Learning to multiply 3's 6's 7's and 9's

3's 6's 7's and 9's are hard numbers to multiply.   There are complete tutoring agencies teaching math because of 3's 6's 7's and 9's

The series does not flow as easily as others.

3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 63 66 69 72 75 78 81 84 87 90

The numbers that are high lighted are the numbers on the 10 x 10 multiplication table that gives students the most problems.

I have my students figure out the series the series to 6 9 18 21 and 27 after they learn to multiply 2 4 5 8 10.  6 and 9 are pretty simple by this time so to complete the threes  18 21 and 27 need to be memorized. 3 x 6 =18 3 x 7 =21 and 3 x 9=27




If the student has learned the 2's 4's 5's 8's and 10's the table will be as follows after the student learns the 3's:

1 2 3 4 5 6 7 8 9 10 1 1 2 3 4 5 6 7 8 9 10 2 2 4 6 8 10 12 14 16 18 20 3 3 6 9 12 15 18 21 24 27 30 4 4 8 12 16 20 24 28 32 36 40 5 5 10 15 20 25 30 35 40 45 50 6 6 12 18 24 30 48 60 7 7 14 21 28 35 56 70 8 8 16 24 32 40 48 56 64 72 80 9 9 18 27 36 45 72 90 10 10 20 30 40 50 60 70 80 90 100

The next series is 6 and 36 42 and 54 are hard numbers for students.  6 x 6=36  6 x 7 = 42 6 x 9 = 54

	1	2	3	4	5	6	7	8	9	10
1	1	2	3	4	5	6	7	8	9	10
2	2	4	6	8	10	12	14	16	18	20
3	3	6	9	12	15	18	21	24	27	30
4	4	8	12	16	20	24	28	32	36	40
5	5	10	15	20	25	30	35	40	45	50
6	6	12	18	24	30	36	42	48	54	60
7	7	14	21	28	35	42		56		70
8	8	16	24	32	40	48	56	64	72	80
9	9	18	27	36	45	54		72		90
10	10	20	30	40	50	60	70	80	90	100

The next series is 9 and 7.  Memorize 9 x 7 =63 and 9 x 9= 81.  The 10 x 10 multiplication table is done.

Do plenty of exercises and you will have this constantly in your memory.

3 Times is a charm

3 divisibility rule

If a number  is divisible by 3, then the sum of the digits of the number are also divisible by 3.

As an example:

63, 123, 2223 are all divisible by 3.  We can easily determine this in our heads without a calculator by adding the digits and then dividing by 3 as follows:

6+3=9 

9÷3=3

63 is evenly divisible by 3.

If we use a calculator, we find 63÷3=21

1+2+3=6

6÷3=2

123 is divisible by 3.

If we use our a calculator, we find 123÷3=41

2+2+2+3=9

9÷3=3

2223 is divisible by 3
If we use our calculator, we find 2223÷3=741

89, 173, and 3113 are not divisible by 3.  Here is why:

8+9=17 and 17 is not divisible by 3

1+7+3=11 and 11 is not divisible by 3

3+1+1+3=8 and 8 is not divisible by 3

This is a very simple rule yet very powerful.  There are other rules that I will present a little later but this is one of the most important rules and this will help you through many tests like the SAT and ACT.

Try these on your own:

Are these numbers divisible by 3?  Add the digits and divide.  Check with your calculator.

1234, 174, 12761, 25437

Hint all are except 12761.