Category Archives: Metric Conversion

How to find the area of a circle

How to find the area of a circle

Circle is a shape in mathematics just like triangle, square, rectangle, oval etc. A circle is a sphere or a ball and it has many parts like the radius, sector, segment etc. Here we will first talk about the parts of a circle so that it is easy to find its area.

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• Radius: It is simply just a line from the center to the wall of the circle whose name you will know as we move on.

How to find the area of a circle

How to find the area of a circle

• Diameter: It is the double of the radius or the line that goes from one point on the circle through the center and connects to another point and it looks like a straight line. If the radius is 3 cm, the diameter will be 6cm.

• Circumference: It is just the wall of the circle or the part covering the circle and giving its shape like a ball. If it is big, the circle will have a big area and if it is small, the area of the circle will be small.

• Chord: It is simply any line on the circle that touches one part of the circumference to the other. The difference between this and the diameter is that it does not run through the center point of the circle.

• Arc: Arc is any part of the circumference.

• Tangent: It is a line that is touching the circumference and it is a straight line.

• Segment: It is a part that is cut off from the original circle.

• Sector: This is completely different from the segment while many people think they are similar. The sector is the part that is covered on one side by the arc and the other two lines are the radii.

To find the formula, you should know that you can make the circle into a rectangle by cutting into as small pieces as possible, therefore we get Area of circle =Area of rectangle

Area of rectangle is = base X height (base X radius)

The base is the same as radius of a circle and the height is half of the circumference of the circle. The circumference is equal to 2πr.

Base = half of circumference, ½ X 2πr

Cancel out the 2s and you will be left with πr.

Now, we know that base is πr and the height is radius,

Therefore, πr X r = πr²

This is the formula to find the area of any type of circle and here is an example. You have a circle with radius 7 inches, calculate the area.

Area = πr²

Area= (3.14) (7) ²

Area= (3.14) (49)

Area= 153.86 in²

In complicated problems, you may be given the diameter and you have to find out the radius. You need to divide the diameter by two.

Tips

• There is many more difficult formula about circle, that you will utilize later on, the formula is (x – h) ² + (y – k) ² = r² where the center is h and k.

• Check your math answers several times and make sure you use the correct value of π. If the question asks you to find it by 3.14159, use that.

How to find the mean

How to find the mean

How to find the mean? Mean is another name for average. Before getting into depth of what it is, think about some real-life daily examples. You have probably heard people talk about average weights of people your age, average heights, etc. The meaning of the word average means in the middle. For example, you can ask someone what is the size of their company: is it big, average or small. You can guess by now that average means mid-sized. In mathematics, it is no different. Some people can be tall at six feet and others can be around 4 feet so what is the average. The common height people have such as five feet five inches.

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You can utilize a number line two find the mean between two numbers. A number line is an illustration of numbers in a precise order to demonstrate values.

How to find the mean

How to find the mean

______________________________

90                                                         100

Here is a number line representing someone’s score in an exam out of hundred. In one exam, he got 90 and in the other he scored 100 out of 100. When it is represented on a number line, you can tell what lies in between them both. Since, we know from the above definitions that it lies in the middle. You can easily tell without any calculations the mean here is 95.

Secondly, it is a method of finding out the typical or central number in a collection of values. For example, you have a lot of numbers: 3, 3, 4, 5, 2, 3. We can easily tell that the result will be 3. To be exact you need to do the exact measurements. You can follow the formula:

If you do the exact measurements, you will see that the result is not just 3 even though 3 is recurrent. Add the numbers you will get 20. Divide 20 by 6. You can tell that the result will be in decimals or factions because 20 is not a multiple of 6. If the answer is 3.3. If it was 5 instead of 6, the answer would have been a whole number because 4 multiplied by 5 gives us 20.

You should solve the mean step-by-step

Here is an example, find out the mean of 3.5, 45.66, 23.90, 11.2 and 34.34

Step 1: You need to start by remembering what the mean is. It is the same as average. Therefore, write down the formula you got above,

Step 2: Break them down and make the formula look small for ease, quantity of numbers can be shown with a “n” and the sum of all the numbers should be the equation. Therefore, count how many “n” you have. You will have five. Therefore, n is equal to five.

Step 3: The equation is the sum of all the numbers, so start adding them. Write down the equation first.

