We all have come across the word “product” in a sentence when studying math books. Ever took the time to conceptualize what does product mean in math? This post will answer what is a product in math relentlessly. Remember to have a cup of coffee as you enjoy the read.
All mathematical formulae and procedures are dependent on four operations; addition, subtraction, division, and multiplication. A unique name identifies the result of each process. Just like ‘sum’ is a result of adding two numbers to each other , the product of two numbers is a result of multiplication of the two numbers.
Quick example, what is the product of 4 and 3? 12 is the product of 4 and 3. Thus it simply means that 12 is the result of multiplying 4 and 3. The order in which the two numbers are multiplied does not matter in mathematics as the product will always be 12.
3 x 4 = 12 and, 4 x 3 = 12.
This is called the arithmetic property of commutation and only works exclusively for multiplication operations and selectively for addition operations.
The product of a sum and a multiplier will always be the same as multiplying the individual numbers of the sum and then adding them. i.e. 3 x (3+1) = 12. The product 12 can be achieved by operating (3x3) + (3x1) which is 9 + 3, where you get 12. Also, 3 x (4+1) is the same as 3 x (4) which still gives you 12. This is called the distributive property of products of multiplication.
The associative property of products of multiplication means that when you are multiplying more than two numbers, then you can put brackets around two of the numbers without affecting the product of the multiplication.
E.g. 2 x 3 x 4 = 24 and (2 x 3) x 4 = 24 or 2 x (3 x 4) = 24.
Because we have different kinds of numbers and variables that we use to do arithmetic operations, the products and approach to achieve the product of the multiplication is dependent on the number of variables under consideration.
The most basic products are the products of natural numbers. The product and approach are simple and is expressed by the examples mentioned above when considering the properties of products. This can also be defined as the product of integers.
The product of fractions can be achieved by multiplying the numerators by each other and the denominators by each other. On the occasion where the alternate numerator is divisible by the subsequent denominator, shortcuts can be used to simplify them to reduce the amount of work done of multiplication and division of larger valued numbers.
The product of complex numbers that are mostly found in linear algebra can be gotten by the use of the distribution law or property discussed above. Example; (4a + 2b) x (c + 2a) = (4a x c) + (4a x 2a) + (2b x c) + (2b x 2a) = 4ac + 8a2 + 2bc 4ab
In more advanced level mathematics, you will find more categories of mathematical products like for example Scalar and Vector products, products of quaternions, products of matrices and many others. The use of functional equations achieves all these products based on the properties and basic operations discussed above.
Although one can use a calculator to solve the product of math elements, there is a requirement to have a solid foundation of how to apply the product concept in your math homework. Therefore, its high time you seek for our guidance in finding the best math homework answers.