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University of Johannesburg
University of Johannesburg

This document provides an introduction to algebra, covering what algebra is, the four basic operations used in algebra (addition, subtraction, multiplication, division), and how to solve linear equations. Algebra uses variables represented by letters and the four basic operations to find unknown values. It explains how to apply each operation to variables through examples. The document concludes by defining a linear equation as one where the highest exponent is 1, and demonstrates how to isolate the variable and solve a simple linear equation of 3x + 2 = 5 by transposing and dividing terms.

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Introduction to Algebra M Halomi
Things to be covered 1. What is algebra? 2. How to use the 4 basic operations in algebra. 3. Solving linear equations in Algebra.
What is Algebra? • Algebra is the art of using the 4 basic operations, equations and expressions to find the unknown. The unknown is called a variable because it can be any number (it varies). The variables used are in the form of alphabets (a-z).
How to use the 4 basic operations • We have 4 basic operations in Mathematics, addition (+), subtraction (-), multiplication (x) and division (./.). How do we use them in algebra? Let us start with addition: let the variable be a • a+a= 2a (we are adding to variable here, a and a or the question says if I have a single a and add it to another a, how many as to I have… 2a) • x+2x=3x (The question says if I have a single x and add 2xs then how many xs do I have?... 3x)
Sutraction a-a=0 (The question here says if I have a single a and then subtract an a, how many as do I have?... 0) 2m-m=m (The question here says if I have 2ms and then subtract 1 m from them, how many ms do I have?... 1m)
Multiplication • axa=a^2 (This question says that what are you going to get if you multiply a variable by itself? That means a is multiplying itself 2 times) • axb=? We will cover this one later…
Division • a/b=a/b (This means that if a is divided by b then the answer is a/b as they cannot cancel each other, look at it like this, if a=3 and b=5,3/5 remains 3/5 as they will not cancel each other.) • a/a=1 how? (This means that if you divide a variable by itself, you get 1 same as dividing a number by itself.)
Solving linear questions • What are linear equations? What is even an equation? An equation is a mathematical statement that states two or more variables are equal to each (there is an equal sign between them). 3x+2=5 (Here is an example of an equation and here it states that what is on the left side of the equation sign (3x+2) is equal to what is on the right side of the equal sign (5). What is a linear equation? That is an equation where the highest exponent of a variable must be 1. We can talk about 3x+2=5 again, the only variable in this equation is x and its exponent is 1 meaning that it is a linear equation. • With that being said, how do we solve these equations?
Solving linear equations • The question is if we have 3x+2=5 then what is x equal to? • 3x+2=5 (We have like terms 2 and 5 so we can transpose 2 to the other side of the equation) • 3x=5-2 • 3x=3 (We want to remove 3 because we are not looking for 3x but x so we are going to divide by 3 both sides (The statement says that 3x=3 meaning that what we do on left we must also do on the right to keep the two sides equal) • x=1 (And it makes because if you put x in the place of x, multiply it by 3 and 2, you will get 5 that is on the right side of the equation).
This is the end! Thank you!

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slideshare.pptx

  • 2. Things to be covered 1. What is algebra? 2. How to use the 4 basic operations in algebra. 3. Solving linear equations in Algebra.
  • 3. What is Algebra? • Algebra is the art of using the 4 basic operations, equations and expressions to find the unknown. The unknown is called a variable because it can be any number (it varies). The variables used are in the form of alphabets (a-z).
  • 4. How to use the 4 basic operations • We have 4 basic operations in Mathematics, addition (+), subtraction (-), multiplication (x) and division (./.). How do we use them in algebra? Let us start with addition: let the variable be a • a+a= 2a (we are adding to variable here, a and a or the question says if I have a single a and add it to another a, how many as to I have… 2a) • x+2x=3x (The question says if I have a single x and add 2xs then how many xs do I have?... 3x)
  • 5. Sutraction a-a=0 (The question here says if I have a single a and then subtract an a, how many as do I have?... 0) 2m-m=m (The question here says if I have 2ms and then subtract 1 m from them, how many ms do I have?... 1m)
  • 6. Multiplication • axa=a^2 (This question says that what are you going to get if you multiply a variable by itself? That means a is multiplying itself 2 times) • axb=? We will cover this one later…
  • 7. Division • a/b=a/b (This means that if a is divided by b then the answer is a/b as they cannot cancel each other, look at it like this, if a=3 and b=5,3/5 remains 3/5 as they will not cancel each other.) • a/a=1 how? (This means that if you divide a variable by itself, you get 1 same as dividing a number by itself.)
  • 8. Solving linear questions • What are linear equations? What is even an equation? An equation is a mathematical statement that states two or more variables are equal to each (there is an equal sign between them). 3x+2=5 (Here is an example of an equation and here it states that what is on the left side of the equation sign (3x+2) is equal to what is on the right side of the equal sign (5). What is a linear equation? That is an equation where the highest exponent of a variable must be 1. We can talk about 3x+2=5 again, the only variable in this equation is x and its exponent is 1 meaning that it is a linear equation. • With that being said, how do we solve these equations?
  • 9. Solving linear equations • The question is if we have 3x+2=5 then what is x equal to? • 3x+2=5 (We have like terms 2 and 5 so we can transpose 2 to the other side of the equation) • 3x=5-2 • 3x=3 (We want to remove 3 because we are not looking for 3x but x so we are going to divide by 3 both sides (The statement says that 3x=3 meaning that what we do on left we must also do on the right to keep the two sides equal) • x=1 (And it makes because if you put x in the place of x, multiply it by 3 and 2, you will get 5 that is on the right side of the equation).
  • 10. This is the end! Thank you!