Equation= {3.5+ 45.66+ 23.90+11.2 +34.34} and n= 5

Now solve them, the result will be 23.72

How to subtract fractions

How to subtract fractions? Fractions just like decimals is an important part of mathematics and children learn them from an early age. It is a must that you understand them or else the further calculation like addition of fraction, subtraction, multiplication and division can get hard. You need to know several things first. First of all, these are regular numbers 1, 2, 3, 4, 5… etc. What exactly likes between them? Do you know there is a huge gap? What if you eat 2 slices of cake and took few bites from a third piece? So what exactly do you say? You had 2 slices of cake or 3? If you are saying two, that makes it less than the original amount you had and saying three makes it more than what you ate. Therefore, there are numbers that you cannot see or but are present among them like 2.1, 2.2, 2.3, 2.4, 2.5…etc. These numbers can be written as fractions as well.

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Here is how you write them as fractions

How to subtract fractions

2.1 =

2.2=

2.3=

2.4=

2.5=

Let us see how we add them

If we are adding 2.5 and 2.5, let us see what we get. The first step is to convert them into fractions. 2.5 means two and a half. Therefore, let us add two and a half together.

Calculation: 2.5 =  (0.5 is one by two in fraction form)

If it is a mixed number, convert it to mixed number and add them. While converting, multiply 2 with 2 and add 1. Therefore, it will be

+  =

Now, simplify the results, and the result with be 5.

You can imagine the situation, that if someone has two and a half buckets of water and there are more two and half buckets of water, you will end up with a total of five buckets.

Addition, is quite easy, let us see how we subtract.

Let us subtract fractions

Question: Subtract  from

Step 1: First of all, start with making the equation consist of only fractions whether proper or improper but get rid of the mixed numbers by the above method. Therefore, change the  (7.5) to mixed numbers.

7 X 2 = 14

14 + 1 = 15

Therefore,

Step 2: Write down the equation as the question and carry out the LCM.

=  –

Step 3: After you get the result of the LCM which is 6, you need to divide 6 with 3 t first and multiply with 53 and repeat the same with two, so that you have something like this

=

Step 4: the trick is to get the same denominator, meaning if you were subtracting  and , there would be less trouble. You could skip the LCM part and simply subtract the numerator.

=  = =

Step 5: The improper fraction in the answer may look improper, so you can either convert it to decimal or to mixed number. If you are converting to decimal, the answer is 10.166666666666666666666666666667, we cannot write like this as well, so just write 10.17.

How to find the area of a triangle

How to find the area of a triangle? Triangle is a shape just like the square, circle, oval, rectangle and etc. There are many kids of tringle such as isosceles triangle, right-angled triangle, equilateral triangle and etc. The one thing common is that they have three sides and three angles. Scalene has all sides of various length, isosceles has two sides to be the same with the other being different, so If you know one side you can know the other and an equilateral triangle is a basic one with all the sides of equal length. That means if you know that one side of the equilateral triangle is 5 cm and the other two sides are not given, you should know that they are also 5 cm. Triangles can be named after their angles. Where all the angles are less than 90 degrees makes it an acute triangle, with one angle as 90 degrees makes it a right angle, one angle more than 90 degrees but less 180 degrees makes it obtuse and when all angles have the same value, it is an equiangular triangle.

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This is the formula for area of triangle. B is base and H is height of the figure. If you have a triangle, the lower part is known as the base and draw a straight line from the tip of the triangle to the bottom. That is the height. It is going to make 90 degrees with the base. If a triangle’s base and height is marked, it would look like there are two of them. One is a small right-angled triangle and the other is a big one.

How to find the area of a triangle

Calculation: Find out the area of a triangle whose height is 10 cm and base is 25 cm.

 

 

Area =

1  

bXh

2

Area =  x 25 cm X 10cm

= 125 cm²

Find out the height is the base is 10 cm and the area is 30 cm²

Area =  x b cm X b cm

30 = 0.5 x 10 x h

5h = 30

Height = 6 cm. (divide 30 by 5)

You can find out the area from its side using the Heron’s formula wps864.tmpwhere s is half of the triangles perimeter, a, b and c are all the sides. S is needed for the formula of the area which is
wps865.tmp

If you know two sides and one angle, that is the angle between the known sides, you can use the formula that involves the sin. That means they could look like this Area = bc sin A. here b and c are going to be the sides you know and A is the angle.

Calculation: Find out the area of a triangle whose height two sides are 8 cm, 5 cm and the angle is 60 degrees.

Area = bc sin A

= 0.5 X 8 x5 x sin 60

= 20sin60 You can use the calculator to get the exact value and write the result in decimal places.

