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Date Written: September 18th, 2016
Shortcuts are ways to do things faster, and the same thing goes for math. Shortcuts in math lets us find the solution of a problem
quicker. Shortcuts are of no use if we don't know why it works. So, cross multiplication is a shortcut for us to utilize. Cross
multiplication works only because when we get the product we have to convert the fraction into lowest terms. To multiply those big numbers,
it might take a lot of time, so that's when cross multiplication comes in. Since the product will be converted into lowest terms, we could
use cross mutiplication to do things a lot faster. One example of this would be whe we are multiplying 6/10 times 50/24. Those are some big
numbers. The multiplication is easy but converting it to lowest terms isn't. We can only utilize the denominator or bottom number by the
numerator or top number. In cross multiplivcation we have to find a common factor between 2 of those numbers. A common factor between 6 and 24
is 6. So, 6 divided by 6 is 1 and 24 divided by 6 is 4. Now the fraction is 1/10 times 50/4. Another common factor would be between 50 and 10
and tha common factor would actually be 10 itself as well. Sometimes the factor will be itself and sometimes it won't be the number itself.
1%0 divided by 10 is 1 and 50 divided by 10 is 5. So, the new fraction would be 1/1 times 5/4. 1 times 5 is 5 and 1 times 4 is 4. So, the answer
is 5/4, but we have to make that into a mixed fraction and that would make the answer 1 and 1/4. Cross multiplication is an easy way of multiplying
fraction and it can help out alot when one has to deal with humongous numbers. Another shortcut to compare fractions is one that most people
don't use. Lets say that we are comparing 3/6 and 4/5. This time we multiply the numerator and go across and multiply with that number. Then,
we have to do teh same thing to the next fraction. 3 times 5 is 15 and 6 times 24 is 24. The 15 will always represent the fraction on the left
and the 24 will always represent the fraction to the right. Since the 24 is bigger and that represents the fractions to the right then the
bigger fraction is 4/5. Another trick only works when the numerator is 1. This trick is that the fraction with a smaller denominator is actually
a greater fraction. The normal way that people do this is that they convert the fraction to have the same denominator and see the fraction with
the greater numerator and that will be the answer. An example of tis process being used is to compare 6/4 and 5/2. First off we have to check if
the denominators are the same and if they aren't the same we have to change it to have the same denominator, If we do that then the fractions will
be 6/4 and 10/4. Since 10/4 is bigger then the answer will result in 6/4 is less than 5/2.
Date Written: August 26rd, 2016
Fractions, decimals and ratios all work together. These chapters are blended into one big chapter! It is easy to do these types of
math. Lets start off with adding fractions. In order to successfully add fractions, we have to make the denominators the same. To do this
we have to find a common denominator. It doesn't matter if it is teh least come multiple, unless the question asks the person to. An example
of 2 fractions would be 5/6 and 6/11. A way to always find a common denominator between any amount of number is to multipy the 2 numbers.
Since we want to find a common denominator, we take the denominators, and multiply them. 6 times 11 is 66., so we know that is a common den-
ominator. 6 times 11 is 66, so we have to multiply 11 to 5 which would conclude to an answer of 55/66. Since 11 times 6 is 66, we have to
6 times 6 which would give us an answer of 46. So, 6/11 is also 36/66. Now, our original problem was to add these, and we still haven't used
the numerators. Now we will, and the numbers that we add are the numerators, and we can only add the numerators when we have the same denominator.
We have the same denominator on both fractions, so we can add the numerators. If we add the numerators, we would get an answer of 91/66. We
have to reduce this into a lowest terms, so the fraction would be 1 and 25/91. We can't reduce this any further, so this is our final answer.
To subtract any fraction, we haae to have common denominators like in addition. Since we arleady know the fractions with common denominators
from before, lets use those fravtions. 55/66 and 36/66 are the fractions. Just like we add the numerators, when we want to add the numerators,
we have to subtract the numerators when we want to subtract the numbers. So, 55 minus 36 is equal to 19/66. SInce 19 is a prime number, we
can't reduce this fraction any more. Multiplication is not similar at all to addition and subtraction. Multiplication has a lot less extra
work. So, lets use the fraction 5/6 and 24/30. When we are doing multipliaction for fraction, would multiply the numerators individually and
the denominators individually. So, 5 times 24 is 120 and 30 times 6 is 180. So, the fraction is 120/180. We can divide both of these numbers
by 60. So, 120 divided by 60 is 2, and 180 divided by 60 is 3. So, the fraction would be 2/3. Their is a much easier route we could've took
and that is cross multiplication. Cross multiplication can make thigs a lot faster. Math can be done by using shortcuts, but a shortcut may
be the wrong way to go, because if you don't understand why the shortcut is working, then that person shouldn't even be using that shortcut.
In order to solve a problem, they have to understand it first.
