Dr. Steve's Wife Drinks Latte

Dr. Steve's wife decided to change to whole milk for her Latte (a mixture of strong coffee and warm milk). She likes to have 300 milliliters of milk and to shop once a week.

A half-gallon of milk contains 1890 millileters. Can she drink 300 milliliters per day and shop once a week?

Suppose she decides to shop once a week and use less milk. How much milk can she use per day, in milliliters?

You may be surprised to find that the answer comes out to be a whole number. Look at the divisibility rules and concentrate on divisibility by 7, printed in red below.

The following is borrowed from "Ask Dr. Math" published by Drexel University in Philadelphia PA.

Divisibility by:

2	If the last digit is even, the number is divisible by 2.
3	If the sum of the digits is divisible by 3, the number is also.
4	If the last two digits form a number divisible by 4, the number is also.
5	If the last digit is a 5 or a 0, the number is divisible by 5.
6	If the number is divisible by both 3 and 2, it is also divisible by 6.
7	Take the last digit, double it, and subtract it from the rest of the number; if the answer is divisible by 7 (including 0), then the number is also.
8	If the last three digits form a number divisible by 8, then so is the whole number.
9	If the sum of the digits is divisible by 9, the number is also.
10	If the number ends in 0, it is divisible by 10.
11	Alternately add and subtract the digits from left to right. (You can think of the first digit as being 'added' to zero.) If the result (including 0) is divisible by 11, the number is also. Example: to see whether 365167484 is divisible by 11, start by subtracting: [0+]3-6+5-1+6-7+4-8+4 = 0; therefore 365167484 is divisible by 11.
12	If the number is divisible by both 3 and 4, it is also divisible by 12.
13	Delete the last digit from the number, then subtract 9 times the deleted digit from the remaining number. If what is left is divisible by 13, then so is the original number. 1890 / 7 Consider the number 1890, what is it divisible by? Double zero and remove from 1890, leaving 189. Double 9 and subtract from 18, leaving zero, which is clearly divisible by 7. So, 1890 is divisible by 7. Dr. Steve's wife gets exactly 270 milliliters of milk per day, which is more than a cup, and works fine. This is a real-life story. Try the number 7560, for more practice. II The last digit is zero, which is even, so it is divisible by 2. III The sum of the digits, 7 + 5 + 6 + 0 = 18, which is divisible by 3, so the number is also divisible by 3. IV The last two digits, 60, are divisible by 4, so the number is divisible by 4. V The last digit is zero, so the number is divisible by 5 VI The number is divisible by 3 and 2; consequently, it is divisible by 6. VII For 7560 to be divisible by 7, 756 must be divisible by 7. Knock off the last digit and consider two numbers, 75 and 6. Double 6 and subtract from 75; 75 -12 = 63.We recognize that 63 is divisible by 7, 63/7 = 9. So 7560 is divisible by 7. VIII The number is divisible by 4 and 2, hence is divisible by 8. Or, looking at the last three digits, 560 divided by 8 is 70, so 7560 is divisible by 8. IX The sum of the digits is 18, which is divisible by 9, so 7560 is divisible by 9. X The last digit is zero, so the number is divisible by 10. The number is not divisible by 11 or 13. XII The number is divisible by 3 and 4, hence is divisible by 12. 7560/12 = 630. In fact, I "cooked up" 7560 as 3 x 5 x 7 x 8 x 9, since 8 x 3 = 24, the number was sure to be divisible by 2, 4, 6 and 12. Methods for divisibility by 11 and 13 will be covered in a subsequent post.