Eureka

Monday, November 17, 2014

Warm up #3 problems 31 thru 40

This is a straight forward problem. 6 factorial is =

6 times 5 times 4 times 3 times 2 times 1

so we can do the arithmetic. But reducing

the ANSWER will take time.

Take a look at this idea:

Divisible by 9
The sum of the digits is divisible by 9
(Note: you can apply this rule to that answer again if you want)
1629 (1+6+2+9=18, and again, 1+8=9) Yes
2013 (2+0+1+3=6) No

Recall #19 and the method we used:
http://mathyoucancounton.blogspot.com/2014/11/warm-up-2-problems-11-thru-20_13.html

Use enough decimals for PI

Hint: Draw a Rectangle 4 by 6
(Change into Inches!)

UNIT means 1
so each side of the BIGGER
SQUARES are 1 by 1

RULES FOR DIVISIBILITY:

A NUMBER IS DIVISIBLE BY_____, IF ______
2 The last digit is even (0,2,4,6,8)
128 is 129 is not
3 The sum of the digits is divisible by 3
381 (3+8+1=12, and 12÷3 = 4) Yes
217 (2+1+7=10, and 10÷3 = 3 1/3) No
4 The last 2 digits are divisible by 4
1312 is (12÷4=3) 7019 is not
5 The last digit is 0 or 5
175 is 809 is not
6 The number is divisible by both 2 and 3
114 (it is even, and 1+1+4=6 and 6÷3 = 2) Yes
308 (it is even, but 3+0+8=11 and 11÷3 = 3 2/3) No
7 If you double the last digit and subtract it from the rest of the number and the answer is: 0, or divisible by 7 (Note: you can apply this rule to that answer again if you want)
672 (Double 2 is 4, 67-4=63, and 63÷7=9) Yes
905 (Double 5 is 10, 90-10=80, and 80÷7=11 3/7) No
8 The last three digits are divisible by 8
109816 (816÷8=102) Yes 216302 (302÷8=37 3/4) No
9 The sum of the digits is divisible by 9
(Note: you can apply this rule to that answer again if you want)
1629 (1+6+2+9=18, and again, 1+8=9) Yes
2013 (2+0+1+3=6) No
10 The number ends in 0
11 If you sum every second digit and then subtract all other digits and the answer is: 0, or divisible by 11
1364 ((3+4) - (1+6) = 0) Yes
3729 ((7+9) - (3+2) = 11) Yes
25176 ((5+7) - (2+1+6) = 3) No
12 The number is divisible by both 3 and 4
648 (By 3? 6+4+8=18 and 18÷3=6 Yes.
By 4? 48÷4=12 Yes) Yes
524 (By 3? 5+2+4=11, 11÷3= 3 2/3 No.
Don't need to check by 4.) No

Thursday, November 13, 2014

Workout #1 Questions 21 thru 30

Workout #1 Questions 21 thru 30
The WORKOUT Questions are usually more difficult.
The one that are the most reasonable are:
24, 25, 26, 29
TRY THOSE FIRST