multiplication shortcuts tricks

Anonymous 12:03 am 0

Multiplication Short cut methods use full for all exams. All the best--------------------

MULTIPLICATION UP TO 20X20 IN YOUR HEAD

• Take 15 x 13 for an example.
• Always place the larger number of the two on top in your mind.
• Then draw the shape of Africa mentally so it covers the 15 and the 3 from the 13 below. Those covered numbers are all you need.
• First add 15 + 3 = 18
• Add a zero behind it (or multiply by 10) to get 180.
• Multiply the covered lower 3 x the single digit above it the "5" (3x5= 15)
• Add 180 + 15 = 195. 

15 X 13 = 195 

MULTIPLICATION SHORT CUT METHODS UP 100 X 100

To multiply two numbers (of two or more digits), split each number into two parts. If the first number is a1 + b1 and the second number is a2 + b2, then the product of the two numbers is:

(a1 x a2) + (a1 x b2 + b1 x a2) + (b1 x b2)

Long Multiplication shortcut technique

The solution comprises three parts (as shown by the boxes and arrows above): the head, the middle, and the tail.

1. The digits on the right are multiplied vertically to get the tail part: b1 x b2 (excess carried over)

2. All digits are multipled crosswise and added together to get the middle part: a1 x b2 + b1 x a2 (excess carried over)

3. The digits on the left are multiplied vertically to get the head part: a1 x a2

Here is a simple example to illustrate this technique.

23 x 41 = 943

Long Multiplication technique example

The steps are:

1. 3 x 1 = 3

2. 2 x 1 + 3 x 4 = 14, put down 4 and carry over 1

3. 2 x 4 = 8, plus the 1 carried over, is 9

The speed gain using this technique (over the conventional method of multi-line long multiplication) becomes more apparent when handling larger numbers. Here is another example involving excess carryover at each stage.

• 108 x 64 = 6912

Long Multiplication technique example

The steps are:

1. 8 x 4 = 32, put down 2 and carry over 3

2. 10 x 4 + 8 x 6 = 88, plus the 3 carried over, is 91; put down 1 and carry over 9

3. 10 x 6 = 60, plus the 9 carried over, is 69

MORE MULTIPLICATION SHOT-CUT METHODS:-------

Square a 2 Digit Number Ending in 5

For this example we will use 25

• Take the "tens" part of the number (the 2 and add 1)=3

• Multiply the original "tens" part of the number by the new number (2x3)

• Take the result (2x3=6) and put 25 behind it. Result the answer 625.

Try a few more 75 squared ... = 7x8=56 ... put 25 behind it is 5625.

55 squared = 5x6=30 ... put 25 behind it ... is 3025. Another easy one! Practice it on paper first!

SINGLE STEP: 35 square
(3x[3+1]) / (5x5) = 12 / 25 = 1225

Square 2 Digit Number: UP-DOWN Method 

Square a 2 Digit Number, for this example 37:

• Look for the nearest 10 boundary

• In this case up 3 from 37 to 40.

• Since you went UP 3 to 40 go DOWN 3 from 37 to 34.

• Now mentally multiply 34x40

• The way I do it is 34x10=340;

• Double it mentally to 680

• Double it again mentally to 1360

• This 1360 is the FIRST interim answer.

• 37 is "3" away from the 10 boundary 40.

• Square this "3" distance from 10 boundary.

• 3x3=9 which is the SECOND interim answer.

• Add the two interim answers to get the final answer.

• Answer: 1360 + 9 = 1369

With practice this can easily be done in your head.

Easy Multiplication By 11

You likely all know the 10 rule (to multiply by 10, just add a 0 behind the number) but do you know the 11 rule? It is as easy! You should be able to do this one in you head for any two digit number. Practice it on paper first!

To multiply any two digit number by 11:

• For this example we will use 54.

• Separate the two digits in you mind (5__4).

• Notice the hole between them!

• Add the 5 and the 4 together (5+4=9)

• Put the resulting 9 in the hole 594. That's it! 11 x 54=594

The only thing tricky to remember is that if the result of the addition is greater than 9, you only put the "ones" digit in the hole and carry the "tens" digit from the addition. For example 11 x 57 ... 5__7 ... 5+7=12 ... put the 2 in the hole and add the 1 from the 12 to the 5 in to get 6 for a result of 627 ... 11 x 57 = 627

Practice it on paper first!

Easy Multiplication By The 11 Rule Expanded

You can directly write down the answer to any number multiplied by 11.

• Take for example the number 51236 X 11.

• First, write down the number with a zero in front of it.

051236

The zero is necessary so that the rules are simpler.

• Draw a line under the number.

