Mental Multiplication Strategies - Orchids The International School
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Mental Maths

Mental Multiplication Strategies

Mental Math refers to a group of skills that allow students to do arithmetical calculations mentally without the use of calculators or other resources. It helps students to understand the basic and higher-level math concepts in a better way.

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Let us learn some of the multiplication tricks:

Let us consider two numbers as a b c d and e f g h.
Now, a b c d × e f g h

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Step 1:(d × h)

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Step 2:[ (c × h) + (d × g)] + add number if any carry over from previous step.

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Step 3: [(b × h) + (c × g) + (d × f)] + add number if any carry over from previous step.

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Step 4: [ (a × h) + (b × g) + (c × f) + (d × e)] + add number if any carry over from previous step.

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Step 5: [ (a × g) + (b × f) + (c × e)] + add number if any carry over from previous step.

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Step 6: [(a × f) + (b × e)] + add number if any carry over from previous step.

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Step 7:(a × e) + add a number if any carry over from the previous step.

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Example:
Find the product: 4532 × 3251

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Step 1: 2 × 1 = 2. Take 2 for an answer (Ans: 2)

Step 2: [ (3 × 1) + (2 × 5)] = 3 + 10 = 13
Take 3 for an answer and 1 to be carried over to the next step. (Ans: 32)

Step 3: [ (5 × 1) + (3 × 5) + (2 × 2)] + 1 = 5 + 15 + 4 + 1 = 25
Take 5 for an answer and 2 to be carried over to the next step. (Ans: 532)

Step 4: [(4 × 1) + (5 × 5) + (3 × 2) + (2 × 3)] + 2 = 4 + 25 + 6 + 6 + 2 = 43
Take 3 for an answer and 4 to be carried over to the next step. (Ans: 3532)

Step 5:[ (4 × 5) + (3 × 3) + (5 × 2)] + 4 = 20 + 9 + 10 + 4 = 43
Take 3 for an answer and 4 to be carried over to the next step. (Ans: 33,532)

Step 6:[ (4 × 2) + (5 × 3)] + 4 = 8 + 15 + 4 = 27
Take 7 for an answer and 2 to be carried over to the next step. (Ans: 7,33,532)

Step 7:(4 × 3) + 2 =12 + 2 = 14
Therefore, the final answer is 1,47,33,532.

Multiplication of a number by a given number which contains all the digits a 9

Step 1:Split the number which contains all the digits as 9 in the form of (multiple of 10 – 1).

Step 2: Now, we multiply (multiple of 10 – 1) by the other given number.

Step 3: Now, we simplify the arithmetic operations.

Example 1:

Multiply 230 by 9999.

Solution:

Step 1:9999 can be written as (1,00,000 – 1).
Hence, the given problem can be written as
230 × (1,00,000 – 1)

Step 2: Now,
230 × (1,00,000 – 1)
= (230 × 1,00,000) – (230 ×1)

Step 3: (230 × 1,00,000) – (230 ×1)
=23,000,000 – 230
=22,999,770
Therefore, the product of 230 and 9999 is 22,999,770.

Example 2:

Multiply 1352 by 99,999

Solution:

Step 1: 99,999 can be written as (1,000,000 – 1).
Hence, the given problem can be written as
1352 × (1,000,000 – 1)

Step 2: Now,
1352 × (1,000,000 – 1)
= (1352 × 1,000,000) – (1352 × 1)

Step 3: (1352 × 1,000,000) – (1352 ×1)
=1352,000,000 – 1352
=1,351,998,648
Therefore, the product of 1352 and 99,999 is 1,351,998,648.

Multiplication trick when a number is multiplied by 11

Rule: Add the digits to the digits on the right side.

Example 1:

Multiply 2541 by 11

Solution:

2541 × 11
(0+2) (2+5) (5+4) (4+1) (1+0)
2       7     9     5     1
2541 × 11 = 27951

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Another method:

We can also do the multiplication by splitting 11 as (10 + 1)
Thus, 2541 × 11
= 2541 × (10 + 1)
= (2541 × 10) + (2541 × 1)
= 25,410 + 2541
=27,951
The answer in both methods is the same.

Multiplication trick when a number is multiplied by 12

Rule: Starting the rightmost digit, then double each digit and add the digit on the right.

If the answer is greater than a single digit, simply carry over the extra digit to the next step. The remaining digit is ones digit of the final result.

Example:

Multiply 3453 by 12

Solution:

3453 × 12
Let us write the number 3453 as 03453
Rightmost digit 3 has no digit in the right
3 × 2 = 6
Next digit 5 has 3 in the right
5 × 2 + 3 = 10 + 3 = 1 3 (we take 3 and carry 1 in the nest step).
Next digit 4 has 5 in the right
4 × 2 + 5 + 1 = 8 + 5 + 1 = 1 4(we take 4 and carry 1 in the nest step).
Next digit 3 has 4 in the right
3 × 2 + 4 + 1 = 6 + 4 + 1 = 1 1 (we take 1 and carry 1 in the nest step).
Next digit 0 has 3 in the right
0 × 2 + 3 + 1 = 0 + 3 + 1 =4

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So, the answer is 41,436.

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