Frank Bought Two Pork Roasts. One Roast Weighed Five And Seven-eighths Pounds, And The Other Roast Weighed Nine And Five-sixths Pounds. What Is The Total Weight Of The Pork Roasts?A. $15 \frac{17}{24}$ Pounds B. $14 \frac{5}{12}$
Understanding the Problem
In this problem, we are given the weights of two pork roasts in mixed number form. We need to find the total weight of the two roasts. To do this, we will first convert the mixed numbers to improper fractions, add them together, and then convert the result back to a mixed number.
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. We then write the result as an improper fraction with the same denominator.
For the first roast, we have:
5 and 7/8 = (5 × 8 + 7)/8 = 47/8
For the second roast, we have:
9 and 5/6 = (9 × 6 + 5)/6 = 59/6
Adding the Improper Fractions
Now that we have the weights of the two roasts in improper fraction form, we can add them together. To do this, we need to find a common denominator. The least common multiple (LCM) of 8 and 6 is 24.
We can rewrite the fractions with a common denominator as follows:
47/8 = (47 × 3)/(8 × 3) = 141/24
59/6 = (59 × 4)/(6 × 4) = 236/24
Now we can add the fractions:
141/24 + 236/24 = (141 + 236)/24 = 377/24
Converting the Result Back to a Mixed Number
To convert the improper fraction back to a mixed number, we divide the numerator by the denominator and write the result as a mixed number.
377 ÷ 24 = 15 with a remainder of 17
So the result is:
15 and 17/24
Conclusion
In this problem, we were given the weights of two pork roasts in mixed number form. We converted the mixed numbers to improper fractions, added them together, and then converted the result back to a mixed number. The total weight of the two roasts is 15 and 17/24 pounds.
Answer
The correct answer is:
A. $15 \frac{17}{24}$ pounds
Real-World Applications
This problem is a real-world example of how to add mixed numbers. In cooking, it is common to measure ingredients in mixed number form. For example, a recipe may call for 3 and 1/4 cups of flour. To add mixed numbers, we need to convert them to improper fractions, add them together, and then convert the result back to a mixed number.
Tips and Tricks
- When adding mixed numbers, it is helpful to convert them to improper fractions first.
- To convert a mixed number to an improper fraction, multiply the whole number part by the denominator and add the numerator.
- To add improper fractions, find a common denominator and add the numerators.
- To convert an improper fraction back to a mixed number, divide the numerator by the denominator and write the result as a mixed number.
Adding Mixed Numbers: A Real-World Example =====================================================
Q&A: Adding Mixed Numbers
Q: What is the difference between a mixed number and an improper fraction? A: A mixed number is a number that is written as a combination of a whole number and a fraction, such as 3 and 1/4. An improper fraction is a fraction where the numerator is greater than or equal to the denominator, such as 7/4.
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 part by the denominator and add the numerator. For example, to convert 3 and 1/4 to an improper fraction, multiply 3 by 4 and add 1, which gives 13. So, 3 and 1/4 is equal to 13/4.
Q: How do I add mixed numbers? A: To add mixed numbers, first convert them to improper fractions. Then, find a common denominator and add the numerators. Finally, convert the result back to a mixed number.
Q: What is the least common multiple (LCM) and why is it important? A: The LCM is the smallest multiple that two or more numbers have in common. It is important because it allows us to add fractions with different denominators by converting them to equivalent fractions with the same denominator.
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 multiple that appears in both lists. For example, the multiples of 4 are 4, 8, 12, 16, ... and the multiples of 6 are 6, 12, 18, 24, ... The smallest multiple that appears in both lists is 12, so the LCM of 4 and 6 is 12.
Q: Can I add mixed numbers with different denominators? A: Yes, you can add mixed numbers with different denominators by converting them to equivalent fractions with the same denominator. To do this, find the LCM of the two denominators and convert each fraction to an equivalent fraction with the LCM as the denominator.
Q: How do I convert a fraction to an equivalent fraction with a different denominator? A: To convert a fraction to an equivalent fraction with a different denominator, multiply the numerator and denominator by the same number. For example, to convert 1/2 to an equivalent fraction with a denominator of 6, multiply the numerator and denominator by 3, which gives 3/6.
Q: What are some real-world applications of adding mixed numbers? A: Adding mixed numbers is used in many real-world applications, such as cooking, carpentry, and finance. For example, a recipe may call for 3 and 1/4 cups of flour, and a carpenter may need to measure 2 and 3/4 inches of wood.
Q: Can I use a calculator to add mixed numbers? A: Yes, you can use a calculator to add mixed numbers. However, it is often more helpful to convert the mixed numbers to improper fractions and add them together manually.
Q: How do I check my answer when adding mixed numbers? A: To check your answer when adding mixed numbers, convert the result back to a mixed number and compare it to the original mixed numbers. If the result is correct, the two mixed numbers should add up to the result.