Choose Yes Or No To Tell If The Statement Is Correct.1. The Sum Of $\frac{1}{2}$ And $\frac{1}{5}$ Is Between $ 1 2 \frac{1}{2} 2 1 ​ [/tex] And 1. - □ \square □ Choose Yes Or No2. The Difference Of

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In mathematics, we often come across various statements that require us to make decisions based on our understanding of mathematical concepts. In this article, we will explore two statements related to fractions and ask you to choose whether they are correct or not.

Statement 1: The Sum of Fractions

The first statement claims that the sum of $\frac{1}{2}$ and $\frac{1}{5}$ is between $\frac{1}{2}$ and 1. To determine whether this statement is correct, let's calculate the sum of the two fractions.

Calculating the Sum of Fractions

To add fractions, we need to have a common denominator. In this case, the least common multiple (LCM) of 2 and 5 is 10. So, we can rewrite the fractions with a denominator of 10:

12=510\frac{1}{2} = \frac{5}{10}

15=210\frac{1}{5} = \frac{2}{10}

Now, we can add the fractions:

510+210=710\frac{5}{10} + \frac{2}{10} = \frac{7}{10}

Analyzing the Statement

The sum of $\frac{1}{2}$ and $\frac{1}{5}$ is $\frac{7}{10}$. To determine whether this sum is between $\frac{1}{2}$ and 1, we need to compare it with these values.

12=0.5\frac{1}{2} = 0.5

710=0.7\frac{7}{10} = 0.7

1=1.01 = 1.0

As we can see, $\frac{7}{10}$ is indeed between $\frac{1}{2}$ and 1. Therefore, the statement is CORRECT.

Statement 2: The Difference of Fractions

The second statement claims that the difference of $\frac{1}{2}$ and $\frac{1}{5}$ is between $\frac{1}{2}$ and 1. To determine whether this statement is correct, let's calculate the difference of the two fractions.

Calculating the Difference of Fractions

To subtract fractions, we need to have a common denominator. In this case, the least common multiple (LCM) of 2 and 5 is 10. So, we can rewrite the fractions with a denominator of 10:

12=510\frac{1}{2} = \frac{5}{10}

15=210\frac{1}{5} = \frac{2}{10}

Now, we can subtract the fractions:

510−210=310\frac{5}{10} - \frac{2}{10} = \frac{3}{10}

Analyzing the Statement

The difference of $\frac{1}{2}$ and $\frac{1}{5}$ is $\frac{3}{10}$. To determine whether this difference is between $\frac{1}{2}$ and 1, we need to compare it with these values.

12=0.5\frac{1}{2} = 0.5

310=0.3\frac{3}{10} = 0.3

1=1.01 = 1.0

As we can see, $\frac{3}{10}$ is less than $\frac{1}{2}$. Therefore, the statement is INCORRECT.

Conclusion

In this article, we explored two statements related to fractions and asked you to choose whether they are correct or not. We calculated the sum and difference of the fractions and analyzed the statements to determine their correctness. The first statement was correct, while the second statement was incorrect. We hope this article has helped you understand the concepts of fractions and how to analyze mathematical statements.

Key Takeaways

  • To add fractions, we need to have a common denominator.
  • To subtract fractions, we need to have a common denominator.
  • The sum of two fractions can be between the two fractions.
  • The difference of two fractions can be less than or greater than the two fractions.

Practice Problems

  1. What is the sum of $\frac{1}{3}$ and $\frac{1}{4}$?
  2. What is the difference of $\frac{1}{3}$ and $\frac{1}{4}$?
  3. Is the sum of $\frac{1}{2}$ and $\frac{1}{3}$ between $\frac{1}{2}$ and 1?
  4. Is the difference of $\frac{1}{2}$ and $\frac{1}{3}$ between $\frac{1}{2}$ and 1?

Answer Key

  1. 712\frac{7}{12}

  2. 112\frac{1}{12}

  3. Yes
  4. No
    Frequently Asked Questions: Fractions and Mathematical Statements ====================================================================

In our previous article, we explored two statements related to fractions and asked you to choose whether they are correct or not. We also provided some practice problems to help you understand the concepts of fractions and how to analyze mathematical statements. In this article, we will answer some frequently asked questions related to fractions and mathematical statements.

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

A: When adding fractions, we need to have a common denominator. We can then add the numerators and keep the denominator the same. When subtracting fractions, we also need to have a common denominator. We can then subtract the numerators and keep the denominator the same.

Q: How do I determine whether a statement is correct or not?

A: To determine whether a statement is correct or not, you need to analyze the statement and calculate the value of the expression. You can then compare the value with the given values in the statement to determine whether it is correct or not.

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. For example, the LCM of 2 and 5 is 10.

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

A: To calculate the LCM of two numbers, you can list the multiples of each number and find the smallest number that is common to both lists. Alternatively, you can use the following formula:

LCM(a, b) = (a * b) / GCD(a, b)

where GCD(a, b) is the greatest common divisor of a and b.

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

A: The greatest common divisor (GCD) of two numbers is the largest number that divides both numbers without leaving a remainder. For example, the GCD of 12 and 15 is 3.

Q: How do I calculate the GCD of two numbers?

A: To calculate the GCD of two numbers, you can use the following formula:

GCD(a, b) = (a * b) / LCM(a, b)

Alternatively, you can use the Euclidean algorithm to calculate the GCD.

Q: What is the Euclidean algorithm?

A: The Euclidean algorithm is a method for calculating the greatest common divisor (GCD) of two numbers. It works by repeatedly dividing the larger number by the smaller number and taking the remainder.

Q: How do I use the Euclidean algorithm to calculate the GCD of two numbers?

A: To use the Euclidean algorithm to calculate the GCD of two numbers, you can follow these steps:

  1. Divide the larger number by the smaller number and take the remainder.
  2. Replace the larger number with the smaller number and the smaller number with the remainder.
  3. Repeat steps 1 and 2 until the remainder is 0.
  4. The GCD is the last non-zero remainder.

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

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

  • Not having a common denominator when adding or subtracting fractions.
  • Not simplifying fractions.
  • Not checking for common factors when simplifying fractions.
  • Not using the correct order of operations when evaluating expressions.

Conclusion

In this article, we answered some frequently asked questions related to fractions and mathematical statements. We hope this article has helped you understand the concepts of fractions and how to analyze mathematical statements. Remember to always be careful when working with fractions and to avoid common mistakes.

Practice Problems

  1. What is the sum of $\frac{1}{3}$ and $\frac{1}{4}$?
  2. What is the difference of $\frac{1}{3}$ and $\frac{1}{4}$?
  3. Is the sum of $\frac{1}{2}$ and $\frac{1}{3}$ between $\frac{1}{2}$ and 1?
  4. Is the difference of $\frac{1}{2}$ and $\frac{1}{3}$ between $\frac{1}{2}$ and 1?

Answer Key

  1. 712\frac{7}{12}

  2. 112\frac{1}{12}

  3. Yes
  4. No