Using Up Digits
The sentence 6.5 x 4.321 = 28.0865 has each of the digits 1, 2, 3, 4, 5, and 6
exactly once on the left-hand side. The number on the right-hand side is close
to but less than 30. Can you find another multiplication sentence that contains
each digit 1, 2, 3, 4, 5, and 6 exactly once on the left side so that the
product is even closer to 30 and yet still under 30? How close can you get? Can
you find a multiplication sentence with 1, 2, 3, 4, 5, and 6 so that the product
is closest to 30 and greater than 30?
Multiply 2 factors that use each of
the digits 1 through 6 one time. The product should be as close as
possible to 30 without going over (like The Price is Right). After
determining the appropriate factors, multiply 2 factors using the same digits to
equal a product as close as possible to 30 that can be greater than 30.
Plans to Solve/Investigate the
Since 6 * 5 = 30, I know that I can
not use both 6 and 5 at the same time for whole numbers if I do not want my
product to be over 30. So I will use 6 and 4 as whole numbers. 6 * 4
= only 24, so I know I will need the larger digits remaining to be in the tenths
When I am ready to find the factors
closest to 30 that may go over, I will use 6 and 5 as whole numbers and the
smaller remaining digits in the tenths place.
Investigation/Exploration of the
I started with pencil and paper and
calculator exploring the products for various factor combinations. 6.5 *
4.321 = 28.0865 was given in the original problem.
I tried 6.3 * 4.521 to = 28.4823
which was closer.
Next I tried 6.2 * 4.531 to = 28.0922
which was farther from 30.
I predict that if I continue to try
other combinations, I will continue to reach products that are less than
28.4823. But to double check... 5.6 * 4.321 = 24.1976, 5.3 * 4.621 =
24.4913. This is not working, so I believe my answer of 6.3 * 4.521 is as
close as I can get to 30 without going over.
Now for the product that can go over
6.1 * 5.234 = 31.9274
6.2 * 5.134 = 31.8308 ---the smallest
6.3 * 5.124 = 32.2812
6.4 * 5.123 = 32.7872
6.3 * 5.214 = 32.8482
Since the first 2 number sentences
were the lowest, I believe my hypothesis is correct, that the whole numbers need
to be larger digits and the tenths need to be smaller digits.
Extensions of the Problem
This is a good way to review place
value and to compare and order decimals. You could also try to start with
30 and divide by 6.1, 6.2, 6.3, 6.4, and 6.5 to get the other factor.
Also, I could try multiplying 6.xxx times 5.x and 6.xxx times 4.x, 6.xx times
5.xx, and 6.xx times 4.xx (changing the number of digits on each factor).
As I tried some of these, I discovered that 6.234 * 5.1 = 31.7934 which is
smaller than my previous answer of 6.2 * 5.134.
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