What Is The Value Of The Expression $\left(\frac{2}{5}+\frac{2}{5}\right) \times \frac{3}{10}$?A. $\frac{6}{125}$B. $\frac{3}{25}$C. $\frac{7}{50}$D. $\frac{6}{25}$

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Understanding the Expression

The given expression involves the addition of two fractions, followed by the multiplication of the result with another fraction. To evaluate this expression, we need to follow the order of operations (PEMDAS), which dictates that we perform the addition first and then the multiplication.

Adding the Fractions

The first step is to add the two fractions $\frac{2}{5}$ and $\frac{2}{5}$. Since both fractions have the same denominator, we can directly add the numerators.

$\frac{2}{5} + \frac{2}{5} = \frac{2+2}{5} = \frac{4}{5}$

Multiplying the Result with the Second Fraction

Now that we have the result of the addition, we can multiply it with the second fraction $\frac{3}{10}$.

$\frac{4}{5} \times \frac{3}{10} = \frac{4 \times 3}{5 \times 10} = \frac{12}{50}$

Simplifying the Result

The fraction $\frac{12}{50}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 2.

$\frac{12}{50} = \frac{12 \div 2}{50 \div 2} = \frac{6}{25}$

Conclusion

Therefore, the value of the expression $\left(\frac{2}{5}+\frac{2}{5}\right) \times \frac{3}{10}$ is $\frac{6}{25}$.

Comparison with the Given Options

Comparing the result with the given options, we can see that the correct answer is:

A. $\frac{6}{125}$ - Incorrect B. $\frac{3}{25}$ - Incorrect C. $\frac{7}{50}$ - Incorrect D. $\frac{6}{25}$ - Correct

Importance of Following the Order of Operations

The given expression highlights the importance of following the order of operations (PEMDAS) when evaluating mathematical expressions. If we had performed the multiplication first and then the addition, we would have obtained a different result, which would be incorrect.

Real-World Applications

The concept of adding and multiplying fractions is essential in various real-world applications, such as:

• Cooking: When a recipe requires the addition of two or more ingredients with different measurements, we need to add the fractions to obtain the correct amount.
• Science: In scientific calculations, we often need to add and multiply fractions to obtain the desired result.
• Finance: In financial calculations, we need to add and multiply fractions to calculate interest rates, investment returns, and other financial metrics.

Tips for Evaluating Expressions with Fractions

When evaluating expressions with fractions, it's essential to follow the order of operations (PEMDAS) and to simplify the fractions by dividing both the numerator and the denominator by their greatest common divisor.

Common Mistakes to Avoid

When evaluating expressions with fractions, some common mistakes to avoid include:

• Not following the order of operations (PEMDAS)
• Not simplifying the fractions
• Not checking for common factors between the numerator and the denominator

Conclusion

In conclusion, the value of the expression $\left(\frac{2}{5}+\frac{2}{5}\right) \times \frac{3}{10}$ is $\frac{6}{25}$. This expression highlights the importance of following the order of operations (PEMDAS) and simplifying fractions to obtain the correct result.

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Q: What is the order of operations (PEMDAS) and why is it important?

A: The order of operations (PEMDAS) is a set of rules that dictate the order in which mathematical operations should be performed when there are multiple operations in an expression. The acronym PEMDAS stands for:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next.
3. Multiplication and Division: Evaluate multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Following the order of operations is essential to ensure that mathematical expressions are evaluated correctly and consistently.

Q: Why is it necessary to simplify fractions?

A: Simplifying fractions is necessary to ensure that mathematical expressions are evaluated correctly and consistently. When fractions are not simplified, it can lead to errors and inconsistencies in calculations. Simplifying fractions involves dividing both the numerator and the denominator by their greatest common divisor (GCD) to obtain the simplest form of the fraction.

Q: What is the greatest common divisor (GCD) and how is it used to simplify fractions?

A: The greatest common divisor (GCD) is the largest number that divides two or more numbers without leaving a remainder. When simplifying fractions, the GCD is used to divide both the numerator and the denominator to obtain the simplest form of the fraction.

