Common words used in the context of calculations:
Of: Of means multiply.
Is: Is means equals.
What: What is the value you are looking for.
From: From means subtract.
Less Than: Less than means subtract.
More Than: More than means addition.
For the purpose of using these tricks, it is assumed that you know your multiplication table well up to 9x9.
Faster subtraction
Subtraction is often faster like this.....
For example:
467 - 58 = 400 + (67 -58) = 409
1056 - 145 = (1000 – 100) + (56 -45) = 900 + 11 = 911
Faster addition
Addition is often faster like this.....
For example:
687 + 98 = (687 + 13) + (98 - 13) = 700 + 85 = 785
1058 + 187 = 1100 + (58 + 87) = 1100 + 145 = 1245
Addition of similar digits
2+22+222+2222
=2x(1234)=2468
Similarly
3+33+333+3333+33333
=3x(12345)
=37035
but if
4+44+444+44444
then
=4x(12345)-4444
=44936
Multiply Up to 20 X 20
With this trick, you will be able to multiply any two numbers from 11 to 19 quickly.
Illustration 1.
- Take 17 x 14 for an example.
- First add 17 + 4 = 21
- Add a zero behind it ....210
- Multiply 7x4=28
- Add 210 + 28 = 238.
Illustration 2.
- Take 18 x 17
- First add 18 + 7 = 25
- Add a zero behind it ....250
- Multiply 8x7=56
- Add 250 + 56 = 306
To multiply by 9, try Finger Math (up to 9x10)
(1) Spread your two hands....all fingers and thumbs....to make ten in front of you.
(2) To multiply by 4, fold down the 4th finger from the left.
(3) READ the answer from the three fingers on the left of the folded down finger and the 6 fingers on the right of it......the answer is 36.
Similarly:
(1)To multiply by 5, it would be the 5th finger from the left (left thumb).
(2) READ the answer from the four fingers on the left of the folded down finger and the five fingers on the right of it......the answer is 45.
When multiplying by 9, (even for larger figures)
multiply by 10, and then subtract the number.
For example:
234×9 = 2340 - 234 = 2106
Division by 5
It is more convenient to multiply the figure first by 2 and then divide by 10.
For example,
2375/5 = 4750/10 = 475
Similarly:
3465/5= 6930/10=693
Multiplication by 5
It's also more convenient to multiply first by 10 and then divide by 2.
For example:
236×5 = 2360/2 = 1180
346x5 = 3460/2 = 1730
Multiplication by 25
For example,
57×25 = 5700/4 = 1425
84x25 = 8400/4 = 2100
Multiplication by 125
For example,
57×125 = 57000/8 = 7125
98x125 = 98000/8 = 12250
Multiplication of two digit numbers:
Illustration 1
Step 1. 43 x 84
Step 2. 32 (3x8)+(4x4) 12
Step 3. 32 40 12
Step 4. + +
Step 5. 3 6 1 2 = 3612
Illustration 2
Step 1. 25 x 38
Step 2. 6 (2x8)+(5x3) 40
Step 3. 6 31 40
Step 4. + +
Step 5. 9 5 0 = 950
Illustration 3
Step 1. 98 x 82
Step 2. 72 (64+18) 16
Step 3. 72 82 16
Step 4. + +
Step 5. 7+1 0 3 6 =8036
10% of a number
10% of a number = 1/10 of a number = Remove 0 if it is the last digit or place decimal if it is not 0
Illustration 1
10% of 4567200 =456720
Illustration 2
10% of 85940 = 8594
Illustration 3
10% of 39846 = 3984.6
Some special points regarding percentage:
12 ½% of a number = 1/8 of a number (one eighth)
20% of a number = 1/5 of a number (one fifth)
25% of a number = 1/4 of that number (one fourth)
33 1/3% of a number = 1/3 of a number (one third)
50% of a number = 1/2 of a number (half the number)
150% of a number = 3/2 of a number
200% of a number = 2 times the number (double the number)
250% of a number = 5/2 of a number
300% of a number = 3 times the number (triple the number)
Finding the product in case of UPS10
Conditions:
1. When the unit places' sum is equal to 10 and
- The remaining digits are same.
Now observe:
16 x 14 = (1 x 2)(6 x 4) = 224
17 x 13=(1 x 2)(7 x 3) = 221
23 x 27 = (2 x 3)(3 x 7) = 621
34 x 36 = (3 x 4)(4 x 6) = 1224
46 x 44 = (4 x 5)(6 x 4) = 2024
67 x 63 = (6 x 7)(7 x 3) = 4221
96 x 94 = (9 x 10)(6 x 4) = 9024
Rule: Multiply the common digit with the next number and multiply both the digits at unit place.
Exception: When the numbers at unit places are 1 and 9,their product should be taken 09 instead of 9 like in case of 11 x 19 = (1 x 2)(1 x 9) = 209
Using UPS10 rule for calculating square of any number ending with 5:
(55)2 = (5 x 6)(5 x 5) = 3025
(75)2 = (7 x 8)(5 x 5) = 5625
(95)2 = (9 x 10)(5 x 5) = 9025
Finding the product in case of CNUP5
Condition: Consecutive numbers with unit place 5
Now observe:
25 x 35 = (32-1)(75) = 875
75 x 85 = (82-1)(75) = 6375
85 x 95 = (92-1)(75) = 8075
95 x 105 = (102-1)((75) = 9975
Rule: Square the greater number on left side -1,75 on right side.(G2-1,75)
Multiplication of numbers with the same base
Condition: the numbers should be 100+ or 200+ or 10+ etc.
Illustration:
For calculating 18 x 17,
Step 1: Add 18+7 = 25 or 17+8 = 25
Step 2: Multiply the above sum with the base 10 i.e. 25 x 10 = 250
Step 3: Multiply 8 x 7 = 56
Step 4: Add the answers in Step 2 and Step 3 i.e.250 + 56 = 306
Illustration:
For getting 230 x 236,
Step 1: 266...(230 + 36)
Step 2: 266 x 200 = 53200...(multiplying with base 200)
Step 3: 30 x 36 = 1080
Step 4: 53200 + 1080 = 54280
Finding the square of a two digit number:
by V square method
Using.....(a+b)2=a2+2ab+b2
Square of 12 = 1, 2x1x2, 4 = 144
Square of 13 = 1, 2x1x3, 9 = 169
Square of 25 = 4, 2x2x5, 25 = 625
Square of 35 = 9, 2x3x5, 25 = 9, 30, 25 = 9+3,25(move from right to left to add) = 1225
Square of 86 = 64, 2x8x6, 36 = 64, 96, 36(move from right to left to add) = 7396
Square of 105 = 100, 2x10x5, 25 = 11025
Square of 157 = 225, 2x15x7, 49 = 24649
Last point to be noted is that for numbers having more digits for addition the figures should be written in symmetry, to save time.