Ratio Definition Math

Definition for ratio:

In mathematics, a ratio expresses the magnitude of quantities relative to each other. Specifically, the ratio of two quantities indicates how many times the first quantity is contained in the second and may be expressed algebraically as their quotient. I like to share this What is a Ratio? with you all through my article.

Example:

For every Spoon of sugar, you need 2 spoons of flour (1:2)

Source :Wikipedia

Ratio formula:

Let A and B be two given points. Let P be a point on the line segment `barA``barB` or on `barA` `barB` produced. Then P divides `barA` `barB` into two segments `barA` `barP` and `barP` `barB`. The lengths of `barA` `barP` and `barP``barB`  are AP and PB.

These lengths are in some ratio: n; that is AP : PB = m : n or  `(AP)/(PB)` `(m)/(n)`

If P lies inside `barA` `barB` we say that P divides `barA``barB` internally in the ratio m : n. If P lies outside `barA` `barB`, that is, P lies on `barA` `barB`  produced, then we say that P divides `barA``barB` externally in the ratio m : n. With a given ratio m : n, `barA``barB` can be divided either internally or externally. Understanding Dividing Radicals with Variables is always challenging for me but thanks to all math help websites to help me out.

Example for ratio:

Example :

Divide the line segment `barA` `barB` of length 16 units in the ratio 3:5

Solution:

i) Let C be the point inside `barA``barB` such that `(AC)/(CB)`= `(3)/(5)`. Since the numerator is smaller than the denominator, C is closer to A than to B . Then

5AC=3 BC or 5AC=3(AB–AC) or 8AC=3AB =3(16)=48

AC=6 units and so CB=AB–AC =16–6 = 10 units.

Hence C lies inside `barA` `barB` 6 units distance from A and 10 units distance from B. The point C is unique and it divides `barA``barB` internally in the given ratio 3:5.

ii) Let D be the point outside `barA``barB` such that `(AD)/(DB)`=`(3)/(5)`?. Since the numerator is smaller than the denominator, D is closer to A than to B. Now we have

5 AD = 3DB or 5 AD = 3(AD + AB) or 5 AD = 3AD + 3AB

2 AD = 3AB = 3(16) = 48 or AD = 24 Then DB = DA + AB = 24 + 16 = 40

Therefore, D lies outside `barA``barB` 24 units distance from A and 40 units distance from B. The point D is unique and it divides   `barA``barB` externally in the given ratio 3:5.

Solving Mathematics Grind

Introduction for Solving Mathematics Grind:

Well experienced tutor (or) graduate Mathematics student offering Junior and Leaving Certificate grinds around Ireland. Grinds contains various subjects such as Mathematics, French, Accounting etc., in this math grind covers all level of students. They are providing explanation of theory with detailed examples with questions and answers. In this article we shall discuss about solving mathematics grind. The following examples are involved in solving mathematics grind. Is this topic Exponential Function Solver hard for you? Watch out for my coming posts.

Solving Mathematics Grind Example: 1

Solve the sum and find the value of ‘x’

50x + 40 = -200

Subtract 40 from both sides:

50x + 40 – 40 = -200 - 40

Simplify both sides:

50x = -240

Divide both sides by 50:

`(50x)/50` = `-240/50`

Simplify both sides:

x   =   `-24/5`

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Solving Mathematics Grind Example: 2

Use Euclid’s algorithms solve the HCF of 2245 and 36548.

Solution:

Since 36548 > 2245, we apply the division lemma to 36548 and 2245, to get

36548 = 2245 × 16 + 628

Since the remainder 628 not equal to 0, we apply the division lemma to 2245 and 628, to get

2245 = 628 × 3 + 361

We consider the new divisor 628 and the new remainder 361, and apply the division lemma to get

628 = 361 × 1 + 267

We consider the new divisor 361 and the new remainder 267, and apply the division lemma to get

361 = 267 × 1 + 94

We consider the new divisor 267 and the new remainder 94, and apply the division lemma to get

267 = 94 × 2 + 79

We consider the new divisor 94 and the new remainder 79, and apply the division lemma to get

94 = 79 × 1 + 15

We consider the new divisor 79 and the new remainder 15, and apply the division lemma to get

79 = 15 × 5 + 4

We consider the new divisor 15 and the new remainder 4, and apply the division lemma to get

15 = 4 × 3 + 3

We consider the new divisor 4 and the new remainder 3, and apply the division lemma to get

4 = 3 × 1 + 1

We consider the new divisor 3 and the new remainder 1, and apply the division lemma to get

3 = 1 × 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 36548 and 2245 is 1.

Notice that 1 = HCF (3, 1) = HCF (4, 3) = HCF (15, 4) = HCF (79, 15) = HCF (94, 79) = HCF (267, 94) = HCF (361, 267) = HCF (628, 361) = HCF (2245, 628) = HCF (36548, 2245).