Date Written: August 25th, 2016
Math is everywhere. Math can go up to a high level, which takes a lot of time, but it also might the easiest thing that one has done
in their lives. Math isn't hard, but time consuming which makes certain people to give up. Math also uses a lot of thinking which also means
that people have to use their common sense, in order to successfully master it! Anyway, the ratio of 5:6 was turned into a decimal of .83333
and so forth. Just because this decimal is a repeating decimal, we will round it to the nearest hundreth. So, if we round this to the nearest
hundreth, then we would get an answer of .83. This is obviously a decimal, and if we want to have a percent, then we have to convert it to a
percent. So, to convert the decimal into a percent, then we would need to move the decimal to the right 2 space. If we do this, then we would
get a answer of 83%. Now, I will do a word problem. So, we have 43 goldfish. We sperate them into different colors. Lets say that we have 11
red, 17 blue, 7 green, and 8 gold. We add these up to make sure that we have 43 goldfish. 7+8+17+11=43, so we have counted right., Now, we have
to write the data down in fractions. Since we hae 11 red, the fraction for red would be 11/43. The fraction for blue would be 17/43, the fraction
for green would be 7/43, and gold would be 8/43. Now we want to convert these fractions into decimals, so 11/43 would be equal to .26 rounded to
the nearest hundreth, 17/43 would be .4 of the whole entire gold fish. 8/43 would be turned into .19, 7/43 is also .16. So, we now have to
convert all of these decimals into a percent, and all of these decimals are rounded to the nearest hundreth. If we convert .26, and that
would be turned into 26%. .4 will be converted into 40%, while .19 is 19 percent and .16 is 16 percent. Lets add these numbers up in order
to find out of we are right, and if we don't get 100 percent, then it is fine because we have rounded the numbers. So, 26 percent plus 40
percent is equal to 66 percent. 66 percent added to 16 percent is 82 percent, and 82 percent added to 19 percent is actually equal 101%. That
doesn't really matter, because we have rounded these numbers. Any math can be done by anyone. Their was a point of time where their were no
zeroes, and the Gregg and Egyptian people found out about zero. Lets say that that a person has 8 million dollars lottery ticket or something
around the lines of that. Well, without zero, he would only have 8 dollars, which makes zero special. A lot of people say that zero isn't
a special number, but zero is the only number when added to, that answer will always be the number that is not zero. An example would be 8+0
which is equal to 8.
Date Written: August 24rd, 2016
Wherever a person goes, they will find math. Math is everywhere, and even in sports. In sports people use numbers to dictate the
score, and if math wasn't a subject, then their will probably be no other way to keep track of the score, making sports never existing. A
lot of people depend n sports for fun, and sports depend on math, which basically means that people depend on math. Math includes a lot of
steps. Math isn't hard, but understanding and breaking the problem down bi by bit give us an answer. Math has a lot to do witha lot of things.
Turning fractions into percentages, isn't hard but contains steps to think a lot more about the problem. To convert a fraction into a percent.
the 1st step is to turn the fraction into a decimal. So, the numerator divided by the denominator will equal to an equal decimal of that
fraction. If the decimal is really long, then I would just round it to the nearest hundreth. If the decimal is a repeated decimal such as
the fraction of 1/3, then that will be equal to .333333333333 and so on. Then, I would do the same thing which is to round it to the nearest
hundreth. .3333333 and so on is round to only .33 when it is rounded to to the nearest hundreth. If we converted this to a percent, then it
will result in 33%. .333333333333333 and so on is actually equal to 1, because that is equal to 1/3, and 1/3 times 3 is 1. Also, that might
not make any sense since .333333333 and so on is equal to .999999999999 and so on, but that is such a close number to 1 that people put that
as 1 instead of .9999999 and another reason why they say that it is equal to 1 is because they round it up. Anyway, the fraction that we
wanted to convert wasn't that big, but bigger numbers will probably be a lot more time consuming. Anyway, as a reminder, percents are way
of showing a number out of a 100. Ratios can be turned into a percent, but their are a lot of steps to go throught. The 1st thing that we
have to do to convert the ratio into a percent is to convert the ratio into a fraction. The antecedant is always the numerator, and the
descendant will always be the denominator. The antecedant is going to be the number all the way to the left, and the descendant will always
be the number all the way to the right. Lets use the ratio of 5:6 as an example. Since the 5 is the antecedant, then it will be the numerator,
and since the 6 is the descendant, then the 6 will be the denominator. So, the fraction will turn out to be 5/6. This fraction will be needed
to turn into a decimal, so 5 divided by 6 is actually equal to .833333 and so on with the threes! Every single problem in this world will have
at least some math in it.
Date Written: August 22rd, 2016
Many people think that math is a subject just like the other ones, but that isn't true. Math is a subject within other subjects. One
can discriminate math from any other subject if they say that math is a subject within other subjects, and no other subjects have a unique
quality up to the amazingness of math! In math, their are lots of chapters. From just normal arithmatic to even calculus, their is one part
of math that isn't like others. That part of math is percentages, fractions, decimals and how they can work together to form into an equal
number in a different units. Lets start off with percentages. Percantages is a way of showing a value out of a 100. So, if something is
67/100, then the percentage will be 67%. One little trick that people barely notice is that the percantage has a 1 and 2 zeroes. The line is
supposed to mean a 1, and the 2 circles are actually supposed to mean 2 zeroes! That is a pretty cool thing! Anyway, percents are used to show
a part of something. To convert a decimal into a percent, the person has to move the decimal point 2 spaces over. An example of this is when
we work with the decimal of 6.3321. The decimal point is right in front of the 3 right now, so we have to move the decimal point 2 space to the
right. So, if we do that, then the answer would result in 633.21%. It is possible to sometimes get a answer of something over 100%. To convert
a percent into a decimal, we have to do the opposite of what we did when we were converting the decimal into a percent. The movement of decimal
was 2 to the right when we wanted to make the decimal into a percent, so to do the opposite of that, then we have to move the decimal 2 places
to the left. So, the perecnt is 633.21. If we wanted to make it into a decimal, then the answer would be 63.321, and that would be a decimal.
