Open Middle®
Directions: Use the digits 1 to 9, at most one time each, to create two numbers that have a product as close to 500,000 as possible. NOTE: You may use any length of factors as you would need. Ex 8 digit by 1 digit. 4 digit by 3 digit.
Hint
What can you estimate to get close to 500,000?
How many digits did you use?
How many digits did you use?
Answer
947 x 528= 500,016
Source: Miles Knight
One of my 5th grade students came up with this one:
731 x 684 = 500,004
She is very, very excited!!
Can we use decimals?
My student also got 500,004 by multiplying 684 by 713!
My student got 500,000!!!!
7812.5×64
No where does it say you can’t use decimals. He talked me through his thinking and it was brilliant. I was so excited and I’ve never seen him with a smile that big before.
I got 499993.6.
7812.4×64
My 5th grade students were excited to find these equations.
947 x 528 = 500016
731 x 684 = 500004
7812.5 x 64 = 500000
124,567 x 4=498268
512 x 976
167 245 x 3 = 501 735
Using only integers, the products closest to 500,000 are:
684 * 731 = 500,004
3,876 * 129 = 500,004
which are both only 4 away from 500,000
Using decimals, the solution 7812.5 * 64 (posted by Mr. Reid and Heather Melville) is the only one to come out to exactly 500,000. Which to me is very surprising, given the sheer number of possibilites to make two decimal numbers (even if all digits have to be distinct).
But the closest one after that is
7352.941 * 68 = 499,999.988
Side note:
To get as close to 500,000 as possible using decimals, you can equivalenty try finding two numbers that multiply as close to 5,000,000 or 50,000,000 or 500,000,000 (5,000,000,000 is greater than any product of two numbers with 9 digits total). Because then all you need to do is shift the comma of one or both of your factors to get back to 500,000.
Another solution for 500,004: 3,876*129