What Is An Identity?
Chapter Name : Algebraic Expressions And Identities |
Sub Topic Code : 104_08_09_10_01 |
Topic Name : What Is An Identity? |
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Sub Topic Name : What Is An Identity? |
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Introduction
When an equality sign exists between two algebraic expressions, it turns out to be true for certain values of the variables.
Pre-Requisites:
Algebraic Expressions, Terms, coefficients, variables, substitution
Activity:
If you know that 1 pencil & 2 erasers cost Rs. 10, you can calculate the individual costs of pencil & eraser. However, this equation becomes an identity only if the cost of pencil = cost of eraser
Real Life Question:
If 2 kgs of groundnut & 3 kgs of sugar purchased is equal to 1 litre of oil & 1 litre of milk purchased, what is the cost of each of the items?
Key Words / FlashCards
| Key Words | Definitions (pref. in our own words) |
|---|---|
| Identity | If an equation is true for all the values of the variables in the algebraic expressions on either side & renders them equal |
Learning aids / Gadgets
| Gadgets | How it can be used |
|---|---|
| Balance, potatoes, onions | Take a weighing balance. Place some onions on one pan & potatoes on the other. For them to be equally balanced is it necessary that there should be equal number of potatoes & onions? Is that an identity then? |
Real life uses :
In manufacturing small machinery parts of a portion of a very big machine, you may need to use the nuts & bolts of same diameter everywhere for convenience as well as proper functioning at times. This is when identity comes into picture
Places to visit :
Grocery store, Games shop, Super Markets, etc.
Practical examples around us
| Examples | Explainations |
|---|---|
| Vehicle | While travelling in a car, if you need to calculate how much money you need to save on fuel (depending on cost of the fuel & mileage of your car), you will need an algebraic expression. For solving it, you need to get a value such that your expression becomes an identity |
What you learn in Theory:
An equation is true for only certain values of the variable in it. It is not true for all the values of the variable in it. But, an identity is true for all values
What you learn in Practice:
Identities are very often used in simplifying algebraic expressions of complex engineering problems