To make a convert a percent into a fraction, we have to first convert it into a decimal. Lets use the examply of 63.3121%. Then, if we would
convert that into a decimal, then the answer would be .633121. Then, we will need to convert that decimal into a fraction. To convert that
decimal into a fraction we have to make the numerator into every single number that we can see in the decimal, and then the denominator will be
1 and then the number of zeroes after the 1 will be the number of digits in the decimal. So, in this case then the answer in a fraction will be
633121/1000000! That is a big fraction, but if we reduced to lowest terms, I am pretty sure that the answer would have small numbers! Anyway,
that is how one can turn a percentage into a fraction. We only have to do the reverse of what we just did to turn the fraction into a percentage,
but their are a lot of steps.
Date Written: August 22rd, 2016
Many people use math. From 12:00 A.M., to 12 A.M the next day. Even time consists math in it! The formula for finding the distance to
go, is the formula of speed times time. A real life situation of this formula being used is when a car has a speed of 50 KM an hour. The time
it takes for the car to go the distance that it needs to go is 6 hours. Well, the formula is speed times time, and that would 300 KM. To do this
we had to use the unitary method, because what if the speed was 240 KM in 4 hours. Then, the 4 would have to turn into a 1, and since 4 divided
by 4 is 1, we divide 240 divided by 4 to get the speed of one hour, which will conclude to an answer of 60 KM per hour. Then, we have to multiply
the time times the speed. The times is 6, so 60 times 6 is 360, and that will be the answer! As you can see, a person will have to know how to
use the unitary method in order to solve some of the time, speed, and distance. The unitary mehod is when a person has to change the number to 1
to see what would hapeen in that 1 unit, and then we have to multiply or divide that to find the answer. A word problem about speed, time and
distance is that if a person goes 60 miles in a half hour, and he has x hours to drive there. Then, what is the distance to go there. Well, the
first thing that we had to do is use the unitary method. We could convert the 30 into one minute and see how fast the car would go in just a minute.
So, if we turn the 30 into a one, then we have to divide that by 60 miles, so we could see what the distance is in just one minte. So, 60 divided
by 30 is 2, and that is how much it goes in a minute. The next step is to see what the speed of the car is in one hour or sixty minutes. Since
the car goes 2 miles in 1 MINUTE, we have to work with minutes, and not hours. So, 1 times 60 is 60, and that means we multiply this by 60, and
2 times 60 is 120. So, the speed of the car is 120 miles per hour. Since the guy has x hours to drive his car, we multiply 60 times x, which would
give us the answer of 60x. Math is a master of masters. It basically rules every single subject, because it is the only subject in this whole
universe that is always in every single subject. Whether it is a tiny bit of math in just a subject or a lot of math in a subject, it will always
be a subject within every other subjects. Even computer programming consists of numbers, because some programs have a lot of numbers, and if one
wants to set up their font size, they type like 60%, or they can choose any font size. Also, another reason how computer programming consists of,
is because if someone is trying to write a special, then they might just need a certain number of lines to write the program, and numbers are a
part of math.
Date Written: August 21rd, 2016
Math is used everywhere. From stores, to even science! The people that work at stores use acalculator to add up the number of prices of each object,
which is using math. Astronomy is included in math and science. In science we observe and look at things, but to sometimes know a certain fact about the thing
that the scientist is observing or making inferences about, we have to use math. In astronomy, some scientists like to know how far away a planet is, and that
takes math to find the answer out. As you can see, math is basically the king of subjects. Within the smaller subjects, their is math. In social studies, we
might observe an artifact from years ago, and some people use math to guess how long ago the artifact was made. In reading, some people test a person's words
per minute which includes math. Even to grade a test, one uses math! Math is everywhere, and it will always be used. Anyway, a chapter of math is Speed, distance
and time. The formula to find the speed is to divide the distance over time. So, the formula is distance/time. One example of this formula being used, is when
a person has to go 60 miles. He drives 3 hours at a steady rate. Then, all we have to do is take the distance and divide it by the time. So, the formula should
be turned into the expression of 60/3, which will conclude into an answer of 3 hours! The formula to find the distance is similar, but slightly different. The
formula of finding the distance is to multiply the speed times the time. Lets say that the speed of an object is 60 KM per hour. The time the object takes is
3 hours. So, the formula is 60 times 3 which wll equal to 180 KM, and that will be the distance. The formula for finding the time is to divide the distance by
speed. So, the formula is distance/speed. An example of a real life situation of using this formula would be when a person needs to go a distance of 30 kilometres,
and his speed is 60 KM per hour. This problem is a bit different than the other 2 scenarios. Lets think of the one whole hour in 60 minutes, because an hour
is also 60 minutes long. Anyway, their are 2 ways to solve this problem. Since we need to go 30 KM, and we travel 60 Kilometers in an hour, we could just
divide our time by 2 , which would give us 30 minutes. The other way we could solve this problem is by using the unitary method. The word unit means 1.
