What Is The Value Of Each Expression?$\[ \begin{array}{l} \frac{7}{8}+\frac{4}{8}=\square \\ \frac{17}{25}-\frac{9}{25}=\square \\ \frac{63}{46}-\frac{81}{46}=\square \end{array} \\]

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In mathematics, expressions are a combination of numbers, variables, and mathematical operations. Evaluating an expression involves simplifying it to a single value. In this article, we will explore the value of each expression in the given problem.

Adding Fractions with the Same Denominator

When adding fractions with the same denominator, we simply add the numerators and keep the denominator the same. Let's evaluate the first expression:

78+48=â–¡\frac{7}{8}+\frac{4}{8}=\square

To evaluate this expression, we add the numerators (7 and 4) and keep the denominator (8) the same:

78+48=7+48=118\frac{7}{8}+\frac{4}{8}=\frac{7+4}{8}=\frac{11}{8}

Therefore, the value of the first expression is 118\frac{11}{8}.

Subtracting Fractions with the Same Denominator

When subtracting fractions with the same denominator, we simply subtract the numerators and keep the denominator the same. Let's evaluate the second expression:

1725−925=□\frac{17}{25}-\frac{9}{25}=\square

To evaluate this expression, we subtract the numerators (17 and 9) and keep the denominator (25) the same:

1725−925=17−925=825\frac{17}{25}-\frac{9}{25}=\frac{17-9}{25}=\frac{8}{25}

Therefore, the value of the second expression is 825\frac{8}{25}.

Subtracting Fractions with Different Denominators

When subtracting fractions with different denominators, we need to find the least common multiple (LCM) of the denominators and then convert each fraction to have the LCM as the denominator. Let's evaluate the third expression:

6346−8146=□\frac{63}{46}-\frac{81}{46}=\square

To evaluate this expression, we need to find the LCM of 46 and 46, which is 46. Since both fractions already have 46 as the denominator, we can simply subtract the numerators:

6346−8146=63−8146=−1846\frac{63}{46}-\frac{81}{46}=\frac{63-81}{46}=\frac{-18}{46}

Therefore, the value of the third expression is −1846\frac{-18}{46}.

Simplifying Fractions

Fractions can be simplified by dividing the numerator and denominator by their greatest common divisor (GCD). Let's simplify the fractions we obtained earlier:

  • 118\frac{11}{8} cannot be simplified further since 11 and 8 have no common factors.
  • 825\frac{8}{25} cannot be simplified further since 8 and 25 have no common factors.
  • −1846\frac{-18}{46} can be simplified by dividing both the numerator and denominator by 2, which is their GCD:

−1846=−18÷246÷2=−923\frac{-18}{46}=\frac{-18\div2}{46\div2}=\frac{-9}{23}

Therefore, the simplified value of the third expression is −923\frac{-9}{23}.

Conclusion

In this article, we evaluated three expressions involving fractions and obtained their values. We also simplified the fractions to their lowest terms. The value of each expression is:

  • 78+48=118\frac{7}{8}+\frac{4}{8}=\frac{11}{8}
  • 1725−925=825\frac{17}{25}-\frac{9}{25}=\frac{8}{25}
  • 6346−8146=−923\frac{63}{46}-\frac{81}{46}=\frac{-9}{23}

In the previous article, we explored the value of each expression involving fractions. However, we understand that you may still have some questions about evaluating expressions with fractions. In this article, we will address some of the most frequently asked questions (FAQs) about this topic.

Q: What is the order of operations when evaluating expressions with fractions?

A: When evaluating expressions with fractions, the order of operations is the same as when evaluating expressions with integers. The order of operations is:

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

Q: How do I 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 you have the same denominator for both fractions, you can add the numerators and keep the denominator the same.

Q: How do I subtract fractions with different denominators?

A: To subtract 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 you have the same denominator for both fractions, you can subtract the numerators and keep the denominator the same.

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

A: When adding fractions with the same denominator, you simply add the numerators and keep the denominator the same. When subtracting fractions with the same denominator, you simply subtract the numerators and keep the denominator the same.

Q: How do I simplify fractions?

A: To simplify a fraction, you need to divide the numerator and denominator by their greatest common divisor (GCD). This will give you a fraction with the smallest possible numerator and denominator.

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

A: The least common multiple (LCM) of two numbers is the smallest number that is a multiple of both numbers. To find the LCM of two numbers, you can list the multiples of each number and find the smallest number that appears in both lists.

Q: How do I find the greatest common divisor (GCD) of two numbers?

A: To find the greatest common divisor (GCD) of two numbers, you can use the Euclidean algorithm. This involves repeatedly dividing the larger number by the smaller number and taking the remainder until the remainder is zero. The last non-zero remainder is the GCD.

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. The numerator represents the number of equal parts, and the denominator represents the total number of parts.

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

A: To convert a fraction to a decimal, you can divide the numerator by the denominator. This will give you a decimal representation of the fraction.

Q: How do I 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 two integers. For example, the decimal 0.5 can be expressed as the fraction 1/2.

Conclusion

In this article, we addressed some of the most frequently asked questions (FAQs) about evaluating expressions with fractions. We hope that this article has provided you with a better understanding of how to evaluate expressions with fractions and has answered any questions you may have had. If you have any further questions, please don't hesitate to ask.