**Mental Maths**

**Mental Multiplication Strategies**

Mental MathÂ refers to a group of skills that allow students to do arithmeticalÂ 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.

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 Ă— e f g h

Step 1:(d Ă— h)

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

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

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

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

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

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

Example:

Find the product: 4532 Ă— 3251

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

Step 2: [ (3 Ă— 1) + (2 Ă— 5)] = 3 + 10 = 13

Take 3 for an answer and 1 to be carried over to the next step. (Ans: 32)

Step 3: [ (5 Ă— 1) + (3 Ă— 5) + (2 Ă— 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 Ă— 1) + (5 Ă— 5) + (3 Ă— 2) + (2 Ă— 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 Ă— 5) + (3 Ă— 3) + (5 Ă— 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 Ă— 2) + (5 Ă— 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 Ă— 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 â€“ 1).

Step 2: Now, we multiply (multiple of 10 â€“ 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 â€“ 1).

Hence, the given problem can be written as

230 Ă— (1,00,000 â€“ 1)

Step 2: Now,

230 Ă— (1,00,000 â€“ 1)

= (230 Ă— 1,00,000) â€“ (230 Ă—1)

Step 3: (230 Ă— 1,00,000) â€“ (230 Ă—1)

=23,000,000 â€“ 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 â€“ 1).

Hence, the given problem can be written as

1352 Ă— (1,000,000 â€“ 1)

Step 2: Now,

1352 Ă— (1,000,000 â€“ 1)

= (1352 Ă— 1,000,000) â€“ (1352 Ă— 1)

Step 3: (1352 Ă— 1,000,000) â€“ (1352 Ă—1)

=1352,000,000 â€“ 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 Ă— 11

(0+2) (2+5) (5+4) (4+1) (1+0)

2 7 9 5 1

2541 Ă— 11 = 27951

Another method:

We can also do the multiplication by splitting 11 as (10 + 1)

Thus, 2541 Ă— 11

= 2541 Ă— (10 + 1)

= (2541 Ă— 10) + (2541 Ă— 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 Ă— 12

Let us write the number 3453 as 03453

Rightmost digit 3 has no digit in the right

3 Ă— 2 = 6

Next digit 5 has 3 in the right

5 Ă— 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 Ă— 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 Ă— 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 Ă— 2 + 3 + 1 = 0 + 3 + 1 =4

So, the answer is 41,436.