In the unitary method, one has to find the distance that the object can go in 1 minute. To do this, we divide 60 KM, by 60 minutes which will get us 1
KM per minute. After that part is done, we need to find how much time it will take us to get to the 30 KM. So, We need to go 30 times faster, which will
make us go for 30 minutes. tHis is just like a ratio. So, lets pretend that we are using a ratio. The ratio will then be 1:1. We want to go 30 KM, so we need
to make something equavilent to this. Since, 1:1 si 1, we need to make the x in 30:x be a number when it is divided by 30, we will get 1. The only number that
can come up to these requirements is the number 30 itself!
Date Written: July 9th, 2016
Algebra ia a type of math. Usually, in algebra, one will have to solve word problems. So, lets do some word problems. One word problem might be that I had X apples,
but my sister had 3 times the apples, but my dad had 6 times more thatn my sister, but then my mom has 3 times my sister, and the total number of apples is 310 apples.Well,
their are a lot odf numbers in this problem, but we can sort them out. Lets make my name x. So, x has 24 apples. Lets say that my sister's name is y. So, I have x apples,
and my sister has 3x apples, because she has 3 times the amount of apple. Since, they have given me the total number of apples, we want to make it into one whole thing,
my mom will have like 10x. Anyway, my dad has 6 times the amount of my sister's. Since, my sister is 3x, we multiply that my 6 to get the amount of how many times I do. 6
times 3 is 18, which would mean that my dad has 18x apples. Now, my mom has 3 times my sister, so 3 times 3 is 9, which would mean that my mom has 9x apples. Now, lets add
all these apples up, and that would be 1x+3x+18x+9x. That expression would have an answer od 31x. So, now we know that 31x will be equal to 310, because both of them are the
total number of apples. To find x we eed to bring the 31 to the other side to leave the x alone. Since the 31 is in a multiplication format, we need to reverse its format,
to come to the other side. The reverse of multiplication is division, which would mean that x is equal to 310 divided by 31. That would have a quotient of 10. We are still
not finished, because that is the answer for x, but we can multiply that by 3 and 18 and 9, to find out everybody else's number of apples. So, my sister would have 3 times
10 apples which would be 30. My dad would have 180 apples, because 10 times 18 is 180. My mom would have 90 apples, because 10 times 9 is 90. Lets now add these apples to
check if we are correct, and if we are right, then we would come up with an answer of 310, because that is the number of apples. So, 10 plus 30 is 40. 40 plus 90 is 130.
130 is a lot farther away, but remember that my dad got a lot of apples. My dad had 180, which would mean that 130 plus 180 would have to equal 310. 180 plus 130 is 310,
which means every single answer of ours was correct. The word problem isn't that hard, but just the math. Anyway, lets do another algrabic word problem. So, a father was 4
times the age of his son, but the son's age was in 2 digits. Also, his mom was 3 years younger than the father, and the total of their ages was 132 years. So, lets take the
mom out of the picture, and in order to do that we have add 3 which would give us the ages of 2 fathers or 135 years. 1 father's age is 4 times son, so 2 would be 8 times
son, plus 1 times son for the son himself. So, 9 sons is equal to 135. Then, we have to divide 135 by 9 to find out the age of just oone son. The quotient would be 15. The
age of the son is 15, while the age of the father is 15 times 4 which is 60. The father will be 60, and the mom is 3 years younger than the father which would make the mom
57 years old. When add all this up, the answer should be 132 and not 135, because we added that 3. So, lets add. 60 plus 15 is equal to 75, and 75 plus 57 is 132! So, we were
right.
Date Written: July 8th, 2016
Ratios can represent fractions. When someone writes 2:8, they can say that as 2 is to 8. That is a ratio, and how one will say a ratio correctly. The number on the
left is always the numerator. The number on the right will be the denominator. So, 2:8 is also 2/8. The number on the left in a ratio is called the antecedant, and the
number on the right is called a consquent. A ratio, like a fraction,, can be converted to lowest terms. The ratio that we were using, could be made into lowest terms.
