Add These Numbers. Make Sure Your Answer Is Fully Reduced.$\[ 1 \frac{1}{4} + 2 \frac{5}{6} \\]
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Understanding Mixed Numbers
In mathematics, a mixed number is a combination of a whole number and a fraction. It is written in the form of ab/c, where a is the whole number part, and b/c is the fractional part. For example, 11/4 is a mixed number, where 1 is the whole number part and 1/4 is the fractional part.
The Problem: Adding Mixed Numbers
The problem we are given is to add the following mixed numbers: 11/4 and 25/6. To solve this problem, we need to follow a step-by-step approach.
Step 1: Convert 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 part by the denominator and add the numerator. The result is then written as the new numerator over the denominator.
For the first mixed number, 11/4, we multiply the whole number part (1) by the denominator (4) and add the numerator (1). This gives us 41/4.
For the second mixed number, 25/6, we multiply the whole number part (2) by the denominator (6) and add the numerator (5). This gives us 175/6.
Step 2: Add the Numerators
Now that we have converted both mixed numbers to improper fractions, we can add the numerators. To add fractions, we need to have the same denominator. In this case, the denominators are 4 and 6. We can find the least common multiple (LCM) of 4 and 6, which is 12.
We can rewrite the fractions with the LCM as the denominator:
- 41/4 = 93/12
- 175/6 = 345/12
Now we can add the numerators:
93/12 + 345/12 = 438/12
Step 3: Simplify the Result
The result we obtained in the previous step is an improper fraction. We can simplify it by dividing the numerator by the denominator and writing the remainder as the new numerator over the denominator.
438/12 = 37/12
Conclusion
In conclusion, the sum of the mixed numbers 11/4 and 25/6 is 37/12. We obtained this result by following a step-by-step approach, converting the mixed numbers to improper fractions, adding the numerators, and simplifying the result.
Tips and Tricks
- When adding mixed numbers, it is essential to convert them to improper fractions first.
- To add fractions, we need to have the same denominator. We can find the LCM of the denominators to achieve this.
- When simplifying the result, we can divide the numerator by the denominator and write the remainder as the new numerator over the denominator.
Practice Problems
- Add the mixed numbers 23/4 and 12/3.
- Add the mixed numbers 35/6 and 21/4.
Real-World Applications
Adding mixed numbers is an essential skill in mathematics, with real-world applications in various fields, such as:
- Cooking: When measuring ingredients, we often need to add fractions of a unit (e.g., cups, tablespoons).
- Building: When constructing a building, we need to add fractions of a unit (e.g., inches, feet) to ensure accurate measurements.
- Science: When conducting experiments, we often need to add fractions of a unit (e.g., grams, milliliters) to ensure accurate measurements.
Conclusion
In conclusion, adding mixed numbers is a fundamental skill in mathematics, with real-world applications in various fields. By following a step-by-step approach, converting mixed numbers to improper fractions, adding the numerators, and simplifying the result, we can obtain accurate results.
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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 ab/c, where a is the whole number part, and b/c is the fractional part.
Q: How do I add mixed numbers?
A: To add mixed numbers, you need to follow a step-by-step approach:
- Convert the mixed numbers to improper fractions.
- Add the numerators.
- Simplify the result.
Q: What is an improper fraction?
A: 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, you multiply the whole number part by the denominator and add the numerator.
Q: How do I find the least common multiple (LCM) of two numbers?
A: To find the LCM of two numbers, you can use the following steps:
- List the multiples of each number.
- Identify the smallest multiple that appears in both lists.
- The LCM is the smallest multiple that appears in both lists.
Q: Can I add mixed numbers with different denominators?
A: Yes, you can add mixed numbers with different denominators. To do this, you need to find the least common multiple (LCM) of the denominators and convert each mixed number to an improper fraction with the LCM as the denominator.
Q: How do I simplify an improper fraction?
A: To simplify an improper fraction, you can divide the numerator by the denominator and write the remainder as the new numerator over the denominator.
Q: What are some real-world applications of adding mixed numbers?
A: Adding mixed numbers has many real-world applications, including:
- Cooking: When measuring ingredients, you often need to add fractions of a unit (e.g., cups, tablespoons).
- Building: When constructing a building, you need to add fractions of a unit (e.g., inches, feet) to ensure accurate measurements.
- Science: When conducting experiments, you often need to add fractions of a unit (e.g., grams, milliliters) to ensure accurate measurements.
Q: Can I use a calculator to add mixed numbers?
A: Yes, you can use a calculator to add mixed numbers. However, it's essential to understand the concept of adding mixed numbers and how to convert them to improper fractions before using a calculator.
Q: How do I practice adding mixed numbers?
A: You can practice adding mixed numbers by:
- Using online resources, such as math websites and apps.
- Working with a tutor or teacher.
- Practicing with worksheets and exercises.
Q: What are some common mistakes to avoid when adding mixed numbers?
A: Some common mistakes to avoid when adding mixed numbers include:
- Not converting mixed numbers to improper fractions.
- Not finding the least common multiple (LCM) of the denominators.
- Not simplifying the result.
Q: Can I add mixed numbers with negative numbers?
A: Yes, you can add mixed numbers with negative numbers. To do this, you need to follow the same steps as adding mixed numbers with positive numbers, but you need to consider the signs of the numbers.
Q: How do I add mixed numbers with decimals?
A: To add mixed numbers with decimals, you need to convert the decimals to fractions and then add the mixed numbers.
Q: Can I add mixed numbers with fractions with different signs?
A: Yes, you can add mixed numbers with fractions with different signs. To do this, you need to follow the same steps as adding mixed numbers with positive numbers, but you need to consider the signs of the numbers.
Q: How do I add mixed numbers with fractions with the same sign?
A: To add mixed numbers with fractions with the same sign, you need to follow the same steps as adding mixed numbers with positive numbers.
Q: Can I add mixed numbers with fractions with unlike denominators?
A: Yes, you can add mixed numbers with fractions with unlike denominators. To do this, you need to find the least common multiple (LCM) of the denominators and convert each mixed number to an improper fraction with the LCM as the denominator.