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Monthly Archives: November 2011

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

 

Feet to Centimeters….

In Math we can be given a problem in one unit and have to give the answer in another. This is called converting of units. We can go from feet to centimeters in a few easy step when knowing the converstions.

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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Posted by on November 16, 2011 in Units of Measure

 

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

 

Out of 100!

Finding a percent can be very intimidating, however if with start with an easy percent to find we can build off that. A percent that is easy to find is 10%, you just move the decimal one place to the left. For example 10% of 52 is 5.2, we also know that 10% of 6.3 is 0.6. Not only can we find 10% of a number but we can find 20 percent. To find 20 percent of a number we can find 10% and the double it. For example if we want to find 20%of 600, we can first find 10 percent which is 60 and then double that to 120, so 20% of 600 is 120.

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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Posted by on November 5, 2011 in Percent

 

Decimals to Fraction!

In math there are many things that go hand in hand, for example addition and subtraction, also multiplication and division. Another thing that goes hand in hand is fractions and decimals. We can take a fraction and make it decimal but we can also have a decimal and make it into a fraction. In order to do so we need to understand the term “rational numbers”. Rational numbers are simply decimals that are terminating or repeating.

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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Posted by on November 3, 2011 in Decimals

 

Decimals….

First we need to know the terminology for decimals before we jump in, the terminology is very important. We can start off by understanding the meaning of the Latin word decem, which mean ten. Some of the other terms that we need to understand are decimal points, and mixed decimals.

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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Posted by on November 2, 2011 in Decimals