How to Find the Area of a Trapezoid (It's way easier than it sounds)

I haven't been on for a few days, but I just got really swamped with school and stuff around the house- but the main thing here is I'M BACK!!!!!! Hahahaha. Now, in this post, I'm going to teach you how to find the area of  a trapezoid if you know the base measures and the height. Give me a second to go onto Google and get a picture for you to look at and I'll be right back....


  There we are, now, the formula for area of a trapezoid is

1/2h (a+b) Now that's read as 'half the height times the sum of the bases.' Now, there are some things you need to know about trapezoids before you start to find their area:

1) Trapezoids have 2 bases
2) These 2 bases are parallel (they could go on and on forever in the same direction and not ever cross paths)
3) It doesn't matter which bases you label 'a' and which one you label 'b,' just make sure to add the lengths of the bases together.

Now, on the picture above (I'm really psyched that I even got a picture on here, so please feel free to draw it on a separate piece of paper :)  ), the bases are labeled 10 meters and 8 meters (the little 'm' next to the numbers is short for meters), and the height of the trapezoid is labeled 9 meters. All you have to do now is plug in your values:

(1/2)x(9)x(10+18)  This should read 'half of 9 times the sum of 10 and 18.' This may look like a lot of scary numbers and parenthesis, but just take it a little bit at a time and don't panic: you're going to start with the (1/2) times (9) bit. Saying 'one half times nine' is the same as just taking half of 9 (it may sound redundant, but it just seems easier to understand that way). If you want to use a calculator, just put in .5 times 9 and you should get 4.5 or 4 and one half. Now you should have 4.5 times the sum of 10 and 18. So, now, add 10 and 18 (you should get 28) and multiply that by 4.5. this would be a pretty good time to use a calculator if you don't want to do the multiplication on paper (or in your head), not that it wouldn't be good practice. Anyway, you should get 126 for the area of the trapezoid. Like I said in the last post I did concerning area, you always tack on 'square units' to the end of your answer; in this case, your final answer would be 126 square meters.

Remember, if you need some more help on finding the area of trapezoids, just go to www.khanacademy.org , type in the topic and a bunch of videos will pop up that will help you further understand it. Thanks for reading! :)

-Meredith

THANK YOU!!!

Thank you all again for all the recommendations!!!!

- Meredith

Adding Fractions With Like Denominators ('like denominators' is just a way of saying that they have the same number on the bottom)

    I just posted a quick one and I think I have time for one more, so I'll do one on how to add fractions with the same number on the bottom (you'll hear them called 'fractions with like denominators').
    Say, for example, you have 4/11 + 6/11 (this is read as 4 over 11 plus 6 over 11, and it would probably benefit you to write this down on a piece of paper straight up and down, just so you can tell the top from the bottom). Since you don't have to change the bottom of the fraction, all you have to do is add the top, straight across.

4+6/11 (to write this straight up and down, write 4+6, then a horizontal bar right underneath that, then write 11 underneath that)
Now, simplify the addition on the top:

10/11 should be your final answer.

NOTE: (you may wonder why you don't add the two 11's on the bottom. Just remember that the only time you mess with denominators is when you multiply or change the denominators. So in this case, you would NOT add the denominators, since they are already the same and since you're not multiplying.)

That was pretty short, so if you need more help on adding fractions with like denominators, go to www.khanacademy.org and a bunch of videos will pop up.

Bye! :)

-Meredith

How to Find the Area of a Triangle (Given the Height)

    Hey, hey! I'm back, and I only have a little bit of time to post this one because I'm doing it from a school computer, but anyway. This one is going to be about how to find the area of a triangle, if you already know the length of the base and the height of the triangle.
    The first thing you need to know is the formula for area of a triangle:

Area=1/2bh (which is read as one half times the length of the base times the height of the triangle)

   So, just for example, say you have a triangle with a base length of 8 and a height of 7.

NOTE: (the 'b' in the formula stands for the length of the base and the 'h' stands for the height and you'll sometimes see the area bit as a capital 'A')

    Now, plug your values into your formula:

A= 1/2(8)(7)

First you're going to multiply your 1/2 by 8. When you multiply fractions (like 1/2) by whole numbers (like 8) just take the fraction amount of the whole number (take one half of 8). You should get 4 (half of 8 is 4):

A=(4)(7)

NOTE: (when you have numbers right next to each other in parenthesis, you multiply them, so in this case, you would multiply 4 and 7)

4 times 7 is 28 so your area is 28 square units

NOTE:(if you're wondering where the 'square units' came from, just know that whenever you find area, you tack 'square units' on the end; however, if you are using a specific measurement while finding the area [say, in the problem we just worked, you were using 8 and 7 inches, you would have, for your final answer, 28 square inches], put that on the end of the square units part.)

