Multiply Up to 20X20 in Your Head

Multiply Up to 20X20 In Your Head In just FIVE minutes you should learn to quickly multiply up to 20x20 in your head. With this trick, you will be able to multiply an y two numbers from 11 to 19 in your head quickly, without the use of a calculator.

I will assume that you know your multiplication table reasonably well up to 10x10. Try this: • • •

• • • •

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 (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.

The 11 Rule 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!

Finger Math: 9X Rule 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

Trusted by over 1 million members

Try Scribd FREE for 30 days to access over 125 million titles without ads or interruptions! Start Free Trial Cancel Anytime.





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!

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!

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.





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.

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

Practice it on paper first!





Multiplying by five •

Jenny Logwood writes: Here is an easy way to find an answer to a 5 times question.

If you are multiplying 5 times an even number: halve the number you are multiplying by and place a zero after the number. Example: 5 × 6, half of 6 is 3, add a zero for an answer of 30. Another example: 5 × 8, half of 8 is 4, add a zero for an answer of 40. If you are multiplying 5 times an odd od d number: subtract one from the number you are multiplying, then halve that number and place a 5 after the resulting number. Example: 5 × 7: -1 from 7 is 6, half of 6 is 3, place a 5 at the end of the resulting number to produce the number 35. Another example: 5 × 3: -1 from 3 is 2, half of 2 is 1, place a 5 at the end of this number to produce 15. •

Doug Elliott adds: To square a number that ends in 5, multiply the tens digit by (itself+1), then append 25. For example: to calculate 25 × 25, first do 2 × 3 = 6, then append 25 to this result; the answer is 625. Other examples: 55 x 55; 5 × 6 = 30, answer is 3025. You can also square three digit numbers this way, by starting with the the first two digits: 995 x 995; 99 × 100 = 9900, answer is 990025.

Multiplying by nine •

•

Diana Grinwis says: To multiply by nine on your fingers, hold up ten fingers - if the problem is 9 × 8 you just put down your 8 finger and there's your answer: 72. (If the problem is 9 × 7 just put down your 7 finger: 63.) Laurie Stryker explains it this way: When you are multiplying by 9, on your fingers (starting with your thumb) count the number you are multiplying by and hold down that finger. The number n umber of fingers before the finger held down is the first digit of the answer and the number of finger after the finger held down is the second digit of the answer.

Example: 2 × 9. your index finder is held down, your thumb is before, representing 1, and there are eight fingers after your index finger, representing 18. •

Polly Norris suggests: When you multiply a number times 9, count back one from that number to get the beginning of your product. (5 × 9: one less than 5 is 4).

To get the rest of your answer, an swer, just think of the add fact families for 9:





5 × 9 = 4_. Just think to yourself: 4 + _ = 9 because the digits in your product always add up to 9 when one of the factors is 9. Therefore, 4 + 5 = 9 and your answer is 45! I use this method to teach the "nines" in multiplication to my third graders and they learn them in one lesson! Tamzo explains this a little differently:

1. Take the number you are multip multiplying lying 9 by and subtract subtract one. one. That number number is the first number in the solution. 2. Then subtrac subtractt that number number from from nine. That That number number is the the second second number number of the solution. Examples:

4 * 9 = 36 1. 4-1=3 2. 9-3=6 3. solu olution = 36 36 8 * 9 = 72 4. 8-1=7 5. 9-7=2 6. solu olution = 72 72 5 * 9 = 45



7. 5-1=4 8. 9-4=5 9. solu olution = 45 45 Sergey writes in: Take the one-digit number you are multipling by nine, and insert a zero to its right. Then subtract the original number from it. For example: if the problem is 9 * 6, insert a zero to the right of the six, then subtract six: 9 * 6 = 60 - 6 = 54

Multiplying a 2-digit number by 11 •

A tip sent in by Bill Eldridge: Simply add the first and second digits and place the result between them.





This can be done using any 2-digit number. (If the sum is 10 or greater, don't forget to carry the one.) Multiplying any number by 11 •

Lonnie Dennis II writes in:

Let's say, for example, you wanted wan ted to multiply 54321 by 11. First, let's look at the problem the long way... 54321 x 11 54321 + 543210 = 597531 Now let's look at the easy way... 11 × 54321 = 5 4+5 4+3 3+2 2+1 1 = 597531 Do you see the pattern? In a way, you're simply adding the digit to whatever comes before it. But you must work from right to left. The reason I work from right to left is that if the numbers, when added together, sum to more than 9, then you have something to carry over. Let's look at another example... 11 × 9527136 Well, we know that 6 will be the last number in the answer. So the answer now is ???????6. Calculate the tens place: 6+3=9, so now we know that the product has the form







1+7=8, so ????8496. 7+2=9, so ???98496. 2+5=7, so ??798496. 5+9=14. Here's where carrying digits comes in: we fill in the h undred thousands place with the ones digit of the sum 5+9, and our product has the form ?4798496. We will carry the extra 10 over to the next (and final) place. 9+0=9, but we need to add the one carried from the previous sum: 9+0+1=10. So the product is 104798496.

Multiply Up to 20X20 in Your Head

Recommend Documents