Q: How do you add fractions with different denominators?

A: To add fractions with different denominators, you need to find the least common multiple (LCM) of the denominators and then convert each fraction to have the LCM as the denominator. Once the fractions have the same denominator, you can add the numerators and keep the same denominator.

Q: How do you multiply fractions?

A: To multiply fractions, you simply multiply the numerators and multiply the denominators. The result is a new fraction with the product of the numerators as the new numerator and the product of the denominators as the new denominator.

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

A: The numerator is the top number in a fraction, and the denominator is the bottom number in a fraction. The numerator represents the number of equal parts, and the denominator represents the total number of parts.

Q: Why is it essential to check for common factors between the numerator and the denominator?

A: It is essential to check for common factors between the numerator and the denominator to ensure that the fraction is in its simplest form. If there are common factors, you can divide both the numerator and the denominator by those factors to simplify the fraction.

Q: What are some common mistakes to avoid when working with fractions?

A: Some common mistakes to avoid when working with fractions include:

• Not following the order of operations (PEMDAS)
• Not simplifying fractions
• Not checking for common factors between the numerator and the denominator
• Not converting fractions to have the same denominator before adding or subtracting

Q: How do you convert a fraction to a decimal?

A: To convert a fraction to a decimal, you can divide the numerator by the denominator. For example, to convert the fraction $\frac{1}{2}$ to a decimal, you can divide 1 by 2, which equals 0.5.

Q: How do you convert a decimal to a fraction?

A: To convert a decimal to a fraction, you can express the decimal as a fraction by writing it as a ratio of the decimal to 1. For example, to convert the decimal 0.5 to a fraction, you can write it as $\frac{0.5}{1}$, which simplifies to $\frac{1}{2}$.

Q: What are some real-world applications of fractions?

A: Fractions have numerous real-world applications, including:

• Cooking: When a recipe requires the addition of two or more ingredients with different measurements, you need to add the fractions to obtain the correct amount.
• Science: In scientific calculations, you often need to add and multiply fractions to obtain the desired result.
• Finance: In financial calculations, you need to add and multiply fractions to calculate interest rates, investment returns, and other financial metrics.

Q: How can you practice working with fractions?

A: You can practice working with fractions by:

• Solving fraction problems and exercises
• Using online resources and tools to practice fraction calculations
• Working with real-world applications of fractions
• Asking a teacher or tutor for help and guidance

Q: What are some tips for mastering fractions?

A: Some tips for mastering fractions include:

• Practicing regularly to build confidence and fluency
• Using visual aids and diagrams to help understand fraction concepts
• Breaking down complex fraction problems into simpler steps
• Asking for help and guidance when needed

Q: How can you use fractions in everyday life?

A: You can use fractions in everyday life by:

• Cooking and measuring ingredients
• Calculating interest rates and investment returns
• Understanding scientific and mathematical concepts
• Making informed decisions about finance and economics

Q: What are some common fraction mistakes to avoid?

A: Some common fraction mistakes to avoid include:

• Not following the order of operations (PEMDAS)
• Not simplifying fractions
• Not checking for common factors between the numerator and the denominator
• Not converting fractions to have the same denominator before adding or subtracting

Q: How can you overcome fraction anxiety?

A: You can overcome fraction anxiety by:

• Practicing regularly to build confidence and fluency
• Using visual aids and diagrams to help understand fraction concepts
• Breaking down complex fraction problems into simpler steps
• Asking for help and guidance when needed

Q: What are some resources for learning fractions?

A: Some resources for learning fractions include:

• Online tutorials and videos
• Textbooks and workbooks
• Online practice exercises and quizzes
• Teachers and tutors
• Online communities and forums

Q: How can you use fractions to solve real-world problems?

A: You can use fractions to solve real-world problems by:

• Calculating interest rates and investment returns
• Understanding scientific and mathematical concepts
• Making informed decisions about finance and economics
• Solving problems in cooking, science, and other fields.