text: # Multiplying Decimals to Make a Whole Number Product
  
  Directions: Using the digits 1 to 9 at most one time each, fill in the boxes to make a whole number product.
  
  ### Hint
  
  How can we tell if it is even possible to make a whole number product?
  What digits would be better or worse choices for making a whole number product?
  
  ### Answer
  
  Number of Unique Solutions: 14
  1: 1.6 x 3.75 = 6
  2: 1.6 x 8.75 = 14
  3: 2.4 x 3.75 = 9
  4: 2.4 x 8.75 = 21
  5: 3.2 x 8.75 = 28
  6: 4.8 x 1.25 = 6
  7: 4.8 x 3.75 = 18
  8: 4.8 x 6.25 = 30
  9: 6.4 x 1.25 = 8
  10: 6.4 x 3.75 = 24
  11: 6.4 x 8.75 = 56
  12: 9.6 x 1.25 = 12
  13: 9.6 x 3.75 = 36
  14: 9.6 x 8.75 = 84
  Note what they all have in common!
  
  Source: Owen Kaplinsky
  
  ## Equivalent Expressions with Fractions
  
  Directions: Using the digits 0 to 9 at most one time each and choosing either …
  
  ### 17 comments
  
  1. another one… 9.6 x 1.25 = 12
  
  2. Thanks! I’ll add it to the answer key.
  
  3. Hi
  If you think about multiplying integers, you need the product to have a factor of 1000. I.e. you need prime factors of the multipliers to include 5^3 and 2^3. Additionally, the factors of 5 and 2 must stay in separate multipliers otherwise one would have to end in zero which is not allowed.
  So possible numbers that would work are:
  1.6,2.4,3.2,4.8,5.6,6.4,7.2,9.6
  multiplied by
  1.25,3.75,6.25,8.75
  Any combination of these will work, if the digits are unique.
  
  4. 3.75 X 4.8 =18 Also Works
  
  5. Please update answer – I thought there was only one solution then looked in the comments.
  
  6. 6.25 x 4.8 = 30
  
  7. I got an answer of 1.25 x 4.8 = 6
  
  8. 6.4 times 1.25 is another answer to get 8… from one of my amazing 5th grade students!
  
  9. The answers have been updated. Thank you for your posts.
  
  10. I am amazed that my high math students couldn’t figure it out. They got pretty frustrated. However, some of my lower students worked hard to figure it out.
  
  11. I think this would be a wonderful investigation to use in the context of the book ‘The 5 Practices in Practice’ book. However, I am struggling to come up with a statement about ‘What am I wanting the students to learn?’
  
  Any thoughts.
  
  • Hi
  For my sixth graders, my learning goal would be to practice the multiplication of a decimal by a decimal. It has them practicing more engaging way, and because they are problem solving and looking for patterns, they aren’t really aware of the boring repeated practice that a worksheet would have.
  
  12. you might see a lot of answer in life.
  
  13. My 5th grade students were excited to find the answer 9.6 * 8.75 = 84.
explanation: The document provides a math problem involving the multiplication of decimals to achieve a whole number product. It includes a hint, an answer section with 14 unique solutions, and comments from users who have found additional solutions or discussed the problem. The document contains both a question and multiple answers.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: # Multiplying Decimals to Make a Whole Number Product
  
  Directions: Using the digits 1 to 9 at most one time each, fill in the boxes to make a whole number product.
  
  ### Hint
  
  How can we tell if it is even possible to make a whole number product?
  What digits would be better or worse choices for making a whole number product?
  
  ### Answer
  
  Number of Unique Solutions: 14
  1: 1.6 x 3.75 = 6
  2: 1.6 x 8.75 = 14
  3: 2.4 x 3.75 = 9
  4: 2.4 x 8.75 = 21
  5: 3.2 x 8.75 = 28
  6: 4.8 x 1.25 = 6
  7: 4.8 x 3.75 = 18
  8: 4.8 x 6.25 = 30
  9: 6.4 x 1.25 = 8
  10: 6.4 x 3.75 = 24
  11: 6.4 x 8.75 = 56
  12: 9.6 x 1.25 = 12
  13: 9.6 x 3.75 = 36
  14: 9.6 x 8.75 = 84
  Note what they all have in common!
  
  Source: Owen Kaplinsky
  
  ## Equivalent Expressions with Fractions
  
  Directions: Using the digits 0 to 9 at most one time each and choosing either …
  
  ### 17 comments
  
  1. another one… 9.6 x 1.25 = 12
  
  2. Thanks! I’ll add it to the answer key.
  
  3. Hi
  If you think about multiplying integers, you need the product to have a factor of 1000. I.e. you need prime factors of the multipliers to include 5^3 and 2^3. Additionally, the factors of 5 and 2 must stay in separate multipliers otherwise one would have to end in zero which is not allowed.
  So possible numbers that would work are:
  1.6,2.4,3.2,4.8,5.6,6.4,7.2,9.6
  multiplied by
  1.25,3.75,6.25,8.75
  Any combination of these will work, if the digits are unique.
  
  4. 3.75 X 4.8 =18 Also Works
  
  5. Please update answer – I thought there was only one solution then looked in the comments.
  
  6. 6.25 x 4.8 = 30
  
  7. I got an answer of 1.25 x 4.8 = 6
  
  8. 6.4 times 1.25 is another answer to get 8… from one of my amazing 5th grade students!
  
  9. The answers have been updated. Thank you for your posts.
  
  10. I am amazed that my high math students couldn’t figure it out. They got pretty frustrated. However, some of my lower students worked hard to figure it out.
  
  11. I think this would be a wonderful investigation to use in the context of the book ‘The 5 Practices in Practice’ book. However, I am struggling to come up with a statement about ‘What am I wanting the students to learn?’
  
  Any thoughts.
  
  • Hi
  For my sixth graders, my learning goal would be to practice the multiplication of a decimal by a decimal. It has them practicing more engaging way, and because they are problem solving and looking for patterns, they aren’t really aware of the boring repeated practice that a worksheet would have.
  
  12. you might see a lot of answer in life.
  
  13. My 5th grade students were excited to find the answer 9.6 * 8.75 = 84.
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document provides a math problem involving the multiplication of decimals to achieve a whole number product. It includes a hint, an answer section with 14 unique solutions, and comments from users who have found additional solutions or discussed the problem. The document contains both a question and multiple answers.
  
  Label: question-and-answer