## 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, 23

### Identities

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 wh

### Modeling in Identities

Modeling in Identities Calculation of area by means of multiplication is an effective visual representation.  Multiplication and Area  $$\displaystyle 3.4$$   ; If we multiply 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

Expansion of Fractions The process of making a 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?’ Let’s find out; Let the fraction be;  $$\displaystyle \frac{2}{3}$$ The unit fraction of   $$\displaystyle \frac{2}{3}$$  is  $$\displaystyle \frac{1}{3}$$ Let’s expand this fraction by 2 without changing its value. We will carry out the expansion with multiplication. We know this; when we multiply a unit/ a number 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°?

Why is the total value of the angles of triangles 180°? The total value of internal angles of all triangles, no matter what type, equals to 180°; let’s try and prove why this is the case. Before the proof, we must remember the angles of two parallel lines at intercepts. The angles that are formed when two parallel lines intersect are equal to each other. The intersecting line continues to cut the lines and comes towards the other parallel line. Let’s create a similar system for a triangle; Let’s create a triangle, showing the angles in different colors, and draw a line parallel to the base. Now let us look at the situation of the angles and carry out the ‘moving’ operation. Let’s focus at the very top, the blue, yellow and red angles show the total value of the angles. Since the horizontal line has an angle of 180°, the total value of the angles in a triangle is equal to 180°

### How to read fractions ?

$$\displaystyle \frac{1}{2}$$ "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 third s " not "two third" ( 2 is plural so we add "s" ) . $$\displaystyle \frac{2}{5}$$  "two fifth s " $$\displaystyle \frac{3}{7}$$ " 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

Types of Triangles You’ve decided to buy a watch and the vendor asks you what sort of specs you want to assist you. For example, there are plastic, metal, leather strapped watches and alarm clocks. We can here speak about some similar characteristics between the watches. In case of triangles, not all triangles are the same. Some triangles have special properties; some are related to edge lengths and some are related to corner angles of  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 edge lengths are different.. Isosceles triangle A triangle where 2 edges of the triangle are of equal length. Think of it like ‘twins’. Equilateral triangle A triangle where all edges 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 are