Meters to Inches

Meters to inches

Meter:

The metre (or meter), symbol m, is the base unit of length in the International System of Units (SI). It is defined as the distance travelled by light in a complete vacuum in 1/299,792,458 of a second.

Inch:

An inch is the name of a unit of length in a number of different systems, including Imperial units, and United States customary units. I like to share this Alternate Exterior Angles with you all through my article.

(Source: wiki)

Let us see how to convert meters to inches in this article.

Formula for meters to inches

1 meter = 39.3700787 inches

Meters to Inches – Examples:
Meters to inches – Example 1:

Convert 5 Meters to inches?

Solution:

Step 1:

Formula for converting meters to inches:

1 meter = 39.3700787 inches

Step 2:

So to find 5 meter

Step 3:

Multiply 5 with 39.3700787 = 196.8503935

Step 4:

Therefore, 5 meter = 196.8503935 inches

Meters to inches – Example 2:

Convert 11 Meters to inches?

Solution:

Step 1:

Formula for converting meters to inches

1 meter = 39.3700787 inches

Step 2:

So to find 11 meter

Step 3:

Multiply 11 with 39.3700787 = 433.070866 inches

Step 4:

Therefore, 11 meter = 433.070866 inches

Meters to inches – Example 3:

Convert 15 Meters to inches?

Solution:

Step 1:

Formula for converting meters to inches

1 meter = 39.3700787 inches

Step 2:

So to find 15 meter

Step 3:

Multiply 15 with 39.3700787 = 590.551181 inches

Step 4:

Therefore, 15 meter = 590.551181 inches

Meters to inches – Example 4:

Convert 26 Meters to inches?

Solution:

Step 1:

Formula for converting meters to inches

1 meter = 39.3700787 inches

Step 2:

So to find 26 meter

Step 3:

Multiply 26 with 39.3700787 = 1 023.62205 inches

Step 4:

Therefore, 26 meter = 1 023.62205 inches

Meters to inches – Example 5:

Convert 0.50 Meters to inches?

Solution:

Step 1:

Formula for converting meters to inches

1 meter = 39.3700787 inches

Step 2:

So to find 0.501 meter

Step 3:

Multiply 0.501 with 39.3700787 = 19.7244094 inches

Step 4:

Therefore, 0.501 meter = 19.7244094 inches

Meters to inches – Example 6:

Convert 0.81 Meters to inches?

Solution:

Step 1:

Formula for converting meters to inches

1 meter = 39.3700787 inches

Step 2:

So to find 0.81 meter

Step 3:

Multiply 0.81 with 39.3700787 = 810

Step 4:

Therefore, 0.81 meter = 31.8897638 inches


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Meters to Inches – Practice Problems

Practice problem -1

Convert 6.5 Meters to inches?

Answer:

255.905512 inches

Practice problem -2

Convert 0.6 Meters to inches?

Answer:

23.6220472 inches

Entrance Exam for College Math

Introduction to entrance exam for college math:

Entrance exam for college evaluates high school students, general educational improvement and their ability to complete college-level work. SAT exam is one of the entrance exams for college math. It is used to find out skills in math, reading comprehension and vocabulary of the students planning to attend college. Now, we are going to see some of the problems on entrance exam for college math.

Entrance Exam for College Math Solved Problems:

Example problem 1:

Solve the quadratic equation by factoring method: x2 - 143x + 142 = 0.

a) 1, 142

b) 1, 132

c) 1, 122

d) 1, 112

Solution:

The given quadratic equation is x^2 - 143x + 142 = 0

Here a = coefficient of x2 = 1

b = coefficient of x = -143

c = constant term = 142

We find a × c = 1 × 142 = 142 = -1 * -142, a + c = (-1) + (-142) = -143 = b.

By splitting the middle term, we get

x2 - 143x + 142 = 0

x2 - 1x - 142x + 142 = 0

x(x - 1) - 142(x - 1) = 0

(x - 1) (x - 142) = 0

x = 1, x = 142

So, the option a is the correct answer.

So, the answer is x = 1, 142. Having problem with word problems in algebra keep reading my upcoming posts, i will try to help you.

