Find The Sum.${ \begin{array}{r} 3 \frac{5}{6} = 3 \frac{?}{24} \ +5 \frac{3}{8} = 5 \frac{?}{24} \ \hline \end{array} }$[ \begin{array}{r} 3 \frac{5}{6} = 3 \frac{\square}{24} \ +5 \frac{3}{8} = 5 \frac{9}{24}
Introduction
In mathematics, finding the sum of fractions can be a challenging task, especially when dealing with mixed numbers. A mixed number is a combination of a whole number and a fraction. In this article, we will explore how to find the sum of two mixed numbers, with a focus on converting them to equivalent fractions with a common denominator.
Understanding Mixed Numbers
A mixed number is a combination of a whole number and a fraction. For example, 3 5/6 is a mixed number, where 3 is the whole number and 5/6 is the fraction. To add mixed numbers, we need to convert them to equivalent fractions with a common denominator.
Converting Mixed Numbers to Equivalent Fractions
To convert a mixed number to an equivalent fraction, we need to multiply the whole number by the denominator and add the numerator. For example, to convert 3 5/6 to an equivalent fraction, we multiply 3 by 6 and add 5, which gives us 23/6.
Finding the Sum
Now that we have converted the mixed numbers to equivalent fractions, we can find the sum. We need to find a common denominator for the two fractions. In this case, the common denominator is 24.
Step 1: Convert 3 5/6 to an Equivalent Fraction
To convert 3 5/6 to an equivalent fraction, we multiply 3 by 24 and add 5, which gives us 73/24.
Step 2: Convert 5 3/8 to an Equivalent Fraction
To convert 5 3/8 to an equivalent fraction, we multiply 5 by 24 and add 3, which gives us 117/24.
Step 3: Find the Sum
Now that we have converted the mixed numbers to equivalent fractions, we can find the sum. We add the two fractions together, which gives us:
73/24 + 117/24 = 190/24
Simplifying the Sum
To simplify the sum, we can divide both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD of 190 and 24 is 2. Dividing both the numerator and the denominator by 2 gives us:
95/12
Conclusion
In this article, we explored how to find the sum of two mixed numbers. We converted the mixed numbers to equivalent fractions with a common denominator and then added them together. The result was a simplified fraction, which is the sum of the two mixed numbers.
Discussion
- What are some common challenges when finding the sum of mixed numbers?
- How can we simplify the sum of mixed numbers?
- What are some real-world applications of finding the sum of mixed numbers?
Answer Key
- The sum of 3 5/6 and 5 3/8 is 8 9/24.
- To simplify the sum, we can divide both the numerator and the denominator by their greatest common divisor (GCD).
- Real-world applications of finding the sum of mixed numbers include cooking, building, and finance.
Additional Resources
- Khan Academy: Adding and Subtracting Fractions
- Mathway: Adding Mixed Numbers
- IXL: Adding and Subtracting Fractions
Final Thoughts
Q: What is the sum of 2 3/4 and 1 2/3?
A: To find the sum, we need to convert the mixed numbers to equivalent fractions with a common denominator. The common denominator is 12. We can convert 2 3/4 to 11/4 and 1 2/3 to 5/3. Then, we can add the fractions together: 11/4 + 5/3 = 47/12.
Q: How do I convert a mixed number to an equivalent fraction?
A: To convert a mixed number to an equivalent fraction, we need to multiply the whole number by the denominator and add the numerator. For example, to convert 3 5/6 to an equivalent fraction, we multiply 3 by 6 and add 5, which gives us 23/6.
Q: What is the sum of 4 1/2 and 2 3/4?
A: To find the sum, we need to convert the mixed numbers to equivalent fractions with a common denominator. The common denominator is 4. We can convert 4 1/2 to 9/2 and 2 3/4 to 11/4. Then, we can add the fractions together: 9/2 + 11/4 = 31/4.
Q: How do I simplify a fraction?
A: To simplify a fraction, we need to divide both the numerator and the denominator by their greatest common divisor (GCD). For example, to simplify 12/16, we can divide both the numerator and the denominator by 4, which gives us 3/4.
Q: What is the sum of 1 1/3 and 2 2/3?
A: To find the sum, we need to convert the mixed numbers to equivalent fractions with a common denominator. The common denominator is 3. We can convert 1 1/3 to 4/3 and 2 2/3 to 8/3. Then, we can add the fractions together: 4/3 + 8/3 = 12/3.
Q: How do I add fractions with different denominators?
A: To add fractions with different denominators, we need to convert them to equivalent fractions with a common denominator. We can find the least common multiple (LCM) of the denominators and then convert each fraction to an equivalent fraction with the LCM as the denominator.
Q: What is the sum of 3 1/6 and 2 5/6?
A: To find the sum, we need to convert the mixed numbers to equivalent fractions with a common denominator. The common denominator is 6. We can convert 3 1/6 to 19/6 and 2 5/6 to 17/6. Then, we can add the fractions together: 19/6 + 17/6 = 36/6.
Q: How do I subtract fractions with different denominators?
A: To subtract fractions with different denominators, we need to convert them to equivalent fractions with a common denominator. We can find the least common multiple (LCM) of the denominators and then convert each fraction to an equivalent fraction with the LCM as the denominator.
Q: What is the sum of 5 3/8 and 2 1/8?
A: To find the sum, we need to convert the mixed numbers to equivalent fractions with a common denominator. The common denominator is 8. We can convert 5 3/8 to 43/8 and 2 1/8 to 17/8. Then, we can add the fractions together: 43/8 + 17/8 = 60/8.
Conclusion
Finding the sum of mixed numbers can be a challenging task, but with practice and patience, it can become second nature. By converting the mixed numbers to equivalent fractions with a common denominator and then adding them together, we can find the sum. Remember to simplify the sum by dividing both the numerator and the denominator by their greatest common divisor (GCD). With these skills, you will be able to tackle even the most complex math problems with confidence.