  A= 28 square units

Remember, if you need more help on finding the area of a triangle given the height, go to www.khanacademy.org

Bye for now
-Meredith

Simplifying Fractions (just a way to get smaller easier numbers to work with :) )

    Alright- last time, I told you that I'd put up a post on how to simplify fractions, so here it is:

    To start with, you have to have a fraction that isn't simplified (you may also hear it called 'a fraction not in simplest form') all the way. Now, a fraction that isn't simplified all the way is just a fraction with common factors in the top and the bottom (technically called the numerator and denominator, respectively). For example, 8/12 (8 is the top and 12 is the bottom, just FYI). 8 and 12 have many common factors; the first and typically most obvious one is 2. If you multiply 2 and 4, you will get 8 (therefore, 2 and 4 are considered factors of 8) and if you multiply 2 and 6 you'll get 12 (so 2 and 6 are also factors of 12. If you list all the numbers that you can multiply to get a couple of numbers and you see some of the same numbers in each list, you have common factors). Since you can multiply 2 by something to get both 8 and 12, 2 is one of their common factors; you can use this to simplify the fraction 8/12.
    Now, you're first going to write the fraction on your paper (it would probably benefit you to write it out if this is your first time, because you'll be able to understand it a little better) straight up and down: write the 8 then a little horizontal line right below it then a 12 below that. Now, know that your 8 is called your numerator and your 12 is called your denominator. Now, take your common factor and write it as a straight up and down fraction, like this: write a 2 then the little horizontal bar right below it then another 2 right below that. Write this right next to your 8/12 with a division sign in between them. You should have: 

8/12 <division sign> 2/2 (only straight up and down)
Your 8 and your top 2 should line up and your 12 and your bottom 2 should also line up.

Now, this is the easy part: divide straight across. Take 8 (the top of your 8/12) and divide by 2 (the top in your 2/2). You should get 4; now, take 12 (the bottom of your 8/12) and divide by 2 (the bottom in your 2/2). You should get 6. Now write your new fraction with the numbers you got just now, remember- keep the top division answer (the quotient) on the top of our new fraction and the bottom division answer on the bottom of your new fraction. You should have:

4/6

As with most fractions that you simplify, you will have to do what I just taught above more than once. In this case, you can divide again by 2/2 again, and you will have your final answer.

NOTE 1: (You know you have a fully simplified fraction when there are no more common factors between the top and the bottom)

NOTE 2: (Dividing by a number over itself, in this case 2/2, is the same as dividing by 1 and therefore, your note actually changing the fraction, you're just rewriting it using smaller numbers)

NOTE 3: (You could have worked this problem by dividing the original fraction by 4/4, basically, you would just be using the common factor of 4 instead of 2. [4x2=8  4x3=12, so they have 4 in common as a factor. Working the problem this way would have given you
8/12 <division sign> 4/4=  2/3 which is a simplified fraction because 2 and 3 have no common factors).

Now, since 4 and 6 have the common factor of 2 (2x2=4  and 2x3=6), divide 4/6 (the fraction you have now) by 2/2 (the common factor of 4 and 6). You should get:

4/6 <division sign> 2/2  (4 divided by 2 = 2 and 6 divided by 2 = 3)

2/3

This is a completely simplified fraction because 2 and 3 have no common factors.
This wasn't the best post that I've ever done so if you need some more help on common factors or on simplifying fractions, just go to www.khanacademy.org and you'll get a bunch of videos that can probably explain it a lot better than I can.

:)  Bye for now
-Meredith                            

Thanks!!!

Thank you to anyone who recommended this on Google or what ever website this is on lol  :D Ya'll peoples rock!!! Thanks again

-Meredith :)

Slope and How to Graph Lines (it's really useful in business charts and stuff like that)

    Hello, again :). I hope you had a nice Valentines Day. In this post, I am going to explain the concept of slope and how to graph a linear equation. Now slope is basically the steepness of a line. The slope formula is actually pretty intimidating if you're not familiar with it, but don't panic. Here it is:

(y1-y2)/ (x1-x2)= m  

NOTE: (the little numbers next to the y's and x's aren't anything mathematical, it's just the first and second y's and x's that you come to. Imagine that you have the set of ordered pairs, that's just another way of saying the coordinates of some points on a graph, like (4,7) and (5,6). The 4 and the 5 would be your x's so you could label 4 x1 the 5 x2 {ordered pairs are always in the form (x,y) so your first number in the pair will always be your x and the second number will always be your y.} and your 7 and your 6 will be your y's so you can label the 7 y1 and the 6 y2.  After you have your numbers labeled, just plug them into the formula.)
    If you read the note above, you'll see how to label the ordered pairs (the sets of numbers hat you use to find slope), so let's do that now: say you have the two ordered pairs (9,2) and (5,8). Now, your x's are your 9 and your 5 you can label them; and since you know that your y's are your 2 and your 8, you can label them too. You should have x1 as 9 and x2 as 5. You should also have y1 as 2 and y2 as 8.

