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Finding Volume Prisms and Pyramids

Finding volume can sound very difficult but it is rather simple if you understand two formulas. The first formula is finding volume for a prism (V=AbaseXh); volume of the area of a base time the height of the objects. For example: The base of this prism is 3.0×2=6 cm^2. After finding the area of the base we can take 6 squared centimeters and multiply it by 5cm giving us 30 cubed centimeters. That is how you find the volume of a prism.

To find the volume of a pyramid we need to know a different formula.This formula is V=1/3pir^2h (1/3 pi time the radius squared time the height). For example a pyramid with a radius of 6cm on the base and a height of 10 cm. can be put into the formula as V=1/3pi(6)^2(10)=376.99 cubed centimeters.  

Finding volume can be very fun and easy if you know how to use the formulas. It is also very helpful! On a side note it is coming to the end of the semester, how sad? I am truly glad that I took math 105 this fall not only did I learn a lot and really have a better understand of math but I have had the privilege to meet some really interesting people (friends). I will always remember my classmates from math 105, Thank you for such a great semester!

 
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Posted by on December 3, 2011 in Uncategorized

 

Area of Shapes!

Finding the area of a square and rectangle are easy to find. The forulma for find the area of a square is 4S, and the forulma for the area of the rectangle is 2W x 2L. These are two basic forulmas that make finding area easy. However when you get into shapes like a triangle and dont know the parts that you need, you can make these shapes in to ones that we know.

When finding the area of a triangle can be difficult if you dont know all the parts or if it is part of another shape. For examlpe if the the triangle is inside a square and we can find the area of the square we can find the area of the triangle. The picture below is a square with a triangle inside it we want to know the area of the triangle.

We know the area of the square by counting the square inside of the big one. The area of this square is 12 square centimeters. After finding the area we can cut out the triangle which we want to find the area. The picture below is cutting out the triangle, notice that when you cut out the one triangle the two extra parts make the same triangle.

With two triangles that are the same, we can conclude that the area of one triangle is half the area of the square. The area of the trangle is 6 square centimeters. The formula for the area of a triangle is 1/2BxH. We can also use this to find other shapes that we do not know. If the shape can be made in to a square or a rectangle this is a good way to find the area of something!

 
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Posted by on November 26, 2011 in Uncategorized

 

Shapes in circles?

Have you even been told to draw a shape in side a circle and not know what they are talking about? Well it is very possible to do, you can do this by taking the central angle of the circle divided by the number of side the shape will have. For example a circle has 360 degrees and a regular hexagon has 6 sides; we would take 360/6= 60, each angle from the center of the circle would then be 60 degrees.

Next we can connect the verticies, creating the six side of the hexagon.

Now that we have our hexagon, another thing that we can find is an angle of the hexagon, we can find the vertex angle by taking 180-the central angle, in this case 180-60=120 degrees.

We can put any shape inside a circle. All you have to do is follow the steps, not only is it interesting but is also fun and can be made into different types of projects!

 
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Posted by on November 18, 2011 in Uncategorized

 

Irrational Numbers

A rational number is a number that can be written as a ratio; which means it can be written as a fraction. 10 is a rational number because it can be written as 10/1. Any number that is not rational is considered an irrational number. An irrational number can be written as a decimal; however not a fraction. Irrational numbers also have a decimal that is not ending but it is not repeated. An example of an irrational number is pi. Pi is equal to 3.141592…….., another example is square root 2. Even though square root 2 is an irrational number, this doesn’t mean that all roots are irrational numbers.

We can also simplify roots with a higher index. An index is a number written in the “check mark” area of the radical, that indicates some other root besides a square root.

When we simplify we need to pay attention to the index. The Index is important when simplifing because that is the number of grouping that you need to take out.

We need to find groups of three when simplifying. We can simplify 162 by using a factor tree.

Then we can rewrite this under the ratical.

Pulling out the group of three and taking it to the front of the ratical leaving the 3*2 underneith the ratical.

Then we can simplify the 3*2 under the ratical.

 
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Posted by on November 15, 2011 in Uncategorized

 

Oh No Not Them Numbers

We have many different kinds of numbers; we have Natural numbers (number {1,2,3,4,5,….} or Counting numbers), Whole number {0,1,2,3,4,….} and we have Interagers {….,-3,-2,-1,0,1,2,3,….}.

when useing negative in math we can become confused very quickly, It seem that as soon as we see the negative symbol (-) our brains freak out. This can be a easy fix if you just have the right tools. Color squares can be big help.

Red- Negative

Black- Possitive

Black + Red = 0

The Picture above are models of using red and black squares to help solve the problems. On the left we have    -3 + 5= 2 and on the right we have -5 + 1 = -4.

We can also look at these problems by creating a “sea of zeros” with problem in the center and solve the problem in a different way.

In the picture above we have -2 (the number in the center circle) and we want to take away 3. Our problem is -2 – 3 = ___. We can get an answer by takeing away three of the black squares in the “sea of zeros”, this will leave us with -5.

These are much easier ways to deal with negative numbers. Not only are the helpful but they are easy to understand!

 
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Posted by on October 19, 2011 in Uncategorized

 

GCF and LCM!

Find the Greatest Common Factor (GCF) or the Least Common Multiples (LCM) can be very intimidating and confusing. However there are tricks that can making find these things simpler.

The Greatest Common Factor can be defined as, the highest common factor between two numbers. In order to find this we need to know what all the parts are. A factor is two numbers that you can multiply together to get another number.

The Factors of 12: 1, 2, 3, 4, 6, and 12

The Factors of 30: 1, 2, 3, 5, 6, 10, 12, and 30

So we can conclude that the Greatest Common Factor is 6.

We can find the Greatest common factors by looking at factors of a number or we can find it by looking that the prime factorization. We can do this be breaking down numbers into primes.

For example:                                                 

The Prime Factors of 12 are 2 x 2 x 3

The Prime Factors of 30 are 2 x 3 x 5

12= 2 x 2 x 3

30=       2 x 3 x 5

We can find the GCF and the LCM by looking that these numbers. To find the GCF we can look at the intersection of the Prime factorization of 12 and 30.  The intersection of 12 and 30 is 2 and 3; therefore the GCF is 2 x 3= 6. We can also find the LCM by looking at these numbers, to find the LCM we look at all the number of the prime factorization (the union of the numbers). The LCM of 12 and 30 is 2^2, 3 and 5; therefor the LCM is 2 x 2 x 3 x 5 =60.

 
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Posted by on October 12, 2011 in Uncategorized

 

Factors & Multiples

Factors and multiples can be scary word if you don’t understand their meaning.

A factor is simply taking apart a number so that it is expressed as a product of the factor. Factors can also be either a composite number or a prime number (0 and 1 are neither.)

The Prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37,…..

Prime numbers can be defined as a number greater than one who’s only factors are one and  itself.

The Composite number are: 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20,……

Composite numbers can be defined as counting number that are not prime.

For example: 16

The factors of 16 are 1,16; 2,8; and 4

therefore we can take one of these factor pairs; such as 2,8 and write a multiplication problem. 2 X 8 = 16

Multiples are a number of a product;that number and any other whole number. Zero is a
multiple of every number.

For example: 12 is a multiple of 3 because 3 divides evenly.

So 3 x 4 = 12 ; 12 is a multiple of 3 and 4.

 
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Posted by on October 8, 2011 in Uncategorized