Can you help with this math problem?

[1GirlTwinBoys]

What number between 110 and 140 is divisible by 12 but doesn't end in a zero.  How would you figure this out?

 

Thanks!

[almondbutterandjelly]

The quickest way for me is to remember my math facts.  12x12=144.  Too high, that's out.  12x11=132.  There ya go.

 

[SparklyUnicorn]

12 x 11

 

Think in terms of multiples of 12.  Can't be 12 x 9 because that is 108.  Can't be 12 x 10 because your answer will end in zero.  It can't be 12 x 12 because that is 144. 

 

 

 

[Ali in OR]

132 (12x11). When I was a kid we learned times tables through 12--my kids' math books only go through 10. If you know your 12 times tables, the number jumps out at you. If you don't know, there aren't that many numbers to check--12x10 is easy but ends in zero. 12x12 is too big for the range (144).

[Muttichen]

Well, to be divisible by 12, it has to be divisible by 3 and 4.  To find out if a number is divisible by 3, you add the digits and see if the sum is divisible by 3.  So 110 isn't but 111 is.  For 4, you check if the last two digits are divisible by 4.  So 112 is.  I'd just list all the numbers from 110-140 and see which meet both criteria.  I'm sure my mathy kids could do it a quicker way, though!

[Arcadia]

I have my 12 times table memorized.

In general though divide the lower number by 12 to give you the lowest number estimate, in this case 10x12.

Since the question specify the number can't end in zero, the next number would be 11x12=132.

The number after that is 12x12 >140 so there is only one solution.

[Aiden]

Sounds like everyone is using a variant of the same basic strategy--guess and check. It's the one I'd use: 12x12 is too big, 12x11--oh, that works!

 

Hopefully there's a more efficient way to do it, though, that none of us happen to know yet?

[wapiti]

I don't think there's any special strategy other than the one(s) mentioned above.  It's as simple as knowing the multiplication table for 12.  (Eta, if the student doesn't know the multiplication table for 12, it should still be a simple matter to figure out what the multiples are, no?)

 

If we were talking bigger numbers for which one wouldn't know the multiplication table, I would use what we know about primes and divisibility.  A number ending in 0 would be divisible by 5 and 2, so the answer would be a multiple of 12 (divisible by both 3 and 4) but NOT also divisible by 5 (or 10, for that matter).

[SparklyUnicorn]

Sounds like everyone is using a variant of the same basic strategy--guess and check. It's the one I'd use: 12x12 is too big, 12x11--oh, that works!

 

Hopefully there's a more efficient way to do it, though, that none of us happen to know yet?

 

I'd think at that level the make a good guess and check method would be expected.  I think we assume there must be some fancy formula we could come up with, but even if so that wouldn't be easier at that level.

 

I think it's difficult to think in terms of what numbers are divisible by another number and easier to think what are the multiples of the number.  And the range given is small so it won't take that many tries. 

[LucyStoner]

There are 2 multiples of 12 in that range and one ends in 0.  Checking all the numbers between 110 and 140 seems quite laborious.  Just "check" the multiples of 12.  Even if you didn't know the times table cold, you'd know that in any consecutive range of 30 or so numbers, only a 2-3 tops could be evenly divisible by 12.  I would probably think 12X10=120, nope.  12x11=132.  Ok, that works.  

[MyThreeSons]

I'd solve it similar to what everyone said above. I'd say that it's really more of a math puzzle or logic problem than a straight-up "math problem". While it involves numbers and you do use mathematical operations to solve it, it's not like you can write a formula to solve to get the answer.