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# Multiplication

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Last updated date: 12th Jul 2024
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## Multiplication Definition

Multiplication in mathematics, which is denoted by the sign ‘x’, is a method of finding the product of two or more values. Multiplication of two numbers represents the repetitive addition of one number concerning another in arithmetic. So, if r is multiplied by s, then it means that either r is added to itself ‘s’ number of times or vice versa. For example, 5 x 3 refers to 5 times of 3, like:

5 + 5 + 5 = 15

In this example, we can see how to multiply two whole numbers. In the same way, we can also multiply fractions and find the product of decimals. Multiplication is one of the main basic concepts in Maths, aside from addition, subtraction, and division.

### What is Multiplication?

The basic explanation of multiplication in mathematics is adding a number concerning another number multiple times. So, multiplication meaning can be described as following:

It is a mathematical process that is an abbreviated method of adding an integer to zero a specified number of times and that is widened to other numbers according to rules that are valid for integers. Such as, if we are multiplying 2 by 4 that means 4 is added to itself two times or 4 + 4 = 8.

Multiplication of single-digit numbers is a simple task. Multiplying two or more numerical digits can be complicated so there are some tricks that you can follow.

### Rules of Multiplication

• The multiplication of two integers is an integer.

• Any number multiplied by 0 is 0.

• Any number, if multiplied by 1, results in that number itself.

• If an integer is multiplied by multiples of 10, then the same number of 0s are added at the end of the original number. Example: 7 × 100 = 700

• The sequence of the numbers, don't matter, when multiplied together. Example: 4 × 5 × 6 × 7 = 7 × 6 × 5 × 4 = 5 × 4 × 6 × 7 = 840

### Properties of Multiplication

• The commutative property of multiplication states that changing the order of factors has no effect on the product.

• The associative feature of multiplication states that changing the grouping of elements has no effect on the product.

• The product of 1 and any number is that number, according to the identity property of multiplication.

• This property states that any number multiplied by zero equals zero, such as A x 0 = 0.

### Multiplication Solved Examples

Example 1: If Rohan has 6 baskets and each has 7 apples. Then find the full number of apples Rohan has.

Solution: Number of baskets Rohan has: 6

Number of apples each basket has: 7

Total number of apples = (Number of the basket) x (Number of apples in each basket)

= 6 x 7 = 42

So, Rohan has 42 apples.

Example 2: Find the product of 85 and 10.

Solution: The product of 85 and 10 = 85 x 10 = 850.

Example 3: What is the result if one positive and one negative integer is multiplied?

Solution: When one positive integer and one negative integer is multiplied or vice versa, then the result is negative.

Example 4: What happens in the case of the multiplication of fractions?

Solution: When two or more fractions are multiplied then the numerators and denominators are multiplied together, such that:

(a/b) × (c/d) = (a×c)/(b×d)

Example 1: Multiply ¾ and 5/2.

(3/4) × (5/2)

= (3x5)/(2×2)

= 15/8

## Conclusion

Although many of these techniques of teaching multiplication are now obsolete, the value of knowing these mathematical fundamentals remains as crucial today as it has always been.

Multiplication is a fundamental technique in many areas of mathematics, including algebra, calculus, equations, and more. It assists children in being acquainted with and confident in the teachings offered to them as they go through education. By studying multiplication and remembering the times tables, you are providing yourself with the necessary building blocks to progress to higher-level arithmetic such as division, fractions, and even algebra.

## FAQs on Multiplication

1. What Does Multiply Mean?

In mathematics to multiply refers to adding equal groups. When we multiply, the number of items in a group enlarges. Both the two factors and the product or result are members of a multiplication problem.

Example:

In the multiplication problem, 7 multiplied by 5, the numbers 7 and 5 are the factors, while the solution is number 35 and it is the product. Hence 7 x 5 = 35.

Here, we have provided the multiplication definition with examples for a better understanding of the concept of multiplication. We are also adding a multiplication definition for 3rd grade along with the properties of multiplication for their better understanding.

2. What are the Properties of Multiplication?

These are the multiplication properties:

• Distributive Property: According to this property if A, B and C are any three integers, then: A x (B + C) = (A x B) + (A x C)

• Commutative Property: According to this property if A and B are any two integers, then: A x B = B x A

• Zero Property: According to this property any number multiplied by zero is equal to 0 such as A x 0 = 0.

• Associative Property: According to this property if A, B and C are any three integers, then: A x (B x C) = (A x B) x C

• Identity Property: According to the property, if we multiply any integer by 1, then its value doesn’t change like, A x 1 = A

3. What is the importance of multiplication in the early years?

Children develop their understanding of simple addition and subtraction in the early years by learning elementary multiplication and division. The ability to answer simple multiplication problems and employ multiplicative thinking is beneficial to children in everyday situations.