Fast Arithmetic Tips : Addition

1. Addition of 5
When adding 5 to a digit greater than 5, it is easier to first subtract 5 and then add 10.
For example,

8 + 5 = 13.
Also 8 - 5 = 3; 3 + 10 = 13.

12 + 5 = 17.
Also 12 - 5 = 7; 7 + 10 = 17.


2. Subtraction of 5
When subtracting 5 from a number ending with a a digit smaller than 5, it is easier to first add 5 and then subtract 10.
For example,

26 - 5 = 21.
Also 26 + 5 = 31; 31 - 10 = 18.

23 - 5 = 18.
Also 23 + 5 = 28; 28 - 10 = 18.

23 - 5 = 18.
Also 23 + 5 = 28; 28 - 10 = 18.

Division by 5
Similarly, it's often more convenient instead to multiply first by 2 and then divide by 10.
For example,

1375/5 = 2750/10 = 275.

980/5 = 1960/10 = 196.

Multiplication by 5
It's often more convenient instead of multiplying by 5 to multiply first by 10 and then divide by 2.
For example,

140×5 = 1400/2 = 700.

135×5 = 1350/2 = 675

120×5 = 1200/2 = 600

it's more quick right ?!

Division/multiplication by 25
Use operations with 4 instead.
For example,

37×25 = 3700/4 = 1850/2 = 925.


Add a sequence from one to a selected
1-digit number and back

Choose a 1-digit number.
Square it.

Example:

If the 1-digit number selected is 7:
To add 1 + 2 + 3 + 4 + 5 + 6 + 7 + 6 + 5 + 4 + 3 + 2 + 1
Square 7: 49
So the sum of all numbers from 1 through 7 and back is 49.

See the pattern?

If the 1-digit number selected is 9:
To add 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1
Square 9: 81
So the sum of all numbers from 1 through 9 and back is 81.

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Squaring a 2-digit number ending in 1 - pangkat dua dari bilangan berakhir 1

Squaring a 2-digit number ending in 1
1. Take a 2-digit number ending in 1.
2. Subtract 1 from the number.
3. Square the difference.
4. Add the difference twice to its square.
5. Add 1.

Example:
1. If the number is 41, subtract 1: 41 - 1 = 40.
2. 40 × 40 = 1600 (square the difference).
3. 1600 + 40 + 40 = 1680 (add the difference twice
to its square).
4. 1680 + 1 = 1681 (add 1).
5. So 41 × 41 = 1681.

See the pattern?
1. For 71 × 71, subtract 1: 71 - 1 = 70.
2. 70 × 70 = 4900 (square the difference).
3. 4900 + 70 + 70 = 5040 (add the difference twice
to its square).
4. 5040 + 1 = 5041 (add 1).
6. So 71 × 71 = 5041.

Mengkalikan 2 buah bilangan yang berakhir 1
1. ambil contoh dua bilangan yang berakhir dengan 1 misal 41, 51, dst
2. kurangkan dengan 1 dari bilangan tersebut
3. kalikan dengan bilangan itu sendiri
4. tambahkan hasil perpangkatan dengan bilangan awal tersebut sebanyak dua kali.
5. tambahkan 1

Contoh:
1. misal 51
2. kurangkan dengan satu, jadi 51-1 = 50
3. pangkatkan dengan 2, atau kalikan dengan bilangan itu sendiri, 50 x 50 2500
4. jumlahkan menjadi 2500 + 50 + 50 = 2600
5. tambahkan satu 2600 + 1
6. jadi 51 x 51 = 2601

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Multiplying two 2-digit- Perkalian 2 Digit

Multiplying two 2-digit numbers(same 1st digit)

1. Select two 2-digit numbers with the same first digit.
2. Multiply their second digits (keep the carry). _ _ _ X
3. Multiply the sum of the second digits by the first digit,
add the carry (keep the carry). _ _ X _
4. Multiply the first digits (add the carry). X X _ _

Example:

1. If the first number is 42, choose 45 as the second number (any 2-digit number with first digit 4).
2. Multiply the last digits: 2 × 5 = 10 (keep carry)
_ _ _ 0
3. Multiply the sum of the 2nd digits by the first:
5 + 2 = 7; 7 × 4 = 28; 28 + 1 = 29 (keep carry)
_ _ 9 _
4. Multiply the first digits (add the carry)
4 × 4 = 16; 16 + 2 = 18
1 8 _ _

5. So 42 × 45 = 1890.

See the pattern?

1. If the first number is 62, choose 67 as the second number
(any 2-digit number with first digit 6).
2. Multiply the last digits: 2 × 7 = 14 (keep carry)
_ _ _ 4
3. Multiply the sum of the 2nd digits by the first (add carry):
2 + 7 = 9; 6 × 9 = 54; 54 + 1 = 55 (keep carry)
_ _ 5 _
4. Multiply the first digits (add the carry)
6 × 6 = 36; 36 + 5 = 41
4 1 _ _

5. So 62 × 67 = 4154.

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