Evaluate The Expression:$\frac{1}{12} + \frac{3}{8}$

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Introduction

When it comes to adding fractions, it can be a bit tricky, especially when the denominators are different. In this article, we will evaluate the expression 112+38\frac{1}{12} + \frac{3}{8} and provide a step-by-step guide on how to add fractions with different denominators.

Understanding the Problem

To evaluate the expression 112+38\frac{1}{12} + \frac{3}{8}, we need to find a common denominator for both fractions. The common denominator is the least common multiple (LCM) of the two denominators, which in this case is 24.

Finding the Least Common Multiple (LCM)

To find the LCM of 12 and 8, we need to list the multiples of each number.

  • Multiples of 12: 12, 24, 36, 48, ...
  • Multiples of 8: 8, 16, 24, 32, ...

As we can see, the first number that appears in both lists is 24, which is the LCM of 12 and 8.

Converting the Fractions

Now that we have found the LCM, we can convert both fractions to have a denominator of 24.

  • 112=1×212×2=224\frac{1}{12} = \frac{1 \times 2}{12 \times 2} = \frac{2}{24}
  • 38=3×38×3=924\frac{3}{8} = \frac{3 \times 3}{8 \times 3} = \frac{9}{24}

Adding the Fractions

Now that both fractions have the same denominator, we can add them together.

224+924=2+924=1124\frac{2}{24} + \frac{9}{24} = \frac{2 + 9}{24} = \frac{11}{24}

Conclusion

In conclusion, the expression 112+38\frac{1}{12} + \frac{3}{8} can be evaluated by finding the least common multiple (LCM) of the two denominators, which is 24. We can then convert both fractions to have a denominator of 24 and add them together to get the final result of 1124\frac{11}{24}.

Tips and Tricks

  • When adding fractions with different denominators, it's essential to find the least common multiple (LCM) of the two denominators.
  • You can use a calculator or a multiplication chart to find the LCM of two numbers.
  • When converting fractions to have a common denominator, make sure to multiply both the numerator and the denominator by the same number.

Real-World Applications

Adding fractions with different denominators is a common problem in real-world applications, such as:

  • Cooking: When a recipe calls for a certain amount of a ingredient, but the ingredient is sold in different sizes, you may need to add fractions with different denominators to get the correct amount.
  • Building: When building a structure, you may need to add fractions with different denominators to get the correct measurements.
  • Science: When conducting experiments, you may need to add fractions with different denominators to get the correct results.

Common Mistakes

  • Not finding the least common multiple (LCM) of the two denominators.
  • Not converting both fractions to have a common denominator.
  • Adding the numerators without converting the fractions to have a common denominator.

Conclusion

In conclusion, adding fractions with different denominators requires finding the least common multiple (LCM) of the two denominators and converting both fractions to have a common denominator. By following these steps, you can evaluate expressions like 112+38\frac{1}{12} + \frac{3}{8} and get the correct result.

Final Answer

The final answer is 1124\boxed{\frac{11}{24}}.

Introduction

Adding fractions with different denominators can be a challenging task, but with the right approach, it can be made easier. In this article, we will answer some of the most frequently asked questions about adding fractions with different denominators.

Q: What is the least common multiple (LCM) and why is it important?

A: The least common multiple (LCM) is the smallest number that is a multiple of two or more numbers. In the context of adding fractions, the LCM is the common denominator that both fractions need to have in order to be added together. The LCM is important because it allows us to convert both fractions to have the same denominator, making it easier to add them together.

Q: How do I find the LCM of two numbers?

A: There are several ways to find the LCM of two numbers. One way is to list the multiples of each number and find the smallest number that appears in both lists. Another way is to use a calculator or a multiplication chart to find the LCM. You can also use the formula: LCM(a, b) = (a × b) / GCD(a, b), where GCD is the greatest common divisor.

Q: What is the greatest common divisor (GCD) and how is it used in finding the LCM?

A: The greatest common divisor (GCD) is the largest number that divides two or more numbers without leaving a remainder. In the context of finding the LCM, the GCD is used to calculate the LCM using the formula: LCM(a, b) = (a × b) / GCD(a, b).

Q: How do I convert fractions to have a common denominator?

A: To convert fractions to have a common denominator, you need to multiply both the numerator and the denominator of each fraction by the same number. This number is the common denominator that you want to use. For example, if you want to convert the fractions 1/2 and 1/3 to have a common denominator of 6, you would multiply the numerator and denominator of each fraction by 3 and 2, respectively.

Q: What is the difference between adding fractions with different denominators and adding fractions with the same denominator?

A: Adding fractions with different denominators requires finding the least common multiple (LCM) of the two denominators and converting both fractions to have a common denominator. Adding fractions with the same denominator, on the other hand, is a simple process that involves adding the numerators and keeping the same denominator.

Q: Can I add fractions with different denominators using a calculator?

A: Yes, you can add fractions with different denominators using a calculator. Most calculators have a built-in function for adding fractions, which can save you time and effort.

Q: What are some common mistakes to avoid when adding fractions with different denominators?

A: Some common mistakes to avoid when adding fractions with different denominators include:

  • Not finding the least common multiple (LCM) of the two denominators
  • Not converting both fractions to have a common denominator
  • Adding the numerators without converting the fractions to have a common denominator

Q: How do I check my answer when adding fractions with different denominators?

A: To check your answer when adding fractions with different denominators, you can convert the result back to a fraction with the original denominators and see if it matches the original expression. You can also use a calculator to check your answer.

Q: Can I use a shortcut to add fractions with different denominators?

A: Yes, you can use a shortcut to add fractions with different denominators. One shortcut is to use the formula: a/b + c/d = (ad + bc) / bd, where a, b, c, and d are the numerators and denominators of the two fractions.

Q: What are some real-world applications of adding fractions with different denominators?

A: Adding fractions with different denominators has many real-world applications, including:

  • Cooking: When a recipe calls for a certain amount of an ingredient, but the ingredient is sold in different sizes, you may need to add fractions with different denominators to get the correct amount.
  • Building: When building a structure, you may need to add fractions with different denominators to get the correct measurements.
  • Science: When conducting experiments, you may need to add fractions with different denominators to get the correct results.

Conclusion

In conclusion, adding fractions with different denominators requires finding the least common multiple (LCM) of the two denominators and converting both fractions to have a common denominator. By following these steps and avoiding common mistakes, you can add fractions with different denominators with ease.