(Notice that the numbers from the same ordered pair have the same numbers in their label- 9 and 2 are from the same pair and they both have a 1 in their label, and the same of 5 and 8.)

Now that you have your values assigned, plug them into your formula and simplify:

(2-8)/(9-5)= m

Note: (a lower-case m stands for slope- DO NOT use an upper-case M- it means something completely different, but we'll get to that later).

Now, 2-8 is -6, and 9-5 is 4, so you should have -6 over 4 which will simplify to -3 over 2. (I'll get to simplifying fractions next post, but basically you just divide the top and the bottom number by the same number.)

In the end, your slope will be -3/2. However, to be able to use this slope effectively, you have to have a starting point on your graph; this is where the y-intercept formula comes in. The y-intercept formula looks like this: 

y=mx+b   the b stands for the y-intercept which is where the line you graph crosses the y- axis (it's the vertical line that makes up the coordinate plane). Once you know this value, you can use that as your starting point on your graph and use your slope from there.
    
Note:  (your slope is rise over run. If your slope was, for example, 3/5 or 3 over 5, and you already had a point on the graph, you would go up- or rise- 3 and go over- run- 5 from that point and plot another point where you stop after all the rising and running)

Now you know, that the lower-case m means slope, so to write out your formula, you plug in your slope into where the m is and solve for b. You should have something like this (given that you're using the same slope from above- it was -3/2 by the way):

y=(-3/2)x+b

Now, from earlier, you know that an ordered pair has numbers that can be labeled with an x and a y, so pick one of the points that you found your slope with (let's use (9,2)) and plug in the x and the y (the 9 will be your x and the 2 will be your y {remember (x,y)}). Once you plug everything in, you should have something like this:

2=(-3/2)(9)+b

Now simplify and solve for b:

2=(-27/2)+b
(I was mistaken when I said these would be easier numbers, but they are workable withable :)... I'm gonna change the 2 to 4 over 2. Then we can subtract the -27 over 2 without it getting messy- and, just FYI, 4 over 2 and 2 are the same thing, but, again, I'll get to that next post)

(4/2)= (-27/2)+b
add (-27/2) to both sides
(31/2)=b  or    15.5=b

With that, you now know that at 15.5 on the up-and-down axis is a point on your line. Now you can use the rise-over-run tidbit that I talked about in the last 'note' to plot your next point. Since your slope is negative, you will first rise 3 (go UP 3 from your point on the y-axis) then go LEFT 2. (you go left, because left is the negative direction and your slope is negative.) you should have a point at... (-2,18.5), and you always go in the left or right direction first then you go either up or down. So... you'll go to the left 2 then up 18.5 and that should be your other point. You'll then draw your line through your point at 15.5 and through (-2,18.5) and you'll have a line.

Alright piece peace out www.khanacademy.org or more help

-bye bye! :D 

Happy valentines

Oh by the way - Happy Valentines Day, personally I think it's embarrassing at the middle school level but still

Surface Area if a Cube (enjoy!)

    Hey, I'm doing this from an I-pad and it isn't mine, so I'm sort of limited. Nonetheless, I'm going to try to explain how to find the surface area of a cube.
    This is sort of self explainitory, but there are a few things you should know before you start adding and multiplying and all:

One: a cube is a geometric figure with all equal faces (flat surfaces) which means that if you have the measurement of one face, you have the measurement of all the faces.

Two: surface area is the sum of the area of all the faces of a figure (in this case if you find the area of one face of a cube, you just multiply that measurement by the number of faces you have)

Now, to start with, draw a cube the best you can (if you can't draw a cube, just draw six squares that are about equal in size, and just know in your head that they represent a cube), then label one side of one of the squares 3 units in length. Now, since all sides of a square are congruent, with one labeled side, you know the length of all the other sides of all the other squares (since you know in your head that all the squares are congruent). To find the area of one square, multiply the square's length by its width (personally, length and width have always confused me, just multiply one side measure by the other, which in this case would be 3x3). You should come out with 9 square units for the area of one square (given that you used 3 for the measurement of one side of the square).
    Now, since you know (in your head) that all the squares you drew are equal, you know that the area of all the squares is 9 square units. Now, every cube that you will ever come across has 6 equal faces, so to find the surface area of the cube you have right now, just multiply the area of one of the faces by the total number of faces (9x6 because you have 6 faces and you know that the area of each one is 9 square units). You should come out with 54 square units for the surface area of a cube with edge lengths of 3units.