How to find circumference

How to find circumference

How to find circumference? A circle is an important shape in the mathematical world. There are a lot of problems involving it and it has many parts. It has a radius, diameter, circumference, center, arc, sector, segment etc. To find out each of them, there are different formula and techniques.  You will have to know the most common ones, that is the area of the circle.

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How to find circumference

How to find circumference

Let us see how we find the circumference. It is the outer part of the circle that gives it the round shape. You will have to know the diameter in order to find the circumference. The diameter is the line from one part of the circle to the other part and crossing through the center. The formula of circumference is circumference=2πr or πd. Based on the question, you decide which one to utilize.

Example: Find the circumference of a circle whose diameter is 5 inches.

Circumference = π x d (the question says diameter so we picked this one)

= 3.14 X 5 inches

= 15.7 inches (The unit will be the same as the unit of the diameter, for cm the result will be in cm)

The units are normally centimeters, meters or inches. If you order a pizza of 12 inches, that is the value of the diameter. The value of pi is 3.14159 but here we are using 3.14

To remember the formula or if you want to know how it originates, then read on:

π = Circumference / Diameter

We know that, diameter is radius plus radius

Therefore, it is 2r.

Now, multiply 2r with π and you will get the formula of the circumference.

People confuse the area of the circle with the circumference.

Look at the difference, one of them is about r² (area) while the other one is just the diameter which is 2r.

To remember them, you can start by memorizing them. Then, understand that the area is the square where is the circumference requires just the radius two time. You can rewrite the formula of circumference as

Circumference = 2 π r or π (r + r) AND Area = π r²

You can already see the difference and when you do the math, you will see that they are completely different.

Calculate the area and circumference of a circle with the radius 3 inches.

Area = π r²

= 3.14 x 3²

= 28.26 inches ² (The unit is inches’ square)

Circumference = 2 π r

C = 2 π r

= 2 x 3.14 x 3

= 18.84 inches

Now, you can tell that they are entirely different and avoid the confusion.

Tips

• If you are allowed to use calculators to solve this, consider purchasing one that has the built-in π so that you can solve the equations easily.

• Not every math problem will let you use pi according to your wish, you may have to use the fraction value which is

How to find horizontal asymptotes

How to find horizontal asymptotes

How to find horizontal asymptotes? The horizontal asymptote is a y-value present on graphs where a function goes by but never really touches it. The value for why will never be a zero. You can look closely when you see the graph, it will be a zero. They are going to meet the lines and intersect with some values of x and they maintain the same direction. You should know that it is a graph representing a function who will never come in contact.

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In this case, both of the polynomials are in second degree. It is the term that contains coefficients and variables that allows the usage of multiplication, addition and subtraction. If you are still not clear, look at the equations below.

How to find horizontal asymptotes

How to find horizontal asymptotes

x² + 5x + 9 has a single variable which is x.

x³ – 3xyz² + 5 has three variables which are x, y and z.

In the above example, when we said second degree it meant the power of them is square. For example, 4x², 5y² and 8z² are all second degree. If the polynomial is a zero it means that there are not terms at all. If you want to add a polynomial, it is quite simple

A = 3x² + 3x – 5

B = 6x² + 4x + 8

A + B = 9x² + 7x + 3

Here is how you can find the horizontal asymptote of the example given above,

Y =  which means y = 6.

When the polynomial is at different degrees, meaning the numerator has a value of x² and the denominator has a x without any power, then there is no horizontal asymptote.

Here is an example,

We can see that 12 has x and the x has a power of 2 or square. The denominator does have an x which does not have a power. Therefore, the result for this one is that there is no horizontal asymptote.

Here is another case,

Do not confuse them or get scared. Look closely at the degrees. The first step is to look at each of the values you have. It is the easiest one because you can see that the numerator has a less degree than the denominator. Here, the result is going to be y = 0. Whenever, you get a question where they have asked you solve the horizontal asymptotes of rational functions, look at the degrees. You will have three kinds of results. One is simplification.

Here is another example

Since, you know all the rules now, it should be easy to solve. You can see that both of them has square as the power. 15 and 5 are divisible. You can either write y =  or if the teacher asks you to write in the shortest term possible, simplify as much as you can. The result with be 3.

Tips

• The teacher may ask you draw a graph, for y = 3, draw a straight line using your scale on the y-axis where it is 3.

 

How to find standard deviation

How to find standard deviation?

