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Algebraic notation

Algebraic notation

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Explainer Video

Tutor: Meera

Summary

Algebraic notation

In a nutshell

Algebra uses letters called 'variables' to represent unknown quantities. The basic rules for algebraic notation help write terms in a concise way. These terms can then be used in expressions, formulae or equations.


Example 1

The letter 'a' could represent an apple. Two apples could be described by 2a‾\underline{2a}2a​.​



Basic rules

​​Adding equal variables

​Add the numbers and copy the variable. If there is no number with the variable, it means 111. For example, xxx means 1x1x1x


Example

​x+x=2xx+x=2xx+x=2x


Subtracting equal variables

Subtract the numbers and copy the variable.


Example

​7x−5x=2x7x-5x=2x7x−5x=2x


Multiplying same variables

​Multiplying the same variables changes the power. When multiplying, add the powers. If there is no number with the variable, it means 111​​.


Example

​x×x=x2x \times x = x^2x×x=x2


Multiplying different variables

Write the letters without the multiplication sign. Multiplying different variables will not change their powers.


Example

x×y=xyx \times y = xyx×y=xy


Adding/subtracting different variables

These cannot be added or subtracted so they will remain the same.


Example

a+b=a+ba+b=a+ba+b=a+b​​



Formulae

Formulae help find quantities.


Examples 
  • ​F=maF=maF=ma 

Calculate the force (FFF​) on an object from its mass (mmm​) and acceleration (aaa​).


  • ​P=2(l+w)P = 2(l+w)P=2(l+w) 

Calculate the perimeter (PPP​) of a rectangle from its length (lll​) and width (www​).


  • ​A=12bhA=\frac{1}{2} bhA=21​bh 

Calculate the area (AAA​) of a triangle from its base (bbb​) and its height (hhh​).​



Equations

An equation is formed when two expressions equal each other.

 

Examples
​x2=5\frac x 2 =5 2x​=5​​
​2x−3=72x-3=72x−3=7​​
​x2−2x−8=0x^2 -2x-8=0x2−2x−8=0​​
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FAQs - Frequently Asked Questions

What is algebraic notation?

Algebraic notation involves writing algebraic terms, with a combination of numbers and letters. These terms can then be used further in expressions and equations.

What are variables?

Variables are a short hand way to name a quantity. The letter variable can then be used in an expression.

What is algebra?

Algebra uses letters called variables to represent unknown quantities.

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