Solve:$\[ 8 \frac{3}{4} + 9 \frac{4}{5} = ? \\]If Needed, Simplify The Mixed Numbers.Now Add The Whole Numbers:$\[ \begin{array}{r} 1 \\ 8 \\ + \quad 9 \\ \hline \end{array} \\]$\[ \square \\]

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Understanding Mixed Numbers

Mixed numbers are a combination of a whole number and a fraction. They are written in the form of a b/c, where a is the whole number and b/c is the fraction. In the given problem, we have two mixed numbers: 8 3/4 and 9 4/5. To add these mixed numbers, we need to first convert them into improper fractions.

Converting Mixed Numbers to Improper Fractions

To convert a mixed number to an improper fraction, we multiply the whole number by the denominator and then add the numerator. The result is then written as the new numerator over the denominator.

For 8 3/4, we multiply 8 by 4 to get 32, and then add 3 to get 35. So, 8 3/4 becomes 35/4.

For 9 4/5, we multiply 9 by 5 to get 45, and then add 4 to get 49. So, 9 4/5 becomes 49/5.

Adding Improper Fractions

Now that we have converted both mixed numbers to improper fractions, we can add them together. To add improper fractions, we need to have the same denominator. In this case, the least common multiple (LCM) of 4 and 5 is 20.

We can rewrite 35/4 as 35*5/4*5 = 175/20 and 49/5 as 49*4/5*4 = 196/20.

Now, we can add the two fractions together: 175/20 + 196/20 = 371/20.

Converting the Result Back to a Mixed Number

To convert the improper fraction 371/20 back to a mixed number, we divide the numerator by the denominator. 371 ÷ 20 = 18 with a remainder of 11. So, the mixed number is 18 11/20.

Adding Whole Numbers

Now, let's add the whole numbers: 8 + 9 = 17.

Conclusion

In this article, we have learned how to add mixed numbers by converting them to improper fractions and then adding them together. We have also learned how to convert the result back to a mixed number. By following these steps, we can solve problems involving mixed number addition.

Real-World Applications

Mixed number addition has many real-world applications, such as calculating the total cost of items when prices are given as mixed numbers. For example, if a shirt costs $8 3/4 and a pair of pants costs $9 4/5, we can add the two prices together to get the total cost.

Tips and Tricks

When adding mixed numbers, it's essential to convert them to improper fractions first. This will make it easier to add the fractions together. Also, make sure to find the least common multiple (LCM) of the denominators to ensure that the fractions have the same denominator.

Common Mistakes

One common mistake when adding mixed numbers is to add the whole numbers and the fractions separately. This can lead to incorrect results. To avoid this mistake, make sure to convert the mixed numbers to improper fractions and then add them together.

Practice Problems

Here are some practice problems to help you reinforce your understanding of mixed number addition:

  • 2 3/4 + 1 2/5 = ?
  • 6 1/3 + 4 2/5 = ?
  • 3 2/5 + 2 3/4 = ?

By practicing these problems, you will become more confident in your ability to add mixed numbers and solve real-world problems involving mixed number addition.

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, written in the form of a b/c, where a is the whole number and b/c is the fraction. An improper fraction, on the other hand, is a fraction where the numerator is greater than or equal to the denominator, written in the form of b/c, where b is the numerator and c is the denominator.

Q: How do I convert a mixed number to an improper fraction?

A: To convert a mixed number to an improper fraction, you multiply the whole number by the denominator and then add the numerator. The result is then written as the new numerator over the denominator.

For example, to convert 8 3/4 to an improper fraction, you multiply 8 by 4 to get 32, and then add 3 to get 35. So, 8 3/4 becomes 35/4.

Q: How do I add mixed numbers?

A: To add mixed numbers, you need to convert them to improper fractions first. Then, you add the improper fractions together by finding the least common multiple (LCM) of the denominators and rewriting the fractions with the same denominator. Finally, you add the numerators together and keep the same denominator.

For example, to add 8 3/4 and 9 4/5, you convert them to improper fractions: 8 3/4 becomes 35/4 and 9 4/5 becomes 49/5. Then, you find the LCM of 4 and 5, which is 20. You rewrite the fractions with the same denominator: 35/4 becomes 175/20 and 49/5 becomes 196/20. Finally, you add the numerators together: 175 + 196 = 371. So, the result is 371/20, which can be converted back to a mixed number as 18 11/20.

Q: How do I add whole numbers and mixed numbers?

A: To add whole numbers and mixed numbers, you need to convert the mixed numbers to improper fractions first. Then, you add the whole numbers together and add the improper fractions together.

For example, to add 8 and 9 4/5, you convert 9 4/5 to an improper fraction: 9 4/5 becomes 49/5. Then, you add the whole numbers together: 8 + 9 = 17. Finally, you add the improper fraction to the whole number: 17 + 49/5. To add this, you need to find the LCM of 1 and 5, which is 5. You rewrite the whole number as an improper fraction: 17 = 85/5. Then, you add the numerators together: 85 + 49 = 134. So, the result is 134/5, which can be converted back to a mixed number as 26 4/5.

Q: What are some common mistakes to avoid when adding mixed numbers?

A: One common mistake to avoid is adding the whole numbers and the fractions separately. This can lead to incorrect results. To avoid this mistake, make sure to convert the mixed numbers to improper fractions and then add them together.

Another common mistake is not finding the least common multiple (LCM) of the denominators. This can also lead to incorrect results. To avoid this mistake, make sure to find the LCM of the denominators before adding the fractions together.

Q: How can I practice adding mixed numbers?

A: You can practice adding mixed numbers by working through problems like the ones in this article. You can also try creating your own problems and solving them. Additionally, you can use online resources or math apps to practice adding mixed numbers.

Q: What are some real-world applications of mixed number addition?

A: Mixed number addition has many real-world applications, such as calculating the total cost of items when prices are given as mixed numbers. For example, if a shirt costs $8 3/4 and a pair of pants costs $9 4/5, you can add the two prices together to get the total cost.

Mixed number addition is also used in cooking and recipes, where ingredients are often measured in mixed numbers. For example, a recipe might call for 2 3/4 cups of flour and 1 2/5 cups of sugar. You can add these mixed numbers together to get the total amount of ingredients needed.

Q: Can I use a calculator to add mixed numbers?

A: Yes, you can use a calculator to add mixed numbers. However, it's often more helpful to practice adding mixed numbers by hand to develop your understanding of the concept and to build your math skills.

If you do use a calculator, make sure to enter the mixed numbers correctly and to check your results to ensure that they are accurate.