Posts

Prime Numbers List

Prime Numbers up to 100
2, 3, 5, 7, 11, 13, 17, 19, 23, 29 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97



Prime Number up to 200
2, 3, 5, 7, 11, 13, 17, 19, 23, 29 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199



Prime Numbers up to 400
2, 3, 5, 7, 11, 13, 17, 19, 23, 29 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397

Prime Numbers up to 600
2, 3, 5, 7, 11, 13, 17, 19, 23, 29 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271,…

Identities

Image
Identities
Identities are ways of expressing algebraic values in different ways. The values of the written expressions are identical. This is why the word ‘identical’ is used.

"Same thing Different form!"

Such following expressions and equations are identical:
\( \displaystyle 3x=2x+x \)
\( \displaystyle 5.(x+1)=5x+5 \)
\( \displaystyle (a+b)²=a²+2ab+b² \)
Identities are valid / true for all real numbers.

 Let us choose a number for this expression  \( \displaystyle 5.(x+1)=5x+5 \)   and try. 
Let \( \displaystyle x=8 \)
 \( \displaystyle 5.(8+1)=5.8+5 \) 
\( \displaystyle 5.(9)=40+5 \)
\( \displaystyle 45=45 \)
The left side is 45, the right side is 45, and they are equal to one another. Whatever number you give \( \displaystyle x \)  the right and left side will equal to one another because the expressions are identical.  They are the same.
Why do we need identities? 
They can help us whilst calculating some mathematical equations.
Sometimes you can change an unsolvable equatio…

Modeling in Identities

Image
Modeling in Identities By making use of the feature of area calculation through multiplication, this is a visual way of showing that the result of multiplication is equal to the value of the area. 

Multiplication and Area 

\( \displaystyle 3.4 \); If we times 3 with 4, we will have found the area (the number of squares) within a rectangle, which has a length of 3 units.

Expansion of Fractions

Image
Expansion of Fractions
The process of making the unit fraction  smaller is called expansion. You may say, ‘How is it that the process of fraction becoming smaller is called expansion, isn’t this strange?’

We will find out;

Let’s take into account the fraction ; \( \displaystyle \frac{2}{3} \)



The unit fraction of  \( \displaystyle \frac{2}{3} \)  is \( \displaystyle \frac{1}{3} \)

Let’s expand the fraction by 2 without changing it’s value. I will carry out the expansion with multiplication. We know this; when we multiply a unit/ a thing by 1, it remains the same, it doesn’t change. So in fact, we do not multiply with 2 but we multiply with 1.

Why is the total value of the angles of triangles 180°?

Image
Why is the total value of the angles of triangles 180°? The total value of angles of all triangles, no matter what type of triangle equals a total of 180°; let’s try and prove why this is the case. Before proving this, we must remember the angles of two parallel lines at intercepts.



The angles that are formed when two lines that are parallel to one another are intercepted, the systems that are formed (centre points) will be the same value. The angle system continues to cut the lines and comes towards the other parallel line.

How to read fractions ?

Image
\( \displaystyle \frac{1}{2} \) "one half" or "a half"

\( \displaystyle \frac{1}{3} \) "one third" or "a third"

\( \displaystyle \frac{1}{4} \) "one quarter" or "a quarter"



\( \displaystyle \frac{2}{3} \) "two thirds" not "two third" ( 2 is plural so we add "s" ) .

\( \displaystyle \frac{2}{5} \)  "two fifths"

\( \displaystyle \frac{3}{7} \) " three sevenths"

\( \displaystyle \frac{5}{6} \) " five sixths"

\( \displaystyle \frac{3}{4} \) " three quarters"

\( \displaystyle \frac{11}{10} \)  "eleven tenths"


\( \displaystyle 2\frac{9}{10} \) " two and nine tenths"  is like \( \displaystyle \text 2 whole \) and  \( \displaystyle \text nine \) \( \displaystyle \frac{1}{10} \)

Types of Triangles

Image
Types of Triangles You’ve decided to by a watch and the watch seller asks you what sort of specialties you want to the watch to have in order to help you. For example, there are plastic, metal, leather strapped watched and alarm clocks. We can here speak about some similar characteristics between the watches.
When you speak of triangles, not all triangles are the same. Some triangles have special properties; some have the same lengths for each of their sides, some of the angles within the triangle etc.

Types of triangles based on sides


Scalene/unequal triangle: The lengths are of various sizes – so this is used for triangles where all of the lengths of the sides are different..
Isosceles triangle A triangle where 2 sides of the triangle are of equal length. Think of it like ‘twins’.
Equilateral triangle A triangle where all sides are of equal length.

Types of triangles based on angles
We are going to name triangles according to their angles.


Acute angled triangle: Triangles where all angles…

Exponents

Image
Earlier you had learnt that adding the same number over and over again is the same thing as multiplication.

For example;

\( \displaystyle 4+4+4+4+4+4+4 \)
instead of this equation we can use multiplication.  Because we are adding the number 4, 7 times:

\( \displaystyle 4+4+4+4+4+4+4=7.4 \)
Now, we are going to focus on multiplying the same number several times. We are going to develop methods to make this easy for us as well as to show this in a simple way.

The area of triangle

Image
We measure an area with squares; therefore we calculate the area of a triangle in the same way.

The area of a triangle is calculated by seeing how many squares can fit inside the triangle.


The triangle above consists of 30 unit squares and 12 half squares. Since 12 half squares equal 6 whole squares, we can say that the square above is 36 unit squared.

Ordering and comparing rational numbers

Image
To order / compare rational numbers;

a )You can order rational numbers either by using logic, based on division which is what a rational number means.

b) You can think of a rational number as a fraction and then sort it. The way
we sort fractions is the same way to sort rational numbers.

We recommend that you also look at the topic of ordering in fractions .