Simplify The Following Expression: $\[ 1 \frac{1}{8} + 2 \frac{3}{4} \\]

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Introduction

In this article, we will simplify the expression 1 1/8 + 2 3/4. This involves converting the mixed numbers into improper fractions, adding them together, and then converting the result back into a mixed number. We will use the concept of equivalent fractions to make the calculations easier.

Understanding Mixed Numbers

A mixed number is a combination of a whole number and a fraction. For example, 1 1/8 is a mixed number where 1 is the whole number and 1/8 is the fraction. To simplify the expression, we need to convert the mixed numbers into improper fractions.

Converting Mixed Numbers to Improper Fractions

To convert a mixed number into an improper fraction, we multiply the whole number by the denominator and then add the numerator. The result is the new numerator, and the denominator remains the same.

For example, to convert 1 1/8 into an improper fraction, we multiply 1 by 8 and add 1:

1 × 8 = 8 8 + 1 = 9

So, 1 1/8 is equal to 9/8.

Similarly, to convert 2 3/4 into an improper fraction, we multiply 2 by 4 and add 3:

2 × 4 = 8 8 + 3 = 11

So, 2 3/4 is equal to 11/4.

Adding the Improper Fractions

Now that we have converted the mixed numbers into improper fractions, we can add them together. To add fractions, we need to have the same denominator. In this case, the denominators are 8 and 4, which are not the same. We can find the least common multiple (LCM) of 8 and 4, which is 8.

We can rewrite 11/4 as 22/8 by multiplying the numerator and denominator by 2:

22/8

Now that we have the same denominator, we can add the fractions:

9/8 + 22/8 = 31/8

Converting the Improper Fraction Back to a Mixed Number

To convert the improper fraction 31/8 back to a mixed number, we divide the numerator by the denominator:

31 ÷ 8 = 3 with a remainder of 7

So, 31/8 is equal to 3 7/8.

Conclusion

In this article, we simplified the expression 1 1/8 + 2 3/4 by converting the mixed numbers into improper fractions, adding them together, and then converting the result back into a mixed number. We used the concept of equivalent fractions to make the calculations easier. The final result is 3 7/8.

Key Takeaways

  • Mixed numbers can be converted into improper fractions by multiplying the whole number by the denominator and adding the numerator.
  • To add fractions, we need to have the same denominator. We can find the least common multiple (LCM) of the denominators.
  • Improper fractions can be converted back into mixed numbers by dividing the numerator by the denominator.

Real-World Applications

Simplifying expressions involving mixed numbers is an important skill in mathematics, particularly in algebra and geometry. It is used in various real-world applications, such as:

  • Calculating the area and perimeter of shapes
  • Finding the volume of solids
  • Solving equations involving fractions

Introduction

In our previous article, we simplified the expression 1 1/8 + 2 3/4 by converting the mixed numbers into improper fractions, adding them together, and then converting the result back into a mixed number. In this article, we will answer some frequently asked questions related to simplifying expressions involving mixed numbers.

Q&A

Q: What is a mixed number?

A: A mixed number is a combination of a whole number and a fraction. For example, 1 1/8 is a mixed number where 1 is the whole number and 1/8 is the fraction.

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

A: To convert a mixed number into an improper fraction, you multiply the whole number by the denominator and then add the numerator. The result is the new numerator, and the denominator remains the same.

For example, to convert 1 1/8 into an improper fraction, you multiply 1 by 8 and add 1:

1 × 8 = 8 8 + 1 = 9

So, 1 1/8 is equal to 9/8.

Q: How do I add fractions with different denominators?

A: To add fractions with different denominators, you need to have the same denominator. You can find the least common multiple (LCM) of the denominators, which is the smallest number that both denominators can divide into evenly.

For example, to add 9/8 and 22/8, you can add the numerators:

9 + 22 = 31

So, 9/8 + 22/8 = 31/8.

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

A: To convert an improper fraction back into a mixed number, you divide the numerator by the denominator:

31 ÷ 8 = 3 with a remainder of 7

So, 31/8 is equal to 3 7/8.

Q: What are some real-world applications of simplifying expressions involving mixed numbers?

A: Simplifying expressions involving mixed numbers is an important skill in mathematics, particularly in algebra and geometry. It is used in various real-world applications, such as:

  • Calculating the area and perimeter of shapes
  • Finding the volume of solids
  • Solving equations involving fractions

Q: How can I practice simplifying expressions involving mixed numbers?

A: You can practice simplifying expressions involving mixed numbers by working through examples and exercises. You can also use online resources, such as math websites and apps, to practice and review the concept.

Tips and Tricks

  • Make sure to convert the mixed numbers into improper fractions before adding or subtracting them.
  • Use the least common multiple (LCM) to find the common denominator when adding or subtracting fractions.
  • Practice, practice, practice! The more you practice simplifying expressions involving mixed numbers, the more comfortable you will become with the concept.

Conclusion

Simplifying expressions involving mixed numbers is an important skill in mathematics, particularly in algebra and geometry. By mastering the concept of simplifying expressions involving mixed numbers, you can solve a wide range of mathematical problems and apply them to real-world situations. We hope this Q&A article has been helpful in answering your questions and providing you with a better understanding of the concept.