Evaluate The Expression: $\frac{2}{12}+\frac{2}{4}=$

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Introduction

When it comes to evaluating mathematical expressions, it's essential to understand the rules and procedures involved. In this article, we will delve into the world of fractions and explore how to evaluate the expression 212+24\frac{2}{12}+\frac{2}{4}. We will break down the steps involved, provide examples, and offer tips for simplifying complex fractions.

Understanding Fractions

Fractions are a fundamental concept in mathematics, representing a part of a whole. They consist of two parts: the numerator and the denominator. The numerator is the number on top, indicating the number of equal parts, while the denominator is the number on the bottom, indicating the total number of parts.

For example, in the fraction 212\frac{2}{12}, the numerator is 2, and the denominator is 12. This means that we have 2 equal parts out of a total of 12 parts.

Simplifying Fractions

Before we can add fractions, we need to simplify them. Simplifying fractions involves finding the greatest common divisor (GCD) of the numerator and the denominator and dividing both numbers by the GCD.

For example, let's simplify the fraction 212\frac{2}{12}. To do this, we need to find the GCD of 2 and 12. The GCD is 2, so we divide both numbers by 2:

212=2÷212÷2=16\frac{2}{12} = \frac{2 ÷ 2}{12 ÷ 2} = \frac{1}{6}

Adding Fractions

Now that we have simplified the fractions, we can add them. To add fractions, we need to have the same denominator. If the denominators are different, we need to find the least common multiple (LCM) of the denominators and convert both fractions to have the LCM as the denominator.

For example, let's add the fractions 16\frac{1}{6} and 24\frac{2}{4}. The denominators are different, so we need to find the LCM of 6 and 4. The LCM is 12, so we convert both fractions to have 12 as the denominator:

16=1×26×2=212\frac{1}{6} = \frac{1 × 2}{6 × 2} = \frac{2}{12}

24=2×34×3=612\frac{2}{4} = \frac{2 × 3}{4 × 3} = \frac{6}{12}

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

212+612=2+612=812\frac{2}{12} + \frac{6}{12} = \frac{2 + 6}{12} = \frac{8}{12}

Simplifying the Result

The result of the addition is 812\frac{8}{12}. We can simplify this fraction by finding the GCD of 8 and 12. The GCD is 4, so we divide both numbers by 4:

812=8÷412÷4=23\frac{8}{12} = \frac{8 ÷ 4}{12 ÷ 4} = \frac{2}{3}

Conclusion

Evaluating the expression 212+24\frac{2}{12}+\frac{2}{4} involves simplifying the fractions and adding them. We need to find the GCD of the numerators and denominators, simplify the fractions, and then add them. The result is 23\frac{2}{3}.

Tips and Tricks

  • Always simplify fractions before adding them.
  • Find the GCD of the numerators and denominators to simplify fractions.
  • Use the LCM of the denominators to add fractions with different denominators.
  • Practice, practice, practice! The more you practice, the more comfortable you will become with simplifying and adding fractions.

Frequently Asked Questions

  • Q: What is the greatest common divisor (GCD)? A: The GCD is the largest number that divides both numbers without leaving a remainder.
  • Q: What is the least common multiple (LCM)? A: The LCM is the smallest number that is a multiple of both numbers.
  • Q: How do I simplify fractions? A: To simplify fractions, find the GCD of the numerator and denominator and divide both numbers by the GCD.

Final Thoughts

Evaluating the expression 212+24\frac{2}{12}+\frac{2}{4} is a simple process that involves simplifying fractions and adding them. By following the steps outlined in this article, you can become more confident in your ability to evaluate complex mathematical expressions. Remember to always simplify fractions before adding them, and use the LCM of the denominators to add fractions with different denominators. With practice and patience, you will become a master of simplifying and adding fractions!

Introduction

Evaluating mathematical expressions can be a challenging task, especially when dealing with complex fractions and algebraic expressions. In this article, we will address some of the most frequently asked questions related to evaluating mathematical expressions.

Q&A

Q: What is the difference between a numerator and a denominator?

A: The numerator is the number on top of a fraction, indicating the number of equal parts. The denominator is the number on the bottom of a fraction, indicating the total number of parts.

Q: How do I simplify a fraction?

A: To simplify a fraction, find the greatest common divisor (GCD) of the numerator and denominator and divide both numbers by the GCD.

Q: What is the greatest common divisor (GCD)?

A: The GCD is the largest number that divides both numbers without leaving a remainder.

Q: What is the least common multiple (LCM)?

A: The LCM is the smallest number that is a multiple of both numbers.

Q: How do I add fractions with different denominators?

A: To add fractions with different denominators, find the least common multiple (LCM) of the denominators and convert both fractions to have the LCM as the denominator.

Q: What is the rule for adding fractions?

A: To add fractions, the denominators must be the same. If the denominators are different, find the LCM of the denominators and convert both fractions to have the LCM as the denominator.

Q: Can I add fractions with unlike signs?

A: Yes, you can add fractions with unlike signs. When adding fractions with unlike signs, subtract the numerators and keep the same denominator.

Q: How do I subtract fractions?

A: To subtract fractions, find the least common multiple (LCM) of the denominators and convert both fractions to have the LCM as the denominator. Then, subtract the numerators and keep the same denominator.

Q: Can I subtract fractions with unlike signs?

A: Yes, you can subtract fractions with unlike signs. When subtracting fractions with unlike signs, add the numerators and keep the same denominator.

Q: How do I multiply fractions?

A: To multiply fractions, multiply the numerators and multiply the denominators.

Q: Can I multiply fractions with unlike signs?

A: Yes, you can multiply fractions with unlike signs. When multiplying fractions with unlike signs, multiply the numerators and multiply the denominators.

Q: How do I divide fractions?

A: To divide fractions, invert the second fraction and multiply.

Q: Can I divide fractions with unlike signs?

A: Yes, you can divide fractions with unlike signs. When dividing fractions with unlike signs, invert the second fraction and multiply.

Q: What is the rule for multiplying and dividing fractions?

A: When multiplying or dividing fractions, the signs of the numerators and denominators must be the same.

Q: Can I simplify a fraction after adding or subtracting?

A: Yes, you can simplify a fraction after adding or subtracting. Find the greatest common divisor (GCD) of the numerator and denominator and divide both numbers by the GCD.

Conclusion

Evaluating mathematical expressions can be a challenging task, but with practice and patience, you can become more confident in your ability to simplify and add fractions. Remember to always simplify fractions before adding or subtracting, and use the least common multiple (LCM) of the denominators to add fractions with different denominators. With these tips and tricks, you will become a master of evaluating mathematical expressions!

Final Thoughts

Evaluating mathematical expressions is an essential skill that is used in a variety of real-world applications, from finance to science. By mastering the skills outlined in this article, you will be able to tackle even the most complex mathematical expressions with confidence. Remember to always simplify fractions before adding or subtracting, and use the least common multiple (LCM) of the denominators to add fractions with different denominators. With practice and patience, you will become a master of evaluating mathematical expressions!