2:8 is also 1:4. One can check this by making 2:8 a fraction, and then converting it into lowest terms. Some ratio word problems will use equavilent ratios. One ratio
word problem could be that I would read a ration of 25:20, and then they would want to know how mny pages I could read in 200 minutes. So, 25:20 is also x:200. Well,
200 divided by 20 is 10, so we have to multiply 25 times 10 to get xor the answer to the problem. 25 times 10 is 250, and that would mean that x will equal 250. The
answer would be that I could read 250 pages in 200 minutes. That happens a lot in ratio word problems. Anyway, some other things about ratios are that ratios could be
a ratio to another ratio. What I mean by that is that 25:10::10:25. Also, another thing about the fact about ratios that I just said, is that 25:10 is also 25/10. 10:25
will also be 10/25. So, the fractions are 25/10:10:25. Well, the number that is diagonal from the other number will be equal to the other numbers that are diagonal to
each other. So, a ratio word problem might give someone the ratios of 40:60, and 9:x. They will ask that person to find the value of x. Lets do this problem, First off,
we always want to convert the ratio into a fraction. So, the antecedant of both the ratios is the numerator, and the consequent is the denominator of the ratios. Here,
the fractions will be 40/60 and 9/x. Given the rule that I just told you, we want to know the value of x. So, 40x is also equal to 60 times 9 or 540. So, we know that
40x is equal to 540. Right now, the 4 is going to multiply times x, but when someone wants to bring a number to the opposite side, they have to use the opposite sign.
Since there is a multiplications sign, we have to make it into the opposite of a multiplication sign which will bring use to a division sign. So, we are bringing the
40 to the other side, which means the x will be alone. If the x is alone, that will then give us the answer. The left side is just x while the right side 540 divided by
40. The answer will be 13 and 1/2. X will be equal to 13 and 1/2. Lets do another problem. Another problem would be 147:199 and 138:x. This one has bigger numbers, but
it uses the same process, except a little bit more math. So, 147 is the antecedant for the first ration, which means it will be the numerator, while 199 is the consquent,
which would make it the denominator. The ratio will be turned into a fraction of 147/199. The other ratio will be turned into 138/x. Okay, so now wwe apply the rules.
147x will be equal to 199 times 138 which would equal 27,462. The 147 is still in a multiplication mode with x, so we want to bring it to the other side to find the value
of x. The left side would be just x, while the right side would be 27,642 divided by 147. So, X would have a value of the answer to that which would be a pretty big
number, and I would reccomend using a calculator, because my teacher said that it isn't about the math, but how one does it. To be continued.
Date Written: July 7th, 2016
Decimals are a lot easier to work with than fractions, but sometimes one needs to use decimals instead of fractions. Lets just start off with comparing decimals.
To compare decimals one needs to go from left to right. If the whole number, or the number all the way tof the left is the same, one will need to look at the next digit
in the number. Once, one digit is bigger than the other one, then that will be the number that is bigger than the other number. Comparing decimals is a lot easier than
comparing fractions. Anyway, lets do some math now. Adddition with decimals is easier than adding fractions. To add any decimal, one needs to add it like a normal number,
but then bring the decimal point down from where it was. One example of this 0.5 plus 0.5. If you add it normally it would be 10, but I have to take that decimal point
down from where it was before. If I were to do that, then the answer would be 1.0. Lets do subtraction with decimals now. IN subtraction, one needs to do the same thing
that they did in addition, except the person has to do a subtraction problem. Multiplication is a little bt complicated, just like fractions. Its not that hard thought.
Lets get straight on to it. In multiplication, one will need to do a normal multiplication problem, but one will need to find how many numbers there are after the decimal
points in the multiplicands. Then, the person doing the math problem will need go the number of places after the decimal. That might make sense, but it will make sense
later on. Division is the weirdest one. To do any decimal division problem, one can turn a decimal into a fraction and then do the division like on does it with a fraction.
Lets talk about how to change a decimal, because one will not be able to do adivision problem without knowing how to change a decimal into a fraction. To change a decimal
such as the decimal of 3.5, into a fraction, we will need to make the numerator all the digits in the fraction. Here, the digits are 35. That will be the numerator. The
denominator will be a 1 and then, we will have to count the number of digits after the decimal place. The number of digits after the decimal place will be the number of
zeroes we will have to put after the 1. We have found the numerator, so let us find the denominator. Since, there is only 1 digit after the decimal point, we add only
one zero after the 1. The fraction will be 35/10, and if we convert that to a mixed fraction, then it would be 3 and 5/10. Remember, that we could always convert it to
lowest terms, and in the this case, the 5/10 would be converted to 1/2. The new fraction would be converted to 3 and 1/2. Lets now do a division problem, because we know
how to do it. Lets say that the problem is 0.5, and 2.4. the numerators will be the numbers in the whole decimal, so the numerators are 5 and 24. The denominators will be
10 for both. So, the fractions are 5/10 and 24/10. The 5/10 will stay like it is, but we will have to change the division sign into a multiplication sign, due to the fact
that one needs to do that to do a division problem. Then, we need to find ot the recipricol of the fraction. The recipricol of 24/10 would be 10 24. We then multiply the
fractions. To be continued.
