# 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.
The text contains a mathematical problem that involves finding combinations of decimal numbers that, when multiplied, result in a whole number. The problem is presented with a hint and an answer section that lists 14 unique solutions. Additionally, there are several comments from users who have found additional solutions or provided insights into the problem.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# 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.
user
The text contains a mathematical problem that involves finding combinations of decimal numbers that, when multiplied, result in a whole number. The problem is presented with a hint and an answer section that lists 14 unique solutions. Additionally, there are several comments from users who have found additional solutions or provided insights into the problem.

TYPE: SINGLE_QUESTION_WITH_ANSWER