It Is  No Puzzle

Multiplication is one mathematical operation that can appear daunting and can sometimes make you feel annoyed. such a situation arrives when you sometimes get wrong answers repeatedly .   

 Lets begin the chapter with a puzzle. Multiplication

                 Three friends were returning from college when -they saw speeding car hitting a cyclist while he was crossing the road.

The car didn’t stop after hitting the cyclist and drove away leaving the man yelling on the road.

                           They shouted, desperate for help, but no passerby responded.

In the meantime, they noticed the registration number of the car and tried to remember it in their own way.

They rushed the person to the nearby hospital.

                   The doctor called the police as this was a road accident and case was registered. In order to do a proper investigation,

the police started questioning the three friends and asked them if they could provide the registration number of the car so that the driver who had hit the person could be caught.

         All three friends tried a lot to remember the car number but failed.

Thus they decided to zero in upon the number of the car as they had remembered it with some mathematical properties behind it.

             first student : Sir, the first two digits of the car number were the same.

      Second student: Sir, the two digits of the car number were same.

 Third student: the four digits made for square number. can you guess  the car number to help the police nab the guilty.

Solution :- The car registration number is a four digit number with the first two digits same and also the last two  digits same. the first two digits are a and last two digits b, then

Multiplication

Number = 1000a+100a+10b+b

                          =1100a+11b

                             =11(100a+b)

The clearly shows that the four digit number is divisible by 11.the policeman was lover of mathematics

so he finally cracked the problem and knew the registration number of the car and later caught the driver.

                Since it is a perfect square number, it will also be divisible by 11²=121

Reminder:

• A number is a not a perfect square if it ends with 2,3,7,or 8.
• A perfect square will end with 0,1,4,5,6,and 9.                                                                                                                               Hence b= 0,1,4,5,6 and 9.This implies a=11,10,7,6,5 or 2                                                                                                            Since a = 11 or 10 ruled out, we will have a = 7,6,5 or 2       

Out of the 4 options, We have 7744- a perfect square .

Hence, car registration number was 7744= (88)² Now let’s begin with number 11.                                                                                                 Most of the times, while solving mensuration problems, you must have used the value of π as 22/7 and multiplication  that with 22.

Let’s explore it with an easier method. You can write  22=2×11 Multiplication. Learning this technique will surely help in mensuration as well.

Rule :-

• Place the number to be multiplied by 11 in bracket and put zeros on either side.
• Start  adding the two numbers one at a time from right to left. If the sum of two numbers in any case exceeds 10, the digit at the tenth place shall be carried over the next sum as is usually done in simple addition.                                                        Multiplication16 by11.

Solution :- Place the number in bracket and put zeros on either side.

0 ( 4 ←8 ←7← 6 ←2 ←5 ←4 ) 0 

Add the digits from the right to the left as shown above Multiplication.

= 0+4|4+8|8+7|7+6|6+2|2+5|5+4|4+0|

= 4 |12| 15 | 13 | 8 | 7 | 9 | 4 |

= 4 | 12 | 16 | 3 | 8 | 7 | 9 | 4

= 4 | 13 | 6 | 3 | 8 | 7 | 9 | 4

= 53638794   

Hence 4876254×11=53638794

Sure! Multiplication is one of the basic arithmetic operations in mathematics. It involves combining two or more numbers to find their total product. The result of a multiplication operation is called the “product.”

The multiplication operation is denoted by the “×” symbol or by placing numbers next to each other without any operator symbol. For example:

1. Using the “×” symbol: 2 × 3 = 6
2. Using numbers next to each other: 2 * 3 = 6

In the above examples, we are multiplying 2 and 3 together, which results in the product 6.

Multiplication is a repeated addition process. For instance, when multiplying 2 by 3, you are essentially adding 2 to itself three times:

2 + 2 + 2 = 6

Here are some more examples of multiplication:

3 × 4 = 12 5 × 7 = 35 10 × 2 = 20

Multiplication is also commutative, which means the order of the numbers does not affect the result:

2 × 3 = 6 3 × 2 = 6

Multiplication is a fundamental operation in various mathematical concepts, including algebra, geometry, and calculus, and it has many practical applications in everyday life, such as calculating areas, volumes, and solving real-world problems.