Add. Use Pencil And Paper To Show Your Work.${ 5 \frac{2}{3} + 7 \frac{2}{3} = }$A. ${ 12 \frac{3}{3}\$} B. ${ 12 \frac{0}{3}\$} C. ${ 13 \frac{1}{3}\$}
Understanding Mixed Numbers
Before we dive into the problem, let's first understand what mixed numbers are. A mixed number is a combination of a whole number and a fraction. It is written in the form of a b/c, where a is the whole number and b/c is the fraction. For example, 5 2/3 is a mixed number, where 5 is the whole number and 2/3 is the fraction.
The Problem
Now, let's take a look at the problem:
5 2/3 + 7 2/3 = ?
We need to add these two mixed numbers together. To do this, we need to follow a step-by-step process.
Step 1: Add the Whole Numbers
The first step is to add the whole numbers together. In this case, we have 5 and 7, so we add them together:
5 + 7 = 12
Step 2: Add the Fractions
Next, we need to add the fractions together. To do this, we need to find a common denominator. In this case, the common denominator is 3, so we can add the fractions together:
2/3 + 2/3 = 4/3
Step 3: Combine the Whole Number and Fraction
Now that we have the whole number and fraction, we can combine them. To do this, we need to convert the fraction to a mixed number. In this case, we can convert 4/3 to a mixed number by dividing the numerator by the denominator:
4 ÷ 3 = 1 with a remainder of 1
So, the mixed number is 1 1/3.
The Final Answer
Now that we have the mixed number, we can write the final answer:
5 2/3 + 7 2/3 = 12 1/3
Conclusion
Adding mixed numbers can be a bit tricky, but by following a step-by-step process, we can make it easier. Remember to add the whole numbers together, add the fractions together, and then combine the whole number and fraction. With practice, you'll become a pro at adding mixed numbers in no time!
Common Mistakes to Avoid
When adding mixed numbers, there are a few common mistakes to avoid:
- Not adding the whole numbers together: Make sure to add the whole numbers together before adding the fractions.
- Not finding a common denominator: Make sure to find a common denominator before adding the fractions together.
- Not converting the fraction to a mixed number: Make sure to convert the fraction to a mixed number before combining it with the whole number.
Real-World Applications
Adding mixed numbers has many real-world applications. For example:
- Cooking: When cooking, you may need to add ingredients together, such as
2 1/4 cups of flourand1 1/2 cups of sugar. By adding mixed numbers, you can easily calculate the total amount of ingredients needed. - Building: When building a project, you may need to add measurements together, such as
5 1/2 feetand3 1/4 feet. By adding mixed numbers, you can easily calculate the total length of the project. - Finance: When managing finances, you may need to add amounts together, such as
5 1/4 hoursand2 1/2 hours. By adding mixed numbers, you can easily calculate the total amount of time spent on a project.
Practice Problems
Here are a few practice problems to help you practice adding mixed numbers:
3 1/2 + 2 1/4 = ?4 3/4 + 1 1/2 = ?2 2/3 + 5 1/6 = ?
Conclusion
Q: What is a mixed number?
A: A mixed number is a combination of a whole number and a fraction. It is written in the form of a b/c, where a is the whole number and b/c is the fraction.
Q: How do I add mixed numbers?
A: To add mixed numbers, you need to follow a step-by-step process:
- Add the whole numbers together.
- Add the fractions together, making sure to find a common denominator.
- Combine the whole number and fraction.
Q: What is the common denominator?
A: The common denominator is the smallest number that both fractions can divide into evenly. For example, if you have 2/3 and 1/6, the common denominator is 6.
Q: How do I find the common denominator?
A: To find the common denominator, you need to list the multiples of each denominator and find the smallest number that appears in both lists. For example, if you have 2/3 and 1/6, the multiples of 3 are 3, 6, 9, 12, ... and the multiples of 6 are 6, 12, 18, 24, .... The smallest number that appears in both lists is 6, so the common denominator is 6.
Q: What if the fractions have different denominators?
A: If the fractions have different denominators, you need to find the least common multiple (LCM) of the two denominators. The LCM is the smallest number that both denominators can divide into evenly. For example, if you have 2/3 and 1/4, the LCM of 3 and 4 is 12, so you need to convert both fractions to have a denominator of 12.
Q: How do I convert a fraction to have a different denominator?
A: To convert a fraction to have a different denominator, you need to multiply the numerator and denominator by the same number. For example, if you have 2/3 and you want to convert it to have a denominator of 12, you need to multiply the numerator and denominator by 4:
2/3 = (2 x 4) / (3 x 4) = 8/12
Q: What if I have a negative mixed number?
A: If you have a negative mixed number, you need to follow the same steps as before, but make sure to keep the negative sign. For example, if you have -3 1/2, you need to add the whole number and fraction together, making sure to keep the negative sign:
-3 1/2 = -3 + (-1/2) = -3 - 1/2
Q: Can I add mixed numbers with different signs?
A: Yes, you can add mixed numbers with different signs. To do this, you need to follow the same steps as before, but make sure to keep the signs. For example, if you have 3 1/2 and -2 1/4, you need to add the whole numbers together and the fractions together, making sure to keep the signs:
3 1/2 + (-2 1/4) = (3 - 2) + (1/2 - 1/4) = 1 + 1/4
Q: What if I have a mixed number with a zero numerator?
A: If you have a mixed number with a zero numerator, you can simply ignore the numerator and keep the denominator. For example, if you have 0 1/2, you can simply ignore the numerator and keep the denominator:
0 1/2 = 1/2
Q: Can I subtract mixed numbers?
A: Yes, you can subtract mixed numbers. To do this, you need to follow the same steps as before, but make sure to subtract the fractions. For example, if you have 3 1/2 and 2 1/4, you need to subtract the fractions:
3 1/2 - 2 1/4 = (3 - 2) + (1/2 - 1/4) = 1 + 1/4
Q: What if I have a mixed number with a negative numerator?
A: If you have a mixed number with a negative numerator, you need to follow the same steps as before, but make sure to keep the negative sign. For example, if you have -3 1/2, you need to subtract the fractions:
-3 1/2 - 2 1/4 = (-3 - 2) + (-1/2 - 1/4) = -5 - 3/4
Conclusion
Adding mixed numbers can be a bit tricky, but by following a step-by-step process and understanding the common denominator, you can easily add mixed numbers and become a pro in no time!