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Geometry/Applications of Algebra, Exponents, and Direct and Inverse Variation

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Question
Hello sir


Sir in our day to day life, algebra, exponents, and direct and inverse variartion where used sir

In this, sir in algebra we add like terms and subtract like terms and multiply unlike and like terms and divide also. In exponents we write it in raised to form and we convert the following into standard form. And in Direct and inverse variation we do eg 1=2 then 3 how much like this we do. But these are not used inour daily life because in case of algebra i had not seen aplying in daily life, in case of standad form i had not seen applying in our daily life and especially in direct and inverse variation we think that like for eg if cost of 1 pen is equal to rupees 5 then cost of 10 pen is eqaul to how much but we dont do cross multiplicaion of dinominator and numirator with one another. So how they are used in our daily life.
Sir this was my question. I hope now it is clear.

Answer
Hi Apsara,

Thank you for asking this question.
Algebra can be used whenever you have unknowns.  You are saving money to buy a camera that costs $300.  You have $35 saved, and you earn $9.50 per hour.  How many hours do you need to work to be able to afford the camera?  What if you had the option of working two hours or overtime each day, earning you time and a half?  What if you wanted to get a $30 dollar case for the camera as well?  What if the camera were on sale for 15% off, but the case was still at the regular price?  Algebra can be used to solve all of the above.

For exponents, they arise naturally in probability.  What are the chances of flipping a coin three times and never getting heads?  You have a password that you know is three lower case letters, but you have forgotten what they are.  How many possibilities are there?  Is it reasonable to try every single one until you find it?

For direct variation, you actually gave an example in your question!
For inverse variation, suppose you and some friends are buying a birthday cake.  The cost of the cake is fixed, but the amount each person pays decreases as the amount of people increase.

As you can see, there are plenty of examples of these concepts.  It is always good to think about where they may come up.

Thanks for asking,
Azeem

Geometry

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Azeem Hussain

Expertise

I welcome your questions on algebra, 2D and 3D geometry, parabolic functions and conic sections, and any other mathematical queries you may have.

Experience

4 years as a drop-in and by-appointment tutor at Champlain College. Private tutor for dozens of clients over the past 8 years.

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CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry

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Bachelor of Science, Major Mathematics and Major Economics, McGill University, 2014. Diploma of Collegiate Studies; Pure and Applied Science, Champlain College Saint-Lambert, 2010.

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