Date Written: July 6th, 2016
Comparing fractions are really easy and won't take much time to do, so let's start this article by comparing. To compare fractions, one needs to have a common
denominator between those fractions. Let's say that I want to compare 5/12 and 5/11. To compare these fractions, we need a common denominator between these number. If
one needs to find a common multiple between two number, they can multiply the 2 numbers. It won't be the lowest multiple, but it sometimes will be. So, 12 times 11 is 132
, and one has to multiply 11 from 12 to get to 132, so 5 times 11 is 55. One of the new fractions that I would be comparing is going to be 55/132. In the other fraction
132 divided by 11 is going to be 12. Now, I have to multiply 12 times 5. 12 times 5 will be equal to 60. So, the new fractions are 55/132 and 60/132. Now, we compare these
2 fractions, and we only compare the numerators of these fractions. The numerators are 55 and 60, which means that 60/132 is bigger. 2 shortcuts to comparing fractions is
to multiply the numbers that are diagonal from each other and the bigger number is the bigger fraction. The other shortcut to compare fractions, can only work if the
numerator on both the fractions that one will be comparing, is one. If the numerators are 1, then that would conclude for us to look at the denominators. In this case,
the fraction with the smaller denominator is the bigger fraction. As you can see, to compare fractionsone doesn't always have to think about big. One example of this
would be by comparing the 2 fractions of 1/2 and 1/3. The shortcut states that it has to have a same numerator, and that is what we have got in these fractions. Now,
let's look at the denominators. The denominators are 2 and 3, but 2 is the smaller one, and that would mean that 1/2 is bigger. Now, let's use the normal way comparing
these fractions. In the normal way we have to find a common denominator, and one common denominator of these numbers is 6. Now, 6 divided by 2 is 3. The 1/2 fraction
would turn into 3/6. The 1/3 fraction would turn into 2/6, because 6 divided by 3 is 2 and 1 times 2 is 2. Now, we compare 3/6 and 2/6. 3/6 is the fraction with the b
igger numerator, and 3/6 used to be 1/2, so 1/2 is bigger than 1/3. Those were 2 easy ways to compare fractions, and that is how people do ascending and descending
order problems. Speaking of those types of problems, let's talk about it and how to do it. In ascending order, one needs to compare numbers from smallest to greatest, and
it is easy doing that with regular numbers, but it is a bit harder with fractions. First of all, one needs to find out a common denominators between all those fractions.
Once the person has found one between then, they make equavilent fractions of themselves, and then that person has to group them from smallest to loweset, or in this case,
the smallest numerator to the biggest numerator. In descending order, we have to group the numbers from greatest to lowest. Once again, we find a common denominator, and
make equavilent fraction, and we group those fractions from greatest to smallest, but for fractions we only look at the numerators to campare fractions. That is all in
today's article. To be continued.
Date Written: July 5th, 2016
Their are a lot more things to math than just fractions and decimals, but we were talking about it, so lets continue. We had finished off talking about how to
add fractions. So, lets talk about how one can subtract fraction. It is basically the same as adding fractions, except the person doing the math problem has to subtract
the numerator instead of adding. Multiplication is a little different. In multiplication, one does not need to make a common denominator, but just to multiply the numerator
times the numerator and the denominator times the denominator. One example would this would be 4/9 times 5/10. The numerators are 4 and 5 ad when somebody multiplies them,
they will get 20. The numerator will be 20 and the denominator will be 9 times 10, which is 90. In conlusion, the answer will 20/90. Most of the time, one will need to
simplify the answer. Simplifying means to make a fraction that is equal to that fraction with smaller numbers. To simplify, one needs to find a common factor between the
denominator and the numerator. In this case, a common factor is 5. Then, the person has to divide the numerator by 5 and the denominator by 5. 20 divided by 5 is 4, while
90 ddivided by 5 is 18. The new fraction will turn out to be 4/18. As you can see, the new fraction be simplified again, and one common factor would be 2. 4 divided by 2 is
2, and 18 divided by 2 is 9. The even newer fraction would turn out to be 2/9. 2/9 can not be simplified further, and a fraction that can not be simplified anymore, is
called lowest terms. Back to the multiplication. 2/9 will be the answer of that multiplication. The fraction may seem than the fraction multiplicands, but if one uses
simplification, then the fraction would make sense. The fraction isn't really smaller than the multiplications though. The most complicated of them all, is actually division.
When someone is doing a fration division, that person will keep the fraction on the left, by itself, but that person will need to change the division sign to a multiplication
sign. ONce that is done, the person will also need to put the recipricol of the fraction on the right. The recprical is when someone flips the fraction around. One example
of this would be when someone will need to find out the recipricol of 5/11. The recipricol would be 11/5. Once they have done every single solitary step, they need to
multiply the fractions. One example of this would be 4/5 divided by 3/5. 4/5 will stay like it is, but the division sign will turn into a multiplication sign. The fraction
of 3/5 will need to be changed to its recipricol, which would be 5/3. Then, you multiply these fractions. The numerators are 4 and 5. 4 times 5 is equal to 20, and that
would be the numerator of the quotient. The denominators in the fractions are 3 and 5. 3 times 5 is 15, and that would make the new fraction be 20/15. 20/15 would also
be the answer to that division problem. 20/15 can also be mad into a mixed number since it is an improper fraction. The mixed number would be 1 and 5/20, while that could be
simplified to 1 and 1/4. Its time to do some decimal stuff, but we will get back to fractions later on. One can change a decimal to a fraction or a fraction to a decimal.
To be continued.
