Multiplication Tips

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 of6 is 3, add a zero for an answer of 30. Another example: 5 × 8, half of8 is 4, add a zero for an answer of 40.

  If you are multiplying 5 times an odd 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 toproduce 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 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, just think of the add fact families for 9:

      1 + 8 = 9        2 + 7 = 9        3 + 6 = 9        4 + 5 = 9
  
      8 + 1 = 9        7 + 2 = 9        6 + 3 = 9        5 + 4 = 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 multiplying 9 by and subtract one. That number is the first number in the solution.
  2. Then subtract that number from nine. That number is the second number of the solution.
  Examples:
  
  4 * 9 = 36
  
  1. 4-1=3
  2. 9-3=6
  3. solution = 36

  8 * 9 = 72

  1. 8-1=7
  2. 9-7=2
  3. solution = 72

  5 * 9 = 45

  1. 5-1=4
  2. 9-4=5
  3. solution = 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.
  

  Here's an example using 24 as the 2-digit number to be multiplied by 11:2 + 4 = 6 so 24 × 11 = 264.

  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 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
  

  ??????96.

  3+1=4, so now we know that the product has the form
  

  ?????496.

  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 hundred 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.

 Multiplying by thirteen

• Fourth grader Mariam Labib has a trick for multiplication by 13.

  Put the tens digit on the left, the unit number on the right, add them up together in the middle. Then add double the number to the previous result.

  For example: 13 × 22
  
  Step 1: (2 × 100) + 2 + [(2 + 2) × 10] = 242.
  
  Step 2: 22 × 2 = 44.
  
  Answer: 242 + 44 = 286.
  

  If the two digits sum to more than ten, then you carry the one to add it to the number on the left and continue.

  For example: 13 × 65
  
  Step 1: (6 × 100) + 5 + [(6 + 5) × 10] = 715.
  
  Step 2: 65 × 2 = 130.
  
  Answer: 715 + 130 = 845.
  

 Multiplying by sixteen

• Ibrahim Labib offers a quick way to find an answer when multiplying by 16.

  First, multiply the number in question by 10. Then multiply half the number by 10. Then add those two results together with the number itself to get your final answer.

  For example: 16 × 24
  
  Step 1: 24 × 10 = 240
  
  Step 2: (24 × 1/2) × 10 = 12 × 10 = 120
  
  Step 3: add steps 1 and 2 and the number = 240 + 120 + 24 = 384
  
  
  
  For more Tips & Tricks
  visit again
  MATHSCIRCLE

Squaring a 2-digit number beginning

with 1

1. Take a 2-digit number beginning with 1.
2. Square the second digit 
   
   (keep the carry)   _ _ X
   
3. Multiply the second digit by 2 and 
   
   add the carry (keep the carry)   _ X _
   
4. The first digit is one 
   
   (plus the carry)   X _ _
   

   Example:

1. If the number is 16, square the second digit:
   
   6 × 6 = 36   _ _ 6
   
2. Multiply the second digit by 2 and
   
   add the carry: 2 × 6 + 3 = 15   _ 5 _
   
3. The first digit is one plus the carry:
   
   1 + 1 = 2   2 _ _
   
4. So 16 × 16 = 256.

   See the pattern?

1. For 19 × 19, square the second digit:
   
   9 × 9 = 81   _ _ 1
   
2. Multiply the second digit by 2 and
   
   add the carry: 2 × 9 + 8 = 26   _ 6 _
   
3. The first digit is one plus the carry:
   
   1 + 2 = 3   3 _ _
   
4. So 19 × 19 = 361.

Squaring a 2-digit number ending in 3

1. Take a 2-digit number ending in 3.
2. The last digit will be _ _ _ 9.
3. Multiply the first digit by 6: the 2nd number will be 
   
   the next to the last digit: _ _ X 9.
   
4. Square the first digit and add the number carried from 
   
   the previous step: X X _ _.
   

   Example:

1. If the number is 43, the last digit is _ _ _ 9.
2. 6 × 4 = 24 (six times the first digit): _ _ 4 9.
3. 4 × 4 = 16 (square the first digit), 16 + 2 = 18 
   
   (add carry): 1 8 4 9.
   
4. So 43 × 43 = 1849.

   See the pattern?

1. For 83 × 83, the last digit is _ _ _ 9.
2. 6 × 8 = 48 (six times the first digit): _ _ 8 9.
3. 8 × 8 = 64 (square the first digit), 64 + 4 = 68 
   
   (add carry): 6 8 8 9.
   
4. So 83 × 83 = 6889.

Squaring numbers made up of nines

1. Choose a a number made up of nines (up to nine digits).
2. The answer will have one less 9 than the number, one 8, 
   
   the same number of zeros as 9's, and a final 1
   

   Example:

1. If the number to be squared is 9999
2. The square of the number has:

one less nine than the number  9 9 9

one 8                                8

the same number of zeros as 9's        0 0 0

a final 1                                    1

3. So 9999 × 9999 = 99980001.

   See the pattern?

1. If the number to be squared is 999999
2. The square of the number has:

one less nine than the number  9 9 9 9 9

one 8                                   8

the same number of zeros as 9's           0 0 0 0 0

a final 1                                           1

3. So 999999 × 999999 = 999998000001.

This is not a very demanding mental math exercise

if you find any problem in this post please reply me.

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MATHSCIRCLE

Magic Numbers (Multiplication Webbing)

Title - Magic Numbers (Multiplication Webbing)
By - Christy Jones
Primary Subject - Math
Secondary Subjects -
Grade Level - 4-5
Objective: Students will apply knowledge of basic multiplication problems to find problems that equal the "magic number."

Materials:
Chalkboard
Scrap paper
Pencil

Procedure:
1. Draw a circle on the board. Draw four lines (about 6 inches) extending from the circle. Draw a rectangle at the end of each extension.

2. Write a number in the circle. This number is the magic number. Example : 6.

3. Ask students to copy the web onto a piece of scrap paper.

4. The students are to think of basic multiplication problems that equal the magic number (6) and fill in the rectangles on their scrap paper. (2x3, 3x2, 6x1, 1x6)

5. Go over the answers as a class.

6. Repeat activity and gradually increase the difficulty level.

Extension:
The teacher may add more rectangles to the web when more possible answers are available. For example: 24.

The teacher may rule out the replication of problems. For example, 2x3 and 3x2 only one of the problems will count in the rectangles.

The activity can be used as a game for speed.

Evaluation:
Did students successfully answer the problems that equal the magic number?

Did students pay attention and copy webs along with class?


This activity also works great with division!!

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