Mental Maths

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As a child I hated math. It was a subject that I struggled with on a daily basis. Whilst in high school I stumbled across a method for easily multiplying numbers. This method is perfect for those who have difficulty with their times tables. By using this method your average primary school student can master their six through to twelve times tables within a matter of minutes.

MULTIPLYING TWO SINGLE DIGITS

This method simplifies calculations by the use of a reference number. To multiply two single digits we use 10 as a reference number. I will use the sum 8 X 9 to demonstrate the method. All three steps in this method can easily be performed mentally. However, when your child is first learning to apply the method they may initially prefer to use a pen and paper.

Step 1

We first mentally subtract the two digits in the sum from our reference number. That is 10 – 8 =2 and 10 – 9 =1. The numbers derived from this subtraction will be written below the original sum like so:

8 X 9

2    1

Step 2

We then subtract diagonally. Either subtract 2 from 9 or 1 from 8. The answer is 7. This is the first digit in the answer.

Step 3

We then multiply the two lower numbers. 2 X 1 = 2. This is the second digit in the answer. So the answer to 8 X 9 is 72.

To give another example we will use the sum 6 X 7. This particular example gives a result at step 2 that needs to be modified in step 3. This modification is common sense so should not prove problematic.

Step 1

6 X 7

4    3

Step 2

Subtract 3 from 6 or 4 from 7. The answer is 3 (This will need to be modified in the next step).

Step 3

4 X 3 = 12

The answer to 6 X 7 is not 312 (3 from step 2 + 12 from step 3) but rather 30 + 12 which is 42.

MULTIPLYING NUMBERS GREATER THAN 10

It is also possible to multiply numbers greater than ten whilst still using 10 as a reference number. The method is similar to that used above but with a few minor differences. Because the numbers that we are multiplying are greater than the reference number we will add rather than subtract diagonally as we did in step 2 in the previous examples. To demonstrate this we will multiply 11 X 12.

Step 1

We first mentally calculate the difference between each of the two numbers in the sum and the reference number. The numbers derived from this will be written above the original sum like so:

1       2

11 X 12

Step 2

We then add diagonally. Either add 11 + 2 or 12 + 1. The answer is 13. We then multiply this by the reference number (10). This gives us 130. This is the first part of the sums answer.

Step 3

We then multiply the two upper numbers. 1 X 2 =2. This is the final digit in the sums answer. We then add the result of step 2 (130) to step 3 (2) to give us the answer to our problem. So the answer to 11 X 12 is 132.

MULTIPLYING WHERE ONE NUMBER IS GREATER THAN AND ONE NUMBER LESS THAN THE REFERENCE NUMBER

The following example will demonstrate the method for multiplying numbers where one number is greater than and the other is less than the reference number. To demonstrate we will calculate the following sum 9 X 12.

Step 1

Since 9 is 1 less than 10 we put 1 underneath the 9. 12 is 2 more than 10 so we put 2 above the 12. Our calculation currently looks like this:

       2

9 X 12

1

Step 2

We can now either add 2 to 9 or subtract 1 from 12. The answer is 11. This should be multiplied by the reference number to give an answer of 110.

Step 3

We next multiply -1 X 2 = -2. The result of this calculation is negative because a positive number multiplied by a negative number gives a negative number as the answer. Where we have a negative number we must subtract this from the number we calculated at step 2 (110). So 110 – 2 =108. This allows us to see that the answer to the calculation 9 X 12 is 108

EXTENDING THE SYSTEM

This system can be extended to handle any multiplication calculation. It is possible to use numbers other than 10 as a reference number. It is also possible to use several different reference numbers within the one problem. With a minimal amount of practice anyone can use these methods to quickly perform mental calculations. Parents who teach these methods can ensure that their children have the best start in maths. Children who use this system rapidly become confident in their ability to perform multiplication. Nobody need fear maths when they have the ability to quickly calculate the answers to sums. The sky truly is the limit for those who use these multiplication methods.

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