with the same denominator, and simplifying the result. By following the steps outlined in this article, you can simplify expressions with fractions and develop a deeper understanding of the mathematical concepts involved.
Introduction
In our previous article, we simplified the expression 3 5/8 + 7/8 by converting the mixed number to an improper fraction, adding the fractions with the same denominator, and simplifying the result. In this article, we will provide a Q&A section to address common questions and concerns related to simplifying expressions with fractions.
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, while an improper fraction is a single fraction with a numerator greater than the denominator.
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 then add the numerator.
Q: How do I add fractions with different denominators?
A: To add fractions with different denominators, find a common denominator and then add the fractions.
Q: What is the least common multiple (LCM) of two numbers?
A: The LCM of two numbers is the smallest number that is a multiple of both numbers.
Q: How do I find the LCM of two numbers?
A: To find the LCM of two numbers, list the multiples of each number and find the smallest number that appears in both lists.
Q: What is the greatest common divisor (GCD) of two numbers?
A: The GCD of two numbers is the largest number that divides both numbers without leaving a remainder.
Q: How do I find the GCD of two numbers?
A: To find the GCD of two numbers, list the factors of each number and find the largest number that appears in both lists.
Q: Can I simplify a fraction by dividing both the numerator and the denominator by a number other than the GCD?
A: No, you can only simplify a fraction by dividing both the numerator and the denominator by the GCD.
Q: What is the difference between adding fractions and adding mixed numbers?
A: Adding fractions involves adding the numerators and keeping the same denominator, while adding mixed numbers involves converting the mixed numbers to improper fractions and then adding the fractions.
Q: How do I add mixed numbers?
A: To add mixed numbers, convert each mixed number to an improper fraction, find a common denominator, add the fractions, and then simplify the result.
Q: Can I add fractions with unlike signs?
A: Yes, you can add fractions with unlike signs by following the same steps as adding fractions with like signs.
Q: What is the rule for adding fractions with unlike signs?
A: When adding fractions with unlike signs, subtract the smaller fraction from the larger fraction.
Q: Can I subtract fractions?
A: Yes, you can subtract fractions by following the same steps as adding fractions.
Q: What is the rule for subtracting fractions?
A: When subtracting fractions, subtract the smaller fraction from the larger fraction.
Common Mistakes to Avoid
- Not converting the mixed number to an improper fraction before adding the fractions.
- Not finding a common denominator before adding the fractions.
- Not simplifying the result after adding the fractions.
- Not following the correct order of operations when adding fractions with unlike signs.
Real-World Applications
- Adding fractions is an essential skill in mathematics, and it has many real-world applications, such as calculating percentages, measuring ingredients for recipes, and determining the cost of items.
- Understanding how to add fractions can also help you to solve problems in science, technology, engineering, and mathematics (STEM) fields.
Conclusion
In conclusion, simplifying expressions with fractions requires a clear understanding of the concepts involved, including converting mixed numbers to improper fractions, finding common denominators, and simplifying results. By following the steps outlined in this article and avoiding common mistakes, you can develop a deeper understanding of the mathematical concepts involved and apply them to real-world problems.
Additional Resources
- For more information on simplifying expressions with fractions, visit the following websites:
- Khan Academy: Adding and Subtracting Fractions
- Mathway: Adding and Subtracting Fractions
- IXL: Adding and Subtracting Fractions
- For practice problems and exercises, visit the following websites:
- Math Open Reference: Adding and Subtracting Fractions
- Purplemath: Adding and Subtracting Fractions
- Math Goodies: Adding and Subtracting Fractions