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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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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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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The Conversion units for Length are:

English Metric Bridges

12in=1ft 1km=1000m 1in=2.54cm

3ft=1yd 1m=1000mm 1mi=1.609

5280ft=1mi 1m=100cm

1cm=10mm

We need the bridges to be able to go from metric to english and viscera. There are also other conversions that can be helpful; Conversions for mass and time.

The Conversion units for Mass are:

English Metric Bridges

16oz=1lb 1000mg=1g 454g=1lb

2000lb=1tons 1000g=1kg 1kg=2.2Lb

The Conversion units for Time are:

60 sec=1 min 52 wk= 1 yr

60 min=1 hr 365 days=1 yr

24 hr= 1 day 10 yr= 1 decade

7 days= 1 wk 100 yr= 1 century

With these conversions units we can do conversions. We can take 2.6 meters and convert it to millimeters. We can do this by starting with 2.6 meters and finding a conversions that will take use to millimeters.

We can also convert 3.0 miles into inches.

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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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We can also use this for finding the new price of an item, for example if we had an item that is $200 and you get 20% off what is the new price? You can start this problem off by finding 10% of 200 which is 20 and then doubling 20 to get 40. The new problem is $40 off $200 so you will pay $160 for the item.

We can also use these methods to find a smaller percent like 5, because 5 is half of 10 we can find 10% of a number and then split it in half. For example 5% of 4200. We can start this problem by finding 10 percent; 10% of 4200 is 420. Then we can take half of 420 and get 210. So 5% of 4200 is 210.

Another way to find a percent is to use a percent chart. Below are to images of percent charts.

These grids have a hundred squares to represent 100%. The problem for the first grid is 40% of 200. Which is 80.

The problem for the second grid is 20%of 40. Which is 8.

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We can take the word “rational” we can take out the word “Ratio” meaning of integers (fraction of integers).

Terminating decimals are numbers like 0.55, 0.205, and 6.1 (these are all decimals that have a clear ending). We can make these decimal into fractions by paying attention to the place values that the digits hold. For example 0.55 is in the hundredths place therefore 0.55 is 55/100.

Repeating Decimal are numbers like 0.333333….., 0.77777….,and 0.242424 (decimals that have a repetition in the number. it may start later in the number). We can make these decimals in to numbers by setting them equal to “X”. A good example is 0.333333…. because we know of the top of our heads that it is 1/3 but do we know why it is? Below are the steps to show why 0.3333…. is 1/3.

Step 1) X=0.333333….

Step 2) 10X=3.333333…. (Find a number of ten that will get rid of the repeating end of the decimal. Then subtract Step 1 and Step 2.)

Step 3) 9X=3

Step 4) 9X/9=3/9 or 1/3

We can use these steps on any repeating decimals. Lets try the decimal 0.242424….! We will start the problem just like we did for 0.333……!

Step 1) X = 0.242424

Step 2) 100x = 24.2424 (We want to set it equal to 100X because it will move the decimal two places to the right and it will get rid of the repetition)

Step 3) 99X = 24

Step 4) 99X/99 = 24/99 or 8/33

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The Decimal point is the dot between the digits in a number. For example 17.63 the dot between the 17 and the 63 is the decimal point. 17.63 can also be considered a mixed decimal! Another important thing to pay attention to is the place values when dealing with decimals.

Above is a picture with Place Values for numbers with decimals. On the Left side of the decimal we can see that the ending is “s” and that on the right side the ending are “ths”. These are very important to pay attention too.

We can also write the number in an extended form.

5(10^3)+ 4(10^2)+ 7(10)+3(1)+ 2(1/10) +8(1/100) +6(1/1000)

When we read the number we read it in a different way than what we would if just reading a whole number. When reading a decimal we say the word “and” when we come across the decimal. Below is a example of this.

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For example we can say that 3/5 + 1/2 is approximately equal to 1 or just over one. We can say this because 3/5 is just over a half. Therefore if we add what they are close to we can see that it will be just over 1.

Not only can we make an estimation of what the answer might be but we can use the rectangle method of multiplication for fractions!

Not only can we use this method with whole number but we can use this for fractions. The picture below shows a few examples of using this method with fractions.

When using the Rectangle Method of Multiplication for fractions you have to be able to think in parts of a whole. For example when we do 1/2 x 2/3 (the bottom problem in the picture above) we start with a 1×1 square, then we have to split the square into halves in one direction, and then into thirds in the other direction. After we do this we can shade in 2/3. By splitting the 1×1 square into half in one direction and thirds in the other we get a box that is sixths, this gives us a final answer of 2/6 because there are six parts and two of them are shaded.

We can also use this method for division of fractions if you change the division into multiplication. Here are some videos that can help explain adding and subtraction of fractions. It will also help explain multiplication and division.

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