# 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

## Add Fractions with Decimal Sums

Directions: Using the digits 1 to 9 at most one time each, place a digit …

1. another one… 9.6 x 1.25 = 12

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!