Assorted Multiplication Tips

Assorted Multiplication Rules

Multiply by 5: Multiply by 10 and divide by 2.
Multiply by 9: Multiply by 10 and subtract the original number.
Multiply by 12: Multiply by 10 and add twice the original number.
Multiply by 13: Multiply by 3 and add 10 times original number.
Multiply by 14: Multiply by 7 and then multiply by 2
Multiply by 15: Multiply by 10 and add 5 times the original number.
Multiply by 16: Double four times, or multiply by 8 and then by 2.
Multiply by 17: Multiply by 7 and add 10 times original number.
Multiply by 18: Multiply by 20 and subtract twice the original number.
Multiply by 19: Multiply by 20 and subtract the original number.
Multiply by 24: Multiply by 8 and then multiply by 3.
Multiply by 27: Multiply by 30 and subtract 3 times the original number.
Multiply by 45: Multiply by 50 and subtract 5 times the original number.
Multiply by 90: Multiply by 9 (as above) and put a zero on the right.
Multiply by 98: Multiply by 100 and subtract twice the original number.
Multiply by 99: Multiply by 100 and subtract the original number.

Try and verify your answers .

Tips on Percentage

Percentages

Understand the word “Percent.”
The first part is PER , PER = FOR EACH.
The second part of the word is CENT, as in 100.
PERCENT = For Each 100.

Find 7 % of 300.

7% of the first hundred is 7.
7% of 2nd hundred is also 7
7% of the 3rd hundred is also 7.
So, 7 % of 300 = 7+7+7 = 21.

If 8 % of 100 is 8,

8% of 50 is half of 8 , or 4.

Break down every number that’s asked into questions of 100,
if the number is less then 100, then move the decimal point accordingly.

EXAMPLES:
8% of 200 = 8 + 8 = 16.

8% of 250 = 8 + 8 + 4 = 20.

8% of 25 = 2.0 (Moving the decimal back).

15%300 = 15+15+15 = 45.

15%350 = 15+15+15+7.5 = 52.5

More tips on multiplication

Multiply by 5

Take any number, then divide it by 2 (in other words, halve the number).
If the result is whole, add a 0 at the end.
If it is not, ignore the remainder and add a 5 at the end.

Example:
2682 x 5
2682 / 2 = 1341 (whole number, so add 0)
So, 2682 x 5 = 13410

Another example :
5887 x 5
2943.5 (fractional number,ignore remainder, add 5)
So, 5887 x 5 = 29435

Multiply by 9

To multiple any number between 1 and 9 by 9 hold both hands in front of your face
- drop the finger that corresponds to the number you are multiplying (for example 9×3 - drop your third finger)
- count the fingers before the dropped finger (in the case of 9×3 it is 2)
- then count the numbers after (in this case 7)
- the answer is 27.

Subtraction from 1000

Subtracting from 1,000

To subtract a large number from 1,000 you can use this basic rule:

Subtract all but the last number from 9,

then subtract the last number from 10

Example -
1000-648

step1: subtract 6 from 9 = 3

step2: subtract 4 from 9 = 5

step3: subtract 8 from 10 = 2

Answer: 352

Multiplication of large numbers

Tough Multiplication

If you have a large number to multiply and one of the numbers is even,
you can easily subdivide to get to the answer:

32 x 125, is the same as
16 x 250 is the same as
8 x 500 is the same as
4 x 1000 = 4,000

Tips -Multiplication by 11

The 11 Times Trick

Easy trick for multiplying a two digit number by 11

Take the original number and imagine a space between the two digits

Example: 52

5_2

Now add the two numbers together and put them in the middle:

5_(5+2)_2

That is it - you have the answer: 572.

If the numbers in the middle add up to a 2 digit number, just insert the second number and add 1 to the first:

9_(9+9)_9

(9+1)_8_9

10_8_9

1089

Easy tips of squaring numbers

Quick Square

If you need to square a 2 digit number ending in 5,

Mulitply the first digit by itself + 1, and put 25 on the end.

