Multiplying two 2-digit numbers - angka ke 2 sama

Multiplying two 2-digit numbers (same 2nd digit)

1. Both numbers should have the same second digit.
2. Choose first digits whose sum is 10.
3. Multiply the first digits and add one second: X X _ _.
4. Multiply the second digits together: _ _ X X.

Example:

1. If the first number is 67, choose 47 as the second number (same second digit, first digits add to 10).
2. Multiply the 1st digits, add one 2nd.
6x4 = 24, 24+7 = 31. 3 1 _ _
3. Multiply the 2nd digits. 7x7 = 49 _ _ 4 9
4. So 67 × 47 = 3149.

See the pattern?

1. If the first number is 93, choose 13 as the second number (same second digit, first digits add to 10).
2. Multiply the 1st digits, add one 2nd. 9x1 = 9, 9+3 = 12.
1 2 _ _
3. Multiply the 2nd digits. 3x3 = 9 _ _ 0 9
4. So 93 × 13 = 1209.

Read more »

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.

Read more »

Squares Trick - Trick Menghitung Pangkat

1. Squares of numbers from 26 through 50.
Let A be such a number. Subtract 25 from A to get x. Subtract x from 25 to get, say, a. Then A2 = a2 + 100x. For example, if A = 26, then x = 1 and 1375/5 = 2750/10 = 275. Hence
262 = 242 + 100 = 676.

Similarly, if A = 37, then x = 37 - 25 = 12, and a = 25 - 12 = 13. Therefore,
372 = 132 + 100·12 = 1200 + 169 = 1369.

Why does this work?
(25 + x)2 - (25 - x)2=[(25 + x) + (25 - x)]·[(25 + x) - (25 - x)] = 50·2x = 100x.

2. Squares of numbers from 51 through 99.
The idea is the same as above.
(50 + x)2 - (50 - x)2 = 100·2x = 200x.

For example,
32 = 372 + 200·13 = 1369 + 2600 = 3969.

3. Squares of numbers from 51 through 99, second approach (this one was communicated to me by my late father Moisey Bogomolny).
We are looking to compute A2, where A = 50 + a. Instead compute 100·(25 + a) and add a2. Example: 572. a = 57 - 50 = 7. 25 + 7 = 32. Append 49 = 72. Answer: 572 = 3249.

4. Squares can be computed sequentially: (a + 1)2 = a2 + a + (a + 1).
For example,
1112 = 1102 + 110 + 111 = 12100 + 221 = 12321.

5. In general, a2 = (a + b)(a - b) + b2.
Let a be 57 and, again, we wish to compute 572. Let b = 3. Then
572 = (57 + 3)(57 - 3) + 32,
or
572 = 60·54 + 9 = 3240 + 9 = 3249.

6. Squares of numbers that end with 5.
Let A = 10a + 5. Then
A2 = (10a + 5)2 = 100a2 + 2·10a·5 + 25 = 100a(a + 1) + 25.

For example, compute 1152, where a = 11. First compute 11·(11 + 1) = 11·12 = 132 (since 3 = 1 + 2). Next, append 25 to the right of 132 to get 13225! Another example: to compute 2452 let a = 24. Then
24·(24 + 1) = 242 + 24 = 576 + 24 = 600.

Therefore 2452=60025. Here is another way to compute 24·25:
24·25 = 2400/4 = 1200/2 = 600.

The rule naturally applies to 2-digit numbers as well. 752 = 5625 (since 7·8 = 56).
7. Product of 10a+b and 10a+c where b+c = 10.
Similar to the squaring of numbers that end with 5:
(10a + b)(10a + c) = 100a2 + 10a·(b + c) + bc = 100a(a + 1) + bc.

For example, compute 113×117, where a = 11, b = 3, and c = 7. First compute 11·(11 + 1) = 11·12 = 132 (since 3 = 1 + 2). Next, append 21 (= 3×7) to the right of 132 to get 13221!

Another example: compute 242×248, with a = 24, b = 2, and c = 8. Then
24·(24 + 1) = 242 + 24 = 576 + 24 = 600.

Therefore 242×2422=60016.
8. Product of two one-digit numbers greater than 5.
This is a rule that helps remember a big part of the multiplication table. Assume you forgot the product 7·9. Do this. First find the access of each of the multiples over 5: it's 2 for 7 (7 - 5 = 2) and 4 for 9 (9 - 5 = 4). Add them up to get 6 = 2 + 4. Now find the complements of these two numbers to 5: it's 3 for 2 (5 - 2 = 3) and 1 for 4 (5 - 4 = 1). Remember their product 3 = 3·1. Lastly, combine thus obtained two numbers (6 and 3) as 63 = 6·10 + 3.

The explanation comes from the following formula:
(5 + a)(5 + b) = 10(a + b) + (5 - a)(5 - b)

In our example, a = 2 and b = 4.

Read more »

Mathematics Trick

1. 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,
137·5 = 1370/2 = 685.

2. 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.

3.Division/multiplication by 4
Replace either with a repeated operation by 2.
For example,
124/4 = 62/2 = 31. Also,
124·4 = 248·2 = 496.

4.Division/multiplication by 25
Use operations with 4 instead.
For example,
37·25 = 3700/4 = 1850/2 = 925.

5.Division/multiplication by 8
Replace either with a repeated operation by 2.
For example,
124·8 = 248·4 = 496·2 = 992.

6.Division/multiplication by 125
Use operations with 8 instead.
For example,
37·125 = 37000/8 = 18500/4 = 9250/2 = 4625.

Read more »

Integral Basic Formula

This formula and table of integral only a basic function and simple product of e, sin x and cos x
rumus yang ada di halaman ini hanya memuat rumus dasar dan rumus dasar untuk nilai e, sin x dan cos x


1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.

Read more »

Mathematics Constants

A mathematical constant is a quantity, usually a real number or a complex number, that arises naturally in mathematics and does not change. Unlike physical constants, mathematical constants are defined independently of any physical measurement
there is some of Mathematics Constants

Phi

Definition :
The constant p (Greek letter pi) is, classically, defined as the ratio of the circumference p of a circle to its diameter d:
p = pd = 2pr
and, as proved by Archimedes of Syracuse (287-212 BC) in his famous Measurement of a Circle, the same constant is also the ratio of the area A enclosed by the circle to the square of its radius r:
A = pr2.

or phi = 3.14159265358979323846264338327950288419716939937510

E Constans

This limit is well defined and it was denoted by the letter e by the Swiss mathematician Leonhard Euler (1707-1783), first around the end of year 1727 in a manuscript entitled Meditatio in Experimenta explosione tormentorum nuper instituta (Meditation upon experiments made recently on the firing of Canon)
value of e
is = 2.71828182845904523536028747135266249775724709369995...

Other Mathematics Constants


-------------------------------------------------------------------------------

------------------------------------------------------------------------------

-----------------------------------------------------------------------------

Read more »