An Expression Is Shown:$\[ 1 \frac{3}{10} + 4 \frac{7}{10} \\]What Is The Value Of The Expression?A. \[$ 5 \frac{10}{20} \$\]B. \[$ 5 \frac{4}{10} \$\]C. 5D. 6

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Understanding Mixed Numbers

In mathematics, a mixed number is a combination of a whole number and a fraction. It is written in the form of a whole number followed by a fraction, such as 3 1/2 or 4 3/4. Mixed numbers are used to represent quantities that are not whole, but can be expressed as a combination of a whole number and a fraction.

Evaluating the Expression: 1 3/10 + 4 7/10

To evaluate the expression 1 3/10 + 4 7/10, we need to follow the order of operations (PEMDAS):

  1. Convert the mixed numbers to improper fractions: To add mixed numbers, we need to convert them to improper fractions. To do this, we multiply the whole number by the denominator and add the numerator.

    1 3/10 = (1 × 10) + 3/10 = 13/10 4 7/10 = (4 × 10) + 7/10 = 47/10

  2. Find a common denominator: To add fractions, we need to find a common denominator. The least common multiple (LCM) of 10 and 10 is 10.

  3. Add the fractions: Now that we have a common denominator, we can add the fractions.

    13/10 + 47/10 = (13 + 47)/10 = 60/10

  4. Simplify the fraction: To simplify the fraction, we divide the numerator by the denominator.

    60/10 = 6

Conclusion

The value of the expression 1 3/10 + 4 7/10 is 6. This is because we converted the mixed numbers to improper fractions, found a common denominator, added the fractions, and simplified the result.

Why is it Important to Evaluate Expressions Correctly?

Evaluating expressions correctly is important in mathematics because it helps us to:

  • Understand mathematical concepts: By evaluating expressions correctly, we can gain a deeper understanding of mathematical concepts and how they relate to each other.
  • Solve problems accurately: Evaluating expressions correctly helps us to solve problems accurately and efficiently.
  • Make informed decisions: In real-life situations, we often need to make decisions based on mathematical calculations. Evaluating expressions correctly helps us to make informed decisions.

Common Mistakes to Avoid

When evaluating expressions, it's easy to make mistakes. Here are some common mistakes to avoid:

  • Forgetting to convert mixed numbers to improper fractions: Failing to convert mixed numbers to improper fractions can lead to incorrect results.
  • Not finding a common denominator: Failing to find a common denominator can lead to incorrect results.
  • Not simplifying the fraction: Failing to simplify the fraction can lead to incorrect results.

Tips for Evaluating Expressions

Here are some tips for evaluating expressions:

  • Read the problem carefully: Before starting to evaluate the expression, read the problem carefully to understand what is being asked.
  • Convert mixed numbers to improper fractions: Convert mixed numbers to improper fractions to make it easier to evaluate the expression.
  • Find a common denominator: Find a common denominator to add fractions.
  • Simplify the fraction: Simplify the fraction to get the final result.

Conclusion

Evaluating expressions is an important skill in mathematics. By following the order of operations and avoiding common mistakes, we can evaluate expressions correctly and accurately. Remember to read the problem carefully, convert mixed numbers to improper fractions, find a common denominator, and simplify the fraction to get the final result.

Q: What is the order of operations?

A: The order of operations is a set of rules that tells us which operations to perform first when evaluating an expression. 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 convert a mixed number to an improper fraction?

A: To convert a mixed number to an improper fraction, follow these steps:

  1. Multiply the whole number by the denominator: Multiply the whole number by the denominator.
  2. Add the numerator: Add the numerator to the result.
  3. Write the result as an improper fraction: Write the result as an improper fraction, with the numerator being the result from step 2 and the denominator being the original denominator.

Example: Convert 3 1/2 to an improper fraction.

  1. Multiply 3 by 2: 3 × 2 = 6
  2. Add 1: 6 + 1 = 7
  3. Write the result as an improper fraction: 7/2

Q: How do I find a common denominator?

A: To find a common denominator, follow these steps:

  1. List the denominators: List the denominators of the fractions.
  2. Find the least common multiple (LCM): Find the least common multiple (LCM) of the denominators.
  3. Use the LCM as the common denominator: Use the LCM as the common denominator.

Example: Find a common denominator for 1/2 and 1/3.

  1. List the denominators: 2, 3
  2. Find the LCM: The LCM of 2 and 3 is 6.
  3. Use the LCM as the common denominator: The common denominator is 6.

Q: How do I add fractions with different denominators?

A: To add fractions with different denominators, follow these steps:

  1. Find a common denominator: Find a common denominator for the fractions.
  2. Convert the fractions to have the common denominator: Convert each fraction to have the common denominator.
  3. Add the fractions: Add the fractions.
  4. Simplify the result: Simplify the result.

Example: Add 1/2 and 1/3.

  1. Find a common denominator: The common denominator is 6.
  2. Convert the fractions to have the common denominator: 1/2 = 3/6 and 1/3 = 2/6
  3. Add the fractions: 3/6 + 2/6 = 5/6
  4. Simplify the result: The result is already simplified.

Q: How do I subtract fractions with different denominators?

A: To subtract fractions with different denominators, follow these steps:

  1. Find a common denominator: Find a common denominator for the fractions.
  2. Convert the fractions to have the common denominator: Convert each fraction to have the common denominator.
  3. Subtract the fractions: Subtract the fractions.
  4. Simplify the result: Simplify the result.

Example: Subtract 1/2 and 1/3.

  1. Find a common denominator: The common denominator is 6.
  2. Convert the fractions to have the common denominator: 1/2 = 3/6 and 1/3 = 2/6
  3. Subtract the fractions: 3/6 - 2/6 = 1/6
  4. Simplify the result: The result is already simplified.

Q: How do I multiply fractions?

A: To multiply fractions, follow these steps:

  1. Multiply the numerators: Multiply the numerators of the fractions.
  2. Multiply the denominators: Multiply the denominators of the fractions.
  3. Write the result as a fraction: Write the result as a fraction, with the numerator being the product of the numerators and the denominator being the product of the denominators.

Example: Multiply 1/2 and 1/3.

  1. Multiply the numerators: 1 × 1 = 1
  2. Multiply the denominators: 2 × 3 = 6
  3. Write the result as a fraction: 1/6

Q: How do I divide fractions?

A: To divide fractions, follow these steps:

  1. Invert the second fraction: Invert the second fraction, i.e., flip the numerator and denominator.
  2. Multiply the fractions: Multiply the fractions.
  3. Simplify the result: Simplify the result.

Example: Divide 1/2 by 1/3.

  1. Invert the second fraction: 1/3 becomes 3/1
  2. Multiply the fractions: 1/2 × 3/1 = 3/2
  3. Simplify the result: The result is already simplified.

Conclusion

Evaluating expressions is an important skill in mathematics. By following the order of operations and using the techniques outlined in this article, you can evaluate expressions correctly and accurately. Remember to read the problem carefully, convert mixed numbers to improper fractions, find a common denominator, and simplify the result to get the final answer.