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The formula for finding standard deviation is:

How to find standard deviation

Where s = sample standard deviation

wps872.tmp

∑ = sum of

Ӿ= sample mean

n = number of scores in sample

People think that finding out the standard deviation is nearly possible plus they face a lot of difficulties with it. It is quite simple and you need to follow the three steps. Are the products at the factory going out of order? How many people are taller than 5 feet 5 inches at the university? How long is it taking for the particle to decay? All of their answers can be found through standard deviation. Let us take an example, if there are five children and they all have different numbers of chocolate bars. One has 5 bars, the other has 6, the other has 7, following one has 8 and the last one has 10. If you are thinking of calculating the mean, you have to add all the numbers and divide by the number of children which is 5.

Calculation: 5 + 6 +7+8+10 = 36

36 ÷ 5 = 7.2

Here the Standard deviation is 1.92354 and the Variance (Standard deviation) is 3.7, the Population Standard deviation is 1.72047 and the Variance (Population Standard deviation) is 2.96. What you can see here that the mean and the standard deviation has a lot of difference. The standard deviation is a graph that looks like it is going up and down. If it was a straight line graph, then there would be no standard deviation. It is represented by sigma “σ” a Greek alphabet.

Let us see how we do it

Step 1: Find out the mean

Take the data you are provided with such as: 5, 10, 15, 20, 30

Mean = Sum of the 5 data ÷ Number of data

= (5+10+15+20+30) ÷ 5

= 80 / 5 = 16

Step 2: Find the variance

Subtract the mean from the given data,

5-16 = -11

10-16 = -6

15-16 = -1

20-16 = 4

30-16 = 14

Step 3: now find the square of the results you got

(-11) ² = 121

(-6) ² =36

(-1) ² = 1

(4) ² = 16

(14) ²= 196

Find the addition of the numbers you got after squaring: 121 + 36 + 1+ 16 +196 = 370. Divide the result with n-1 and n is the number of data you had at the start meaning 5.

370 / (5-1) = 270 / 4 = 92.5

Therefore, the variance is 92.5.

Step 3: To find the standard deviation, carry out the square root of the result you got as variance

√ (92.5)   therefore the result is 9.62.

For this one, variance (Standard deviation) = 92.5, Population Standard deviation=8.60233 and Variance (Population Standard deviation) =74.

Tips:

· While you are just learning it or doing it for the first time, make sure you have all the data and get everything you need like a calculator.

· Write down all the steps and do not skip any part thinking of short-cuts.

· Do your work neatly.

How to factor

How to factor? Are you scared of factor? Do you face trouble while doing these math’s?  They are not as hard as you think and since they are a part of algebra you will understand it once you start practicing. Let us start with knowing what is a factor. You are definitely familiar with the times table such as 3 X 3 = 9 or 4 X 3 = 12. The 3 and 4 are factors and the result is the product (9 and 12). It is a whole number that divides precisely into another number. Here are the whole numbers: 1, 2, 4, 8 and not 3 or 5.

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How big is an acre?

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Five or three are not whole numbers because you cannot divide them equally unlike the other numbers. Suppose, there are four sweets. You can divide them equally between two people. Two for each and you can divide the four sweets among four people and again equally. Therefore, you can say.

How to factor

2 x 2 = 4

4 x 1 =4

The factors are 2, 1 and 4.

Let us factor second degree polynomials. The format is ax2 + bx + c = 0

Rearrange your equation with the smallest one at the beginning such as 3 + 3x2 + 11x = 0

For example, you have an equation x²+ x + 12

x² + 4x – 3x +12

x(x+4) -3(x+4)

(x+4) (x-3) are factors.

Here is how you do it. First of all, look at the numbers. Arrange them and make sure there is no number on the other side, that means on the other side it should be zero. If the equation was x²+3x+12= -3x, rearrange them and make them as small as possible. It will be x²+ 3x+ 3x+ 12 =O, later add the two 3x and your final equation is x²+6x+12 as you have shortened it out, it is now ready to have its factors.

For the previous equation, if you had a zero at the end with an equal sign, you would have to find the value of the x. Then, the result would be x= -4 and x =3. Here is how you do it.

(x=4)(x-3)
x + 4 = 0 & x-3=0

x = -4          x= 3

Let us see how we got the 4 and 3. We look at the single number of the equation that does not have any x with it. In this case, it is the 12. Go through the times tables and think which numbers that can be multiplied to get 12 and also be added or subtracted to get 1. We know,

6 x 2 = 12

3 x 4 = 12

12 x 1 = 12

Adding or subtracting 6 and 2 will never get you 1 neither will 12 and 1. It is clear that 4 and 3 can be subtracted to get 1.

