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# 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?

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

## Balanced Equations 2

Directions: Use the operation symbols (+, -, x, ÷) and equal sign (=) to make …

1. another one… 9.6 x 1.25 = 12

2. 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. • Ok I will.

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. 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.

• Problems like this make you re-evaluate the labels we give students including whether they’re true or useful.

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.