Date Written: July 4th, 2016
We left off talking about 2 step equations, but we will do some other stuff in math. We will talk about Time and distance and speed. To find time, the formula
would be distance divided by speed. One such example of this would be when one needs to go 50 kilometres. Also, his speed is 25 kilometres an hour. Now, the formula
to find the time states that distance over time is te way to figure it out. In this case, the distance is 50 and the speed is 25 kilometres an hour, which means that
it would be 50 divided by 25. The quotient would be 2, and it would take that person 2 hours to go 50 kilometres. That is for time, but for speed, it is a little different.
To find the speed of something, one needs to use a formula of distance divided by time. One example of this would be when a person would need to go a distance of 25
kilometres, and walked for 5 hours. Then, the expression would be 25 divided by 5 and the answer would be 5 and that would result to 5 kilometres an hour. That's how
anybody can find speed, but distance is a lot more different. the reason I say that is because the other formulas were division ones, but the distance one is has to
do with multiplication. The formula to find the distance is to use the formula of speed times time. One example of this would be when one goes 20 kilometres an hour.
That person also takes 5 hours to reach his destination. So, if someone uses this formula to find out the answer, then the expression would conclude to 20 times 5,
and that would have a result of 100 kilometres, and that would be the distance. Those are all the formulas and examples about Speed, time and distance. Now, we will
get onto fractions and decimals. A fraction is a number that represents how many parts are taken out of a whole. The topp number in a fraction is called the numerator,
and the bottom part in a fraction is called the denominator. Sometimes, the numerator will be bigger than the denominator. That is called an improper fraction. Anybody
can change an improper fraction to a mixed number. A mixed number is a number with a whole and a fraction. The way you can change an improper fraction to a mixed number
is by dividing the numerator by the denominator. The quotient would be the whole number and the numerator of the fraction would be the reamainder and the denominator
would be the divisor. You can also multiply fractions, add them, subtract them or even divide them. Lets start off talking about adding fractions. To add fractions
you need a common denominator, and then you add the numerator, but not the denominators. One example of this would be when when you ad 1/4 and 1/5. To add them, one
needs to find a common multiple of the denominator. A common multiple of 4 and 5 is 20. So, what you need to do the bottom, you need to do to the top. 20 divided
by 4 is 5. So, 1 times 5 is 5 and the denominator is going to be 20. The new fraction would be 5/20. Now, lets get on to the other fraction. 20 divided by 5 is 4.
The denominator will be 20 and 1 times 4 is 4, and the new fraaction will be be 4/20. Now, if someone adds these fractions, the answer will be 9/20, because one can't
add the denominators.
Date Written: July 3rd, 2016
We took a big leap from June 18th to July 3rd, but its back to math! Negative number are numbers below 0. One will say 1 below 0 or negative 1 to describe -1.
To add a negative number one has to think about it 1st. Here's an example:-7+5. Lets think about this. So, if you have to give someone 7 apples, and then you give
them 5 apples, then you would need to give the person 2 more apples. That's how anybody can add a negative number to a whole number. The same method can not be used
when one is adding a negative number to another negative number. An example of this is to add the number -8 and -24. The equation would look like -8+-24. If a person
had to give 8 bananas to a person, and had to give the person 24 more bananas, then the person owing the other person would have to owe 32 bananas, and that makes the
person owing the bananas have to give 32 bananas and is 32 bananas short of what he is supposed to pay. The answer would then be -32 bananas. Now, onto multiplying
negative numbers. To multiply negative numbers, one will need to follow the rules. So, if anybody is multiply a negative number by a negative number, then the answer
will be the multiplication of the numbers and it would be in positive form instead of a negative form. So, -3*-24 would be 72, because when a problem has the same
form, then the answer will be in a positive form. 24*3=72 by itself, and then the problem has the same forms which means the answer will be 72. Some other types of
maths are 2 or more step equation word problems. I think having the problem with a word problem is easier for me. Anyway, one 2 step equation word problem would be
that I have 16 balls, and then I give out 3/4 of my balls. Then I get 5/4 of my amount of balls that I had before. So, we have 16 balls and then we give out 3/4 of them.
When anyone sees of, then that would mean multiplication. The problem would then be 3/4 times 16. Well, 3 times 16 = 48 and then divide that by 4 which is 12. So,
we give out 12 and 16-12 is 4. We have 4 balls left, but we get 5/4 the amount of balls that we had before, so 5/4 times 16 is 80 divided by 4 which is 20. We also
had that 4 balls from before, and if we add that, then the answer will be 24 balls! Another word problem would be if I had to owe somebody 64 balls and then he gives me,
64 balls, but I don't take them. After I give the 64 ball he owes me 28 balls. He then gives me 6/4 of the amount of balls that he owed me. What would be the amount
of balls I then owe him. This one is a bit more confusing. It starts off with me owing him 64 balls, so I am -64 in balls. He wanted to give me 64 more balls, but I
did not take them. I then paid him 64 balls, but then he owed me 28 balls. The other person gave me 6/4 the amount of balls that he needed to give me. So, 6/4 times
28 is going to be 28 times 6 divided by 4. 28 times 6 168 and then divide that by 4. 168 divided by 4 would be 42. Now, the question says how many balls that I would
have to give him after he gave me 6/4 the amount of balls he needed to give me. He gave me 42 of them, so you subtract 42-28, then the answer would be 14 and that is
the answer to the whole problem. To be continued.
