## Multiply By 11

This technique teaches you how to multiply any number by 11, easily and quickly. we will take a few examples and from these you will see the pattern used and also how easy they are to do.

So, to begin let’s try 12 times 11.

First things first you will ignore the 11 for the moment and concentrate on 12.

Split the twelve apart,like so:

# 1<–>2

Add these two digits together 1+2 = 3

# 1+2 =3

Place the answer, 3 in between 12 to give 132

**11*12 = 132**

Let’s try another:

**48*11**

again, leave the 11 alone for a moment and work with 48

**4+8 = 12**

So now we have to put the 12 in between the 4 and 8 but **don’t **do this:

4128 as that is **wrong…**

First, do this; Place the 2 from the twelve in between the 4 and 8 giving 428.

Now we need to input the 1 from the twelve into our answer also, and to do this just add the one from 12 to the 4 of 428 giving 528!

## Multiply By 12

Here is a trick to multiply any** 2 digit number** by 12 which is far better than regular method so have a look at it.

So how does the 12’s shortcut work? Let’s take a look.

**12 X 7**

the first thing is to always multiply the 1 of the twelve by the number we are multiplying by, in this case 7. So 1 X 7 = 7.

Multiply this 7 by 10 giving 70. (Why? We are working with BASES here. **Bases are the fundamentals to easy calculations for all multiplication tables.**)

*Now multiply the 7 by the 2 of twelve giving 14.*

* Add this to 70 giving 84. *

*Therefore 7 X 12 = 84*

**Let’s try another: 17 X 12**

Remember, multiply the 17 by the 1 in 12 and multiply by 10 (**Just add a zero to the end**):

*1 X 17 = 17, multiplied by 10 giving 170.*

*Multiply 17 by 2 giving 34.*

*Add 34 to 170 giving 204.*

*So 17 X 12 = 204*

**lets go one more 24 X 12**

*Multiply 24 X 1 = 24. Multiply by 10 giving 240.*

*Multiply 24 by 2 = 48. Add to 240 giving us 288*

*24 X 12 = 288 *(these are Seriously Simple Sums to do aren’t they?!)

## Multiplication of two numbers that differ by 2

**This trick only works if you have memorised or can quickly calculate the squares of numbers. When two numbers differ by 2, their product is always the square of the number in between these numbers minus 1.**

Let me explain these rule with the help of some examples.

Example 1. Suppose we have to multiply 14 and 16

Solution :- For that just take the square of smaller number and substract one from it. Like This

14 * 16 = (14+1)^{2} – 1 = 225-1 = 224

Example 2. Suppose we have to multiply 28 and 30

Solution :- Similar as above

28 * 30 = (28+1)^{2} – 1 = 841-1 = 840

**Same Base Method**

**When both the numbers are more than the same base.**

**Example 1:** 12 × 14

**Step 1:** Here base is 10

12 + 2 [12 is 2 more than 10 also called surplus]

14 + 4 [14 is 4 more than 10 also called surplus]

**Step 2:** Cross add: 12 + 4 =16 or 14 + 2 = 16,(both same) which gives first part of answer = 16

**Step 3:** Vertical multiplication: 2 × 4 = 8

So, 12 + 2

14 +4

16 / 8So, 12 × 14 = 168(14 + 2 = 12 + 4)

**Example 2: **105x 107

**Step1:** Here base is 100

105 + 05 [105 is 5 more than 100 or 5 is surplus]

107 + 07 [107 is 7 more than 100 or 7 is surplus]

Base here is 100 so we will write 05 in place of 5 and 07 in place of 7

**Step 2:** Cross add: 105 + 7 = 112 or 107 + 5 = 112 which gives first part of the answer = 112

**Step 3:** Vertical multiplication: 05 × 07 = 35 (two digits are allowed)

As the base in this problem is 100 so two digits are allowed in the second part.

So, 105 × 107 = 11235

**Both numbers less than the same base**

**Example1:** 99 × 98

**Step 1:** Check the base: Here base is 100 so we are allowed to have two digits on the right hand side.

99 – 01 (1 less than 100 ) i.e. 01 deficiency

98 – 02 (2 less than 100) i.e. 0 2 deficiency

**Step 2:** Cross – subtract: 99 – 02 = 97 = 98 – 01 both same so first part of answer is 97

**Step 3:** Multiply vertically – 01 × – 02 = 02 (As base is 100 so two digits are allowed in second part

So, 99 × 98 = 9702

**Example 2 :** 89 × 88

**Step 1:** Here base is 100

So, 89 – 11 (i.e. deficiency = 11)

88 – 12 (i.e. deficiency = 12)

**Step 2**: Cross subtract: 89 – 12 = 77 = 88 – 11(both same)

So, first part of answer can be 77

**Step 3: **Multiply vertically – 11 × – 12

Again to multiply 11 × 12 apply same rule

11 + 1 (10 + 1)

12 + 2 (10 + 2)

11 + 2 = 13 = 12 + 1 / 1 × 2 = 12 so, 11 × 12 = (1) 32 as only two digits are allowed on right hand

side so add 1 to L.H.S.

So, L.H.S. = 77 + 1 = 78

Hence 89 × 88 = 7832

**These are very simple tricks as compared to regular method of multiplying each numbers hence a little practice of this trick will save our time in competitive exams. If you find any difficulty regarding any of these tricks please let us know in the comment box below.**

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