    Now please note that surface area and volume are COMPLETELY different. Volume is how much water (or any other liquid, but water is a better example) you can fit in a figure, but surface area is how much paper it would take to completely cover the surface of a figure.

    And remember that if you need extra help with this, go to www.khanacademy.org for some videos to further explain surface area.
-Bye bye : )

The Pythagorean Theorm (scary name, I know, but it's real easy once you get it)

For my first mathematical post, I'm going to explain the Pythagorean Theorm. The name makes it sound scary but I guarentee you it is very simple once you understand it.

Now, rule number one- this theorm only works with RIGHT TRIANGLES

Rule number two- you can use it to find the length of ANY side of a right triangle so long as you have the lenght of two other sides.

And now for the Theorm itself:
a^2+b^2=c^2              Yep, that's it. It would look nicer if this thing was more exponent friendly but still. 


Now, for the explanation: 
 First, since I can't get a picture on here, draw a right triangle. Then you're going to label the legs (the straight sides) a and b, it doesn't matter which one you label which way. Now label the other side, the slanted one (technically it's called the hypotenuse, but 'slanted side' is easier to say), c. Now write in measures for sides a and b; use the measures 3 and 4 if this is your first time because you'll get some nicer numbers.

Now, plug the numbers you have for sides a and b into your formula (assuming you used 3 for side a and 4 for side b), and you should have something that looks like this:

3^2+4^2=c^2   (the symbol that looks like a roof-top, ^, like that, is another way of writing a number raised to a certain power, so in the formula you ought to have right now, it will read 3 to the second power plus 4 to the second power equals c to the second power)

Now, simplify what you've got: (when you raise something to a power, you multiply it by itself however many times the exponent (the tiny number at the top right or the number right after the roof-top sign) tells you. So if you had 6^2 it would be 6 times itself twice; like this: 6x6 and that would give you 36 :)  )

9+16=c^2

Now, to solve for the variable you don't know (or the side you don't know - which, in this case, is shown as c ), simplify the '9+16' bit ( it equals 25). Now you still have the c to the second power to get rid of; to do that, you have to take the square root of both sides (what you  do on one side of the equal sign, you have to do to the other, and if you don't know what the square root symbol looks like, just imagine a long division bar that has a check-mark-like thing on the shorter end). Since taking the square root of something is the opposite of raising it to a power, the c squared under the square root bar (more specifically called the radical bar, that's what I'm gonna call it from now on) cancel out, you  should just have c on one side of the equal sign. Since you have to do the same thing to both sides of the equation, you also have to take the square root of 25. Now, to take the square root of something, you have to find a number that, when multiplied by itself, equals the number you're taking the square root of; in this case, when you take the square root of 25, you get 5 (since 5x5=25, 5 times itself equals 25; that also makes 25 a 'perfect square" just FYI)
    After all that you should have:

5=c which gives you the measure of the missing side of the triangle I had you draw earlier... you can do this with any right triangle that has two side measures given- and they don't always have to be the two legs of the triangle that are given to you, it could be the hypotenuse (the slanted side) and a leg- just remember to plug in your measures given into the equation.


If you have any  questions, leave a comment, and I'll get back to you as soon as I can! Happy mathing!

Remember- if you need extra help on this go to www.khanacademy.org
and type in Pythagorean Theorem and a bunch of videos will pop up.

-Bye :)


  

Intro: math is life

    Hey, hey peoples of the world! This is my first ever blog that isn't for school so I'm pretty excited. You may be wondering what the whole 'math loving' bit was about and it's as simple as this- I LOVE MATH! Everybody says "music is life" or "food is life" but if I had a say in what life really is, I'd say it's math.
     Every time I post on here, I'll include a mathematically related tidbit at the end or at the beginning or just somewhere in the post. If you have questions about the formula or concept that I post, just write a comment and I'll get back to you as soon as I can to explain it in the best way I know how. Now note that I don't know everything there is to know about all the topics I'm posting but I will give you a place to go for more help- khan academy. I'll post the link here at the very bottom of this post and sporadically throughout the post that I put on here just incase you lost access to this post.
    Okay- that's all I've got so here's the link:

             http://www.khanacademy.org/

I know the whole 'make an account' process can be a little intimidating and I usually don't make accounts if a website asks for one, but this one is legit. It's free (like, COMPLETELY free, not the kind where it says it is then charges you a million bucks) and it has videos that don't run on Adobe Flash Player (for all those people out there whose PC won't download Flash Player- at least I hope there's a bunch out there; it would suck if I was the only on :(  ) and it is SUPER helpful. you just type in a topic you're having trouble with and a bunch of videos will pop up for different levels of understanding- it's EPIC - just take my word for it.

    Alright peoples- math geek out!!     : D