Date Written: June 18th, 2016
Geometry. Geometry is where we had left off. Geometry is also used for lots of things. We had left off talking about angles. Their are 3 different
types of angles, and they are obtuse angles, acute angles, and right angles. We talked about 2 of them and the last one we did not talk about was the acute
angle. The acute angle is an angle that is less than 90 degrees. If someone thinks about it this, then will undersatnd why a 0 degree angle will not be
classified as an acute angle. The only reason why it can't be classified as an acute angle is because it is no angle. A 0 degree angle will just be a straight
line. A 0.1 degree angle would be an acute angle, but it would be very hard to meausure. One can meausure an angle with a protractor. Proctractors look
like semicircles. That was about angles, and now we move on to measurements. Their are different types of meausurements for different objects. One can use
Kilolitres, or gallons to meausure a liquid. Their are 2 types of meausurements, because one of them is metric system, while the other is in the customary
system. The customary system is only used in the United States of America, while the customary system is used everywhere, but America. Well, in the customary
system one gallon is worth 4 quarts, one quart is worth 2 pints, one pint is worth 2 cups, and 1 cup is 8 ounces. Now, onto the metric system. In the metric
system, 1 Kiloliter(You can also say KL) is worth 10 HL, 1 HL is worth 10 DL, and 1 DL is worth 10 L, 1 L is worth 10 dL, 1 dL is worth ten CL, and 1 CL is
worth 10 mililiters. The same thing works to meausure other things, but that's only for a metric system. Well, since the same thing doesn't go for the
customary system, the units that you have to use to meausure length is feet, yards, inches and miles. In 1 foot, there is 12 inches. So, when someone is 5
feet tall, then the person is 12 inches * 5 feet which will equal 60 inches. In one yard there is 3 feet. So a 3 point shot in basketball is 21 feet away, and
that is also equal to 7 yards. So, 7 yard sticks would equal a 3 point shot. In one mile, there is 1760 yards and that is a lot. to find the number of feet,
thee would be 1760*3 and that would equal 5280 feet. That is a lot of feet! Well, one thing that is true, is that the metric system has way easier numbers to
work with, because it is 10s and 100s, while here you have 1760, and that is such an odd number. The customary system is still a system and it is pretty useful.
You have to know a lot to meausure to meausure things perfectly, like to meausure a 0.1 degree angle. That would be pretty hard to determine. That was all the
facts about geometry and now we are onto numbers. You might be thinking that adding and doing math with negative numbers might be easy, but it has a special
twist. See if you can find it in this problem. -8+-7= -1. The twist is that the negative numbers start at -1 and goes backwards. So, -1 is bigger than -2. To be
Continued.
Date Written: June 17th, 2016
Math. Math is a great subject to learn any time or day. If one thinks about how important math is, then that person will realize that you
use math in almost everything. Some examples are, when you find the area of a house, to put a type of flooring, and another example is when you play
a game. You might be thinking how a game can help you in math, but in games, there is always a place where you can earn coins or something like that.
Well, you can always buy something with that amount of coins you have, and you might be doing math, in order to find out how many coins you need to
get what you want. So, math is almost everywhere. Their are different types of topics and I will start off with geometry. The easiest part in my
opinion, of geometry is to find the area and volume. Sometimes, finding the area and volume isn't that easy, be shapes might be irregular shapes. The
equation to find the area of a square is base times height, but that is only for a square. The area for a triangle is base times height divided by 2.
So, if a square's height was 4, and the base was 4 as well, then the area is 16, because 4*4=16. That equation only applies for a square and a
rectangle. Now, if the base of a triangle is 24 and the height is 4, then the area will be 48. The reason it is 48, is because the height is 4 and
the base is 24. If you multiply those 2 numbers, then it is 96, but you have to remember that you divide by 2. So, 96 divided by 2 is 48. Some irregular
shapes are just weird looking, but there are ways to find the area. A lot of times someone will see 3 stairs, and then it will be asking to find the area
of the whole thing. It will also give you the lengths of each side. So, if you think about it, there is 3 stairs. Each square is 1 rectangle. So you
find the area of each rectangle, with the given lengths of each side. Once you have done that, you add the areas up, and then you find the area. It is
as simple as that. Also, the test may give you the question, to find the length of one side. The test taker may be thinking of how to do that. Well,
all you have to do is to divide the whole area by the given length that they have given you. That was just the easy part of Geometry, but angles are
very hard to determine, without a protractor. Their are 3 different types of angles. The right angle, the obtuse angle, and the acute angle. The right
angle is an angle that is exactly 90 degrees on the spot. A right angle usually will have a square corner. Right angles are also in squares and other shapes.
Now, onto obtuse angles. Well, obtuse angle have a pretty big size. An obtuse angle is an angle that is more than 90 degrees and less than 18 degrees.
So, an obutuse angle can be 90.1 degrees or 179.9 degrees. Their is one common error though. The error is that most people will count a 90.1 degree as
a 90 degree angle or a right angle. It is very hard to discriminate between those two. To be Continued.
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