How to Multiplication of Three Digit Numbers Higher then the Base

Multiplication is a fundamental arithmetic operation that involves combining or repeating a certain number, known as the multiplicand, a specific number of times, represented by another number called the multiplier. It is a way of adding a number to itself repeatedly.

In multiplication, the multiplicand and the multiplier are multiplied together to produce the product. The product represents the total value obtained by combining or repeating the multiplicand by the multiplier.

For example, consider the multiplication 3 × 4. Here, 3 is the multiplicand, 4 is the multiplier, and the product is 12. This means that when you multiply 3 by 4, you are essentially adding 3 to itself four times, resulting in a total of 12.

Multiplication can be performed with various numerical values, including whole numbers, decimals, fractions, and even negative numbers. It follows certain properties such as the commutative property (changing the order of the numbers doesn’t affect the result), the associative property (changing the grouping of the numbers doesn’t affect the result), and the distributive property (distributing a factor over a sum or difference).

In practical terms, multiplication is widely used in everyday life for tasks such as calculating areas, finding total quantities or prices, scaling objects, and solving various mathematical problems across different fields of study.

In the previous chapters, we multiply Two digit numbers which were higher then the base.

Now let us learn the technique where the Three digit numbers are higher then the base.

( Using a base of 100 ) . ( Both numbers are higher than the base). Now you will learn how to calculate the numbers above 100.

Example – 1 : Multiply 107 by 112

STEP – 1: Take the nearest power of 100 to these numbers. Powers of 100 are 100,1000,10000,100000….. Thus nearest power of 100 to the numbers 107 and 112 is 100. So we take 100 as our base.

STEP – 2: Write the numbers one below the other. 

STEP -3 : Subtract 100 from each of them.

STEP -4: Write down the answer obtained as difference on the right side with a (+) sign to show that the numbers are above 100.

STEP -5 : The product will have two parts, one on the left side and the other on the right hand side. Draw a slant (slash) (/) to demarcate the two parts.

Multiply the difference. The product is the Right Hand Side part of the answer.

STEP – 6: The Left Hand Side of the answer can be obtained by cross add, i.e. the number and the difference so we have.

ANSWER : 11984 

Example – 2: Multiplication 162 by 103

ANSWER :16686

Example – 3: Multiplication 106 by 131

ANSWER :13886

By now, you should know why we added 1 to the left hand side of the number.

Example -4: Multiplication 102 by 103

ANSWER :10506

In conclusion, multiplication is a fundamental arithmetic operation used to combine or repeat a number, known as the multiplicand, a certain number of times, represented by another number called the multiplier. It is a way of adding a number to itself repeatedly.

By multiplying the multiplicand and the multiplier together, the product is obtained. The product represents the total value obtained by combining or repeating the multiplicand by the multiplier.

Multiplication can be performed with various numerical values, including whole numbers, decimals, fractions, and negative numbers. It follows properties such as the commutative property, associative property, and distributive property.

Multiplication is a crucial operation in mathematics and is used in a wide range of applications in everyday life. It is employed for tasks such as calculating areas, determining total quantities or prices, scaling objects, and solving various mathematical problems across different fields of study.

Overall, understanding multiplication is essential for basic arithmetic calculations and serves as a foundation for more advanced mathematical concepts and operations.