In case of simple equations, you will be able to figure it out yourself with just looking at it. For example, 4x²+ 4x+1 will result in (2x + 1) (2x +1) when you try to factor it.

How big is an acre?

How big is an acre? 43560 square feet is an acre.

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Let us examine the acre which is a popular term for calculating the size of lands. It could be that you heard someone is selling a specific number of acres of land and you are wondering what is the actual size. Is it big or is it small? It could be that your math papers require you to find out acres to all the units possible like square meters and square feet.

How big is an acre

You should keep in mind when dealing with acres that it can be in any shape like circles, square or rectangle. The rule is that it has to be 43 560 square feet no matter what its shapes. A regular shape of an acre is 660 feet by 66 feet. It is a usually misinterpreted information when looking for plots for a new home is that you should have minimum 1 acre of land in order to start construction.

 

Let us find by calculating:

660 feet X 66 feet = 42 560 square feet

Two feet make square feet.

If you are thinking of converting into other units, then you can first convert into another unit popular for measuring land which is the yard. It is 4840 square yard. There are two basic ways. One of them is through calculation and other is using formulae.

 

The first method

There are 0.00020661 acres in a square yard which means you have to multiply this with 4840 to get the result.

The result will be 0.9999924 which is approximately equal to 1.

0.00020661 X 4840 = 0.9999924 (approx. 1)

The second method

acres = feet square ÷ 4,840

The formula to convert from acres to ft. square is:

Feet square = acres x 4,840

 

If you are calculating in miles, then you should know that 1 acre is 0.0015625 square mile. 1 square mile is equal to 540 acres. To find out multiply by the factor or use the line “1 Square mile = 640 acre” Square mile is another popular unit used in both the British and American systems used to measure land. It goes like this, 1 square mile is 640 acres and 2 square miles is 1280 acre, 3 square miles is 1920 acre and so on.

To be more precise, 1 acre is 90 percent of a hundred yard or 91.44 meters long by 53.33 yards (48.76 meters) wide American field for football excluding the end zones. If you take into account the end zones, it will be about 1.32 acres.

1 Acre = 43,560 square feet

1 Acre = 160 square rods

1 Acre = 10 square chains

1 Acre = 160 square rods

1 Acre = 160 perches 1 Acre = 160 poles

1 Acre = .4047 hectare

1 Acre = 4047 square meters

1 Acre = is about 208 3/4 feet square

If you can remember them, you will be able to calculate the size of an acre using any formula.

How much does a gallon of milk weigh?

How much does a gallon of milk weigh? A gallon of milk weights about 8.6 pounds.

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The density of milk is about 1.03 kilograms per liter therefore 1 liter of milk weighs very near to 1 kilogram. There are many ways to calculate how much a gallon of milk weighs.  Everybody in every countries drink milk almost on a daily basis.

How much does a gallon of milk weigh

Children specially drink them every day. The first food of a newborn is the milk. Milk is an important source of food because it is one of the super drinks. It is just as good as an egg. It is full of nutrition. A glass of milk can provide you with enough energy to do a lot of work without getting tired or hungry. The farmers sell the milk and they are calculated in gallons. They send big trucks of milk from the farm to the city. The weight of the milk varies on the type of milk whether it is light or heavy. The heavy milk has a higher weigh per gallon than a light one.

Let us see how we can find how much a gallon of milk weighs. 

The answer is always in a decimal because we can never be sure about the precise weight as it is an organic product. Due to the fat present in milk, the weight can be different at different times. We know that 1 liquid gallon is equal to 128 fluid ounces. It means that 1 gallon is equal to more than 15 cups and 128 fluid ounces is equal to 4 liquid quarts.  You can first calculate how much is in 1 pound. Later, divide 1 by 16. Then, multiply with 128 fluid ounces.

Calculation:

1 gallon = 128 fluid ounce

1 pound = 16 fluid ounce

16 oz. = 1 lb.

1 oz. = (1 / 16) lb.

128 oz. = (1/16) X 128 = 8

It means that there is more than 8 pounds in a gallon of milk. It is slightly more than 8 because of its density and the fat content.

Another way to know is by knowing the amount of milk in liters. There is 3.79 liters in a gallon of milk. 3.79 liters is equal to 128.6 fluid ounces. 3.79 liters is 3.79 kilograms in case of water. We can use these term here because milk is 90 percent water. Hence 3.79 kilogram is 8.35552 pound. Again, we are with the result that a gallon of milk is more than 8 pounds.

Calculation: 

3.70 l = 3.79 kg

3.79 kg = 8.35552 pounds