• Bear with me on this one. It is simple if you work through it slowly. To do this, all you have to do this is "Add the neighbor". Look at the 6 in the "units" position of the number. Since there is no number to the right of it, you can't add to its "neighbor" so just write down 6 below the 6 in the units col.

• For the "tens" place, add the 3 to the its "neighbor" (the 6). Write the answer: 9 below the 3.

• For the "hundreds" place, add the 2 to the its "neighbor" (the 3). Write the answer: 5 below the 2.

• For the "thousands" place, add the 1 to the its "neighbor" (the 2). Write the answer: 3 below the 1.

• For the "ten-thousands" place, add the 5 to the its "neighbor" (the 1). Write the answer: 6 below the 5.

• For the "hundred-thousands" place, add the 0 to the its "neighbor" (the 5). Write the answer: 5 below the 0.

That's it ... 11 X 051236 = 563596

Finger Math: 9X Rule Easy Multiplication By 9

To multiply by 9,try this:

(1) Spread your two hands out and place them on a desk or table in front of you.

(2) To multiply by 3, fold down the 3rd finger from the left. To multiply by 4, it would be the 4th finger and so on.

(3) the answer is 27 ... READ it from the two fingers on the left of the folded down finger and the 7 fingers on the right of it.

This works for anything up to 9x10!

Multiply By 4

To quickly multiply by four, double the number and then double it again.

Often this can be done in your head.

Multiply By 5

To quickly multiply by 5, divide the number in two and then multiply it by 10. Often this can be done quickly in your head.

MULTIPLICATION TABLES UPTO 20

	TABLES (from 1 TO 20)
1x1=1	2xl=2	3x1=3	4xl=4	5xl=5
1x2=2	2x2=4	3x2=6	4x2=8	5x2=10
1x3=3	2x3=6	3x3=9	4x3=12	5x3=15
1x4=4	2x4=8	3x4=12	4x4=16	5x4=20
1x5=5	2x5=10	3x5=15	4x5=20	5x5=25
1x6=6	2x6=12	3x6=18	4x6=24	5x6=30
1x7=7	2x7=14	3x7=21	4x7=28	5x7=35
1x8=8	2x8=16	3x8=24	4x8=32	5x8=40
1x9=9	2x9=18	3x9=27	4x9=36	5x9=45
1x10=10	2xlO=20	3xlO=30	4x10=40	5xlO=20
6x1=6	7x1=7	8x1=8	9xl=9	lOx1=10
6x2=12	7x2=14	8x2=16	9x2=18	10x2=20
6x3=18	7x3=21	8x3=24	9x3=27	10x3=30
6x4=24	7x4=28	8x4=32	9x4=36	10x4=40
6x5=30	7x5=35	8x5=40	9x5=45	10x5=50
6x6=36	7x6=42	8x6=48	9x6=54	10x6=60
6x7=42	7x7=49	8x7=56	9x7=63	10x7=70
6x8=48	7x8=56	8x8=64	9x8=72	10x8=80
6x9=54	7x9=63	8x9=72	9x9=81	lOx9=90
6x10=60	7x10=70	8x10=80	9xlO=90	10x10=100
11x1=11	12xl=12	13x1=13	14x1=14	15x1=15
11x2=22	12x2=24	13x2=26	14x2=28	15x2=30
11x3=33	12x3=36	13x3=39	14x3=42	15x3=45
11x4=44	12x4=48	13x4=52	14x4=56	15x4=60
11x5=55	12x5=60	13x5=65	14x5=70	15x5=75
11x6=66	12x6=72	13x6=78	14x6=84	15x6=90
11x7=77	12x7=84	13x7=91	14 x7=98	15x7=105
11x8=88	12x8=96	13x8=104	14x8=112	15x8=120
11x9=99	12x9=108	13x9=117	14x9=126	15x9=135
11xl0=110	12xl0=120	13xl0=130	14xlO=140	15xl0=150
16x1=16	17x1=17	18x1=18	19x1=19	20x1=20
16x2=32	17x2=34	18x2=36	19x2=38	20x2=40
16x3=48	17x3=51	18x3=54	19x3=57	20x3=60
16x4=64	17x4=68	18x4=72	19x4=76	20x4=80
16x5=80	17x5=85	18x5=90	19x5=95	20x5=100
16x6=96	17x6=102	18x6=108	19x6=114	20x6=120
16x7=112	17x7=119	18x7=126	19x7=133	20x7=140
16x8=128	17x8=136	18x8=144	19x8=152	20x8=160
16x9=144	17x9=153	18x9=162	19x9=171	20x9=180
16xl0=160	17xlO=170	18x10=180	19x1O=190	20x10=200

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