252 = (2x(2+1)) 25

= (2 X 3)25

= 625

Try with other numbers ending in 5

Divisibility Tests

2 - Even (units digit is 0, 2, 4, 6, or 8).
Eg - 4587216 is divisible by 2 as units digit is 6

3 - Sum of digits is divisible by 3.
Eg - 5684121 is divisible by 3 as sum of digits that is 27 is divisible by 3

4 - Number formed by the tens and ones digits is divisible by 4
Eg - 68452196 is divisible by 4 as 96 1s divisible by 4

5 - Units digit is 0 or 5.
Eg - 56487690 is divisible by 5 as units digit is 0

8 - Number formed by the hundreds,tens and units digits is divisible by 8.
Eg - 784580816 is divisible by 8 as 816 is divisible by 8

9 - Sum of digits is divisible by 9.
Eg - 59684121 is divisible by 9 as sum of digits that is 36 is divisible by 9

10 - Units digit is 0.
Eg - 58746210 is divisible by 10 as units digit is 0

11 - The difference between the sum of the odd numbered digits (1st, 3rd, 5th...)

and the sum of the even numbered digits ( 2nd ,4th ,6th …) Is divisible by 11

Example: 34871903

3+8+1+0=12

4+7+9+3=23

23-12=11

11 is divisible by 11

So,34871903 is divisible by 11

Divisibility tests by 7

Divisibility by 7 ( First method)

Take the two left-most digits, multiply the left digit by 3 and add it to the second digit. Replace these two digits with the result. Then we can keep repeating, always dealing with only the two left-most digits, until we end up with a small number which is either divisible by 7 or not.

4712954379 4 x 3 +7 = 19
1912954379 1 x 3 +9 = 12 so on
1212954379
512954379
162954379
92954379
29954379
15954379
8954379
3354379
1254379
554379
204379
64379
22379
8379
2779
1379
679
259
119
49
49 is divisible by 7. Since 49 is divisible by 7, every number above it is also divisible by 7.

Test for divisibility by 7. ( second method )

Double the last digit and subtract it from the remaining number. If the result is divisible by 7, then so was the original number. Apply this rule over and over again as necessary.
Example: 826.
Twice 6 is 12.
So take 12 from 82.
Now 82-12=70.
This is divisible by 7, so 826 is divisible by 7 also.

Divisibility tests for some prime numbers

Test for divisibility by 13.
Add four times the last digit to the remaining number. If the result is divisible by 13, then so was the first number. Apply this rule over and over again as necessary.
Example: 50661
5066+4=5070
507+0=507
50+28=78
78 is 6*13, so 50661 is divisible by 13.

Test for divisibility by 17.
Subtract five times the last digit from the remaining number. If the result is divisible by 17, then so was the first number. Apply this rule over and over again as necessary.
Example: 3978
397-5*8=357
35-5*7=0. So 3978 is divisible by 17.

Test for divisibility by 19.
Add two times the last digit to the remaining number. If the result is divisible by 19, then so was the first number. Apply this rule over and over again as necessary.
Example: 101156
10115+2*6=10127
1012+2*7=1026
102+2*6=114 and 114=6*19, so 101156 is divisible by 19.

Test for divisibility by 23.
Add seven times the last digit to the remaining number. If the result is divisible by 23, then so was the first number. Apply this rule over and over again as necessary.
Example: 17043
1704+7*3=1725
172+7*5=207
20+7*7=69 which is 3*23, so 17043 is also divisible by 23.

Test for divisibility by 29.
Add three times the last digit to the remaining number. If the result is divisible by 29, then so was the first number. Apply this rule over and over again as necessary.
Example: 15689
1568+3*9=1595
159+3*5=174
17+3*4=29, so 15689 is also divisible by 29.

Test for divisibility by 31.
Subtract three times the last digit from the remaining number. If the result is divisible by 31, then so was the first number. Apply this rule over and over again as necessary.
Example: 7998
799-3*8=775
77-3*5=62 which is twice 31, so 7998 is also divisible by 31.

Test for divisibility by 37.
Subtract eleven times the last digit from the remaining number. If the result is divisible by 37, then so was the first number. Apply this rule over and over again as necessary.
Example: 23384
2338-11*4=2294
229-11*4=185 which is five times 37, so 23384 is also divisible by 37.

Test for divisibility by 41.
Subtract four times the last digit from the remaining number. If the result is divisible by 41, then so was the first number. Apply this rule over and over again as necessary.
Example: 30873
3087-4*3=3075
307-4*5=287
28-4*7=0, remainder is zero and so 30873 is also divisible by 41.

Test for divisibility by 43.
Add thirteen times the last digit to the remaining leading number. If the result is divisible by 43, then so was the first number. Apply this rule over and over again as necessary.
Example: 3182
318+13*2=344
34+13*4=86 which is recognisably twice 43, and so 3182 is also divisible by 43.

Test for divisibility by 47.
Subtract fourteen times the last digit from the remaining leading truncated number. If the result is divisible by 47, then so was the first number. Apply this rule over and over again as necessary.
Example: 34827
3482-14*7=3384
338-14*4=282
28-14*2=0 , remainder is zero and so 34827 is divisible by 47.