## 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 9×9.

## 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 7×4=28
- Add 210 + 28 = 238.

Illustration 2.

- Take 18 x 17
- First add 18 + 7 = 25
- Add a zero behind it ….250
- Multiply 8×7=56
- Add 250 + 56 = 306

## To multiply by 9, try Finger Math (up to 9×10)

(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

346×5 = 3460/2 = 1730

## Division/multiplication by 25

For example,

57×25 = 5700/4 = 1425

84×25 = 8400/4 = 2100

## Division/multiplication by 125

**
**For example,

57×125 = 57000/8 = 7125

98×125 = 98000/8 = 12250

## Multiplication of two digit numbers:

Illustration 1

Step 1. 43 x 84

Step 2. 32 (3×8)+(4×4) 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 (2×8)+(5×3) 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 = (3^{2}-1)(75) = 875

75 x 85 = (8^{2}-1)(75) = 6375

85 x 95 = (9^{2}-1)(75) = 8075

95 x 105 = (10^{2}-1)((75) = 9975

**Rule:** Square the greater number on left side -1,75 on right side.(G^{2}-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}=a^{2}+2ab+b^{2}

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.