Select The Correct Answer.Alice Bought \[$\frac{8}{9}\$\] Of A Pound Of Grapes And Ate \[$\frac{1}{3}\$\] Of A Pound. How Many Pounds Were Left?A. \[$\frac{8}{6}\$\]B. \[$\frac{7}{3}\$\]C. \[$\frac{7}{9}\$\]D.

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Introduction

In this problem, we are presented with a scenario where Alice buys a certain fraction of a pound of grapes and then eats a portion of it. We need to determine the remaining pounds of grapes after Alice's snack. To solve this problem, we will use basic arithmetic operations and fraction manipulation.

Understanding the Problem

Alice bought 89\frac{8}{9} of a pound of grapes and ate 13\frac{1}{3} of a pound. We need to find out how many pounds of grapes are left. To do this, we will first find the total amount of grapes Alice had initially and then subtract the amount she ate.

Step 1: Find the Initial Amount of Grapes

Alice bought 89\frac{8}{9} of a pound of grapes. This means she had 89\frac{8}{9} pounds of grapes initially.

Step 2: Find the Amount of Grapes Eaten

Alice ate 13\frac{1}{3} of a pound of grapes. We need to find the amount of grapes she ate in terms of the initial amount she had.

Finding the Common Denominator

To add or subtract fractions, we need to have a common denominator. In this case, the common denominator is 9. We can rewrite 13\frac{1}{3} as 39\frac{3}{9}.

Subtracting the Amount Eaten

Now that we have the amount eaten in terms of the initial amount, we can subtract it from the initial amount to find the remaining amount.

89−39=59\frac{8}{9} - \frac{3}{9} = \frac{5}{9}

Conclusion

Therefore, Alice had 59\frac{5}{9} pounds of grapes left after eating 13\frac{1}{3} of a pound.

Answer

The correct answer is 59\boxed{\frac{5}{9}}. However, since this option is not available, we can simplify the fraction to find the closest answer.

59=5×39×3=1527=59\frac{5}{9} = \frac{5 \times 3}{9 \times 3} = \frac{15}{27} = \frac{5}{9}

Since 59\frac{5}{9} is not an option, we can try to simplify it further.

59=5×39×3=1527=59\frac{5}{9} = \frac{5 \times 3}{9 \times 3} = \frac{15}{27} = \frac{5}{9}

However, we can see that 59\frac{5}{9} is not equal to any of the options. This means that the correct answer is not among the options provided.

Discussion

This problem requires a basic understanding of fractions and arithmetic operations. It also requires the ability to manipulate fractions and find the common denominator. The problem is designed to test the student's ability to solve a real-world problem using mathematical concepts.

Tips and Tricks

  • When solving problems involving fractions, it's essential to find the common denominator.
  • When subtracting fractions, make sure to subtract the numerators while keeping the denominators the same.
  • When simplifying fractions, look for common factors between the numerator and denominator.

Conclusion

Introduction

In our previous article, we solved the problem of finding the remaining pounds of grapes after Alice ate a portion of them. In this article, we will provide a Q&A section to help clarify any doubts and provide additional insights into the problem.

Q: What is the initial amount of grapes Alice had?

A: Alice had 89\frac{8}{9} of a pound of grapes initially.

Q: What is the amount of grapes Alice ate?

A: Alice ate 13\frac{1}{3} of a pound of grapes.

Q: How do we find the common denominator for the fractions?

A: To find the common denominator, we need to identify the least common multiple (LCM) of the denominators. In this case, the LCM of 9 and 3 is 9.

Q: Why do we need to find the common denominator?

A: We need to find the common denominator to add or subtract fractions. In this case, we need to subtract the amount eaten from the initial amount.

Q: How do we subtract the amount eaten from the initial amount?

A: To subtract the amount eaten from the initial amount, we need to have the same denominator. We can rewrite 13\frac{1}{3} as 39\frac{3}{9} and then subtract it from 89\frac{8}{9}.

Q: What is the remaining amount of grapes after Alice ate a portion of them?

A: The remaining amount of grapes after Alice ate a portion of them is 59\frac{5}{9} pounds.

Q: Why is 59\frac{5}{9} not an option among the choices?

A: 59\frac{5}{9} is not an option among the choices because the options are not simplified fractions. However, we can simplify 59\frac{5}{9} to find the closest answer.

Q: How do we simplify 59\frac{5}{9}?

A: We can simplify 59\frac{5}{9} by finding the greatest common divisor (GCD) of 5 and 9. The GCD of 5 and 9 is 1, so 59\frac{5}{9} is already in its simplest form.

Q: What is the closest answer among the options?

A: Since 59\frac{5}{9} is not an option among the choices, we can try to find the closest answer. However, we can see that none of the options are equal to 59\frac{5}{9}.

Conclusion

In conclusion, this Q&A section provides additional insights into the problem and helps clarify any doubts. It also provides tips and tricks for solving similar problems.

Tips and Tricks

  • When solving problems involving fractions, it's essential to find the common denominator.
  • When subtracting fractions, make sure to subtract the numerators while keeping the denominators the same.
  • When simplifying fractions, look for common factors between the numerator and denominator.

Common Mistakes

  • Not finding the common denominator when adding or subtracting fractions.
  • Not simplifying fractions when possible.
  • Not checking the options carefully before selecting the answer.

Conclusion

In conclusion, this Q&A section provides additional insights into the problem and helps clarify any doubts. It also provides tips and tricks for solving similar problems. By following these tips and tricks, you can improve your problem-solving skills and become more confident in your abilities.