Mathematics

Algebra - Explanation and Worked Examples on Algebra

len Alfred Ajibola - Thu, 24th January, 2019 @ 19:11

Topics in Mathematics

Conversion of Number Bases explained with examples Angles: Types and Categories of Angles Lines and Types in Mathematics Number Base System - Table showing the Number Bases with explanations Mathematics Scheme of Work, SS1, 3rd Term Mathematics Scheme of Work, SS1, 2nd Term Mathematics Scheme of Work, SS1, 1st Term Trigonometry - Sine, Cosine and Tangent explained with worked examples Quadratic Equation - Factorization of Quadratic Equation Algebra - Explanation and Worked Examples on Algebra


Academic Questions in Mathematics

Please check out our Test Your Knowledge page to see all Questions and Answers

Slanted or tilted lines that will finally meet at some point but NOT at a right angle are referred to as _____.

  • A. oblique
  • B. curved
  • C. vertical
  • D. perpendicular
  • E. parallel
  • F. horizontal

The two sides that forms an angle are referred to as the _____.

  • A. arms
  • B. vertexes
  • C. bays
  • D. zones
  • E. limbs
  • F. dune

The point where the two sides of an angle meet is termed the _____.

  • A. arms
  • B. vertex
  • C. bays
  • D. zones
  • E. limbs 
  • F. dune

How many digits are there in -223.00

  • A. 1
  • B. 2
  • C. 3
  • D. 4
  • E. 5
  • F. 6

30% of 2 is equal to _____.

  • A. 30
  • B. 0.6
  • C. 75
  • D. 0.25
  • E. 0.3
  • F. 60

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Meaning of Algebra:

Consider this simple statement:

I am a number. When you subtract 3 from me, the result is 9. what number am I ?

Of course we know the answer is 12. You probably guessed it from your mind because it was that simple. The truth is, We could have a much more complicated statement of such; and that is where algebra comes into play.

Now, to apply algebra in the above statement, we use letters or alphabets to represent the unknown number(s). So using algebra, we can write:

  • Let the number be y
  • y - 3 = 9
  • y = 9 + 3
  • y = 12

Please read on the Number Base System here.


So why is it easier using letters?

if we had a question of several unknowns, the question can become complicated, so using letters actually make things easier for us.

To simplify a mathematical expressions, we need to represent them in the least complicated form as much as we can, making them more easier to work with.

One skill you need to know is the combination of "Like Terms".

Like Terms refer to those variables that are exactly the same, although they may still have different coefficients.

Consider the instance below

  • 5a2 and 12a2 are considered to be like terms because the have the same variable a2.
  • 3ab and 3bc are not like terms because the have different variables (ab & bc) respectively.

So, to combine the like terms will mean to "add" or "subtract" them, so that we can have a single term.

Please read on Factorization of Quadratic Equation here.

 

Worked Examples

Example 1:

  • Simplify 10ab + 7ab
  • Since "10ab" and "7ab" are like terms; (They both have the same variable ab), we will add their coefficients together in order to get our answer
  • (10 + 7)ab = 17ab
  • Answer is 17ab

 

Example 2:

  • Solve y2 + 5 + 7y2 - 5y + 10
  • First, let's combine the like terms
  • Note: A variable without a coefficient in front of it is always assigned the value of 1. Also, when moving coefficients, we always take into account the "+" and "-" values in front of them.
  • (1 + 7)y2 - 5y + (5 + 10)
  • Answer is 8y2 - 5y + 15

 

Example 3:

  • Solve 4b + 4 = 20
  • Step 1: Let's move over like terms
  • Note: When a like term is moved over the "=", the "+" value before it turns to "-". If the like term has "-" value in front of it, then it turns to a "+".
  • 4b = 20 - 4
  • 4b = 16
  • Stet 2: To get b, Let divide both side by b's coefficient (4)
  • 4b/4 = 16/4
  • Answer is b = 4

 

Example 4:

  • Solve 4a + 5 = 2a - 1
  • Step 1: Let us move the like terms
  • 4a - 2a = -1 - 5
  • 2a = -6
  • Step 2: Let's divide both sides by a's coefficient (2)
  • 2a/2 = -6/2
  • Answer is a = -3

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Alfred Ajibola is a Medical Biochemist, a passionate Academician with over 7 years of experience, a Versatile Writer, a Web Developer, a Cisco Certified Network Associate and a Cisco CyberOps Associate.


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Amazing facts in Mathematics

31,556,926 seconds makes one year

1000

From 0 to 1000, the only number that has the letter “a” in it is “one thousand”.

÷

The division symbol "÷" is actually called an obelus

4

Four is the only number in the English language that is spelt with the same number of letters as the number (4) itself. 

40

40 is spelt as FORTY and not FOURTY. It is the only number that is spelt with letters arranged in alphabetical order 🙄

An odd number is a number that cannot be divisible by 2

Every odd number has an “e” in its spelling. They include:

  • One
  • Three
  • Five
  • Seven
  • Nine

555 in Thailand should sound like “hahaha”. This is because the word 5 means “ha” in Thailand

10! Actually means 10 factorial.

10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 3628800

3628800 seconds is the same as 42 days

42 days is the same as 6 weeks

When you multiply 111,111,111 by 111,111,111; the result equals 12,345,678,987,654,321

With regards to numbers,

Forty is the only number that is spelt with letters arranged in alphabetical order.

One is the only number that is spelt with letters arranged in descending order.


NOTABLE POINTS IN Mathematics

Circumference in mathematics means the distance around the edge of a circle (or a another curverd surface).

Perimeter means the distance around a square or rectangle or polygon.

Circumference is to circle or any other curved surface

Image Credit: Ducksters

Perimeter is to square or rectangle or polygon

Image Credit: Maths is Fun