Additional Solved Problems-entrance Exam for College Math:

Example problem 2:

Solve the following simultaneous equations using substitution method:

9x – y = 18 ----------Equation (1)

1x + y = 22--------------Equation (2)

a) (2, 25)

b) (3, 27)

c) (5, 27)

d) (4, 18)

Solution:

Step 1: Let us consider the Equation (1)

9x – y = 18

Subtract 9x on both sides of the equation

9x – y –9x = 18 – 9x

-y = -9x + 18

y = 9x - 18---------Equation (3)

Step 2: Substitute the value of y in Equation (2). We get

1x + y = 22

1x + (9x – 18) = 22

10x – 18 = 22

Add 18 on both sides of the equation

10x – 18 + 18 = 22 + 18

10x = 40

Divide by 10 on both sides of the equation

`(10x) / 10 = 40 / 10`

x = 4

Step 3: Substituting this value of x in Equation (3), we get

y = 9x – 18

y = 36 – 18

y = 18

So, the option d is the correct answer.

So, the answer is (4, 18).

Thoughts on Distance Learning

Introduction to thoughts on distance learning:

In this article, we shall discuss about thoughts on distance learning. In mathematics, distance is defined as an object moves from one particular point to another point which is calculated by speed and time. That is, when we multiply the time and speed we will get the distance. Please express your views of this topic Define Permutations by commenting on blog.

Formula for the calculating distance is

Distance = speed `xx` time

Now we shall solve some example problems regarding thoughts on distance learning.

Examples to Thoughts on Distance Learning:

Example 1:

A train is driven at average speed of 3 kilometers per hour to the station 6 hours. If the train is droved at the average speed of 2, how many hour would need to reach the station?

Solution:

3 km/h needs 6 hours

2 km/h needs x hours

This can be written as,

3 = 6 and

2 = x

Also we can written as

3 `xx` 6 = 2x

18 = 2x Also we can written as

2x  = 18 now we have to divide both sided by 2

`(2x)/2`  = `18/2`

X = 9

therefore, if the train is droved at 2 kilometers per hour, it would need 9 hours
Example 2:

Bus and car are leaving from the same place in opposite direction. Bus goes at 3mph and the car goes at 2 mph. how many hours will they need to 22 miles apart?
Solution:

Distance = speed time

Speed of  bus = 3mph

Time of bus = t

Therefore, distance of the bust = 3t

Speed of  car = 2mph

Time of bus = t

Therefore, distance of the bust = 2t

Therefore,

3t + 2t  = 22 miles

5t  =  22   now we have to divide both sides by 5. so we get

`(5t)/5` = `22/5`

t =4.4 hours

Bus and car will reach 22 miles apart in 4.4 hours


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Practices Problems to Thoughts on Distance Learning :

Problem 1:

A train is driven at average speed of 6 kilometers per hour to the station 6 hours. If the train is driven at the average speed of 4, how many hour would need to reach the station?

Answer: 9 hours

Problem 2:

Bus and car are leaving from the same place in opposite direction. Bus goes at 10 mph and the car runs at 6mph. how many hours will they need to 39 miles apart?

Answer: 2.4 hours

Exact Distribution

Introduction to exact distribution:

The exact distribution refers the probability distribution the probability theory. The probability distribution is used to determine the number of possibility for the occurrence of an event. The most commonly used probability distributions are the binomial distribution, geometric distribution, normal distribution and the gamma distribution. These above mentioned distributions are included in the discrete and continuous probability distribution. The major type of the probability distribution is the discrete probability distribution and the continuous probability distribution. This article has the study about exact distribution.

Types of Exact Distribution:

The major types of the probability distribution are

Discrete probability distribution
Continuous probability distribution
Discrete probability distribution:

The probability for a countable number of occurrences for the event is calculated in the discrete probability distribution.
Continuous probability distribution:

The probability values in this are the continuous ranged value it is calculated in the continuous probability distribution.

Examples for Exact Distribution:

Example 1 to exact distribution:

If X is normally distributed the mean value is 1 and its standard deviation is 2. Determine the value of P (0 ≤ X ≤ 7).

Solution:

The given mu value is 1 and the standard deviation is 2.

Z = `(X- mu)/ sigma`

When X = 0, Z = `(0- 1)/ 2`

= -`1/2`

= -0.5

When X = 7, Z = `(7- 1)/ 2`

= `6/2`

= 3

Therefore,

P (0 ≤ X ≤ 7) = P (-0.5 < Z < 3)

P (0 ≤ X ≤ 7) = P (0 < Z < 0.5) + P (0 < Z < 3) (due to symmetry property)

P (0 ≤ X ≤ 7) = (0. 6915- 0.5) + (0.9987 - 0.5)

P (0 ≤ X ≤ 7) = 0.1915 + 0.4987

P (0 ≤ X ≤ 7) = 0.4987

The value for P (0 ≤ X ≤ 7) is 0.4987.

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Example 2 to exact distribution:

The probability for destroying the target in only one time is 0.37. Compute the probability that it would be destroyed on the third attempt itself.

Solution:

The probability of destroying the target in one trial is p = 0.37.

The value of the q is calculated by q = 1-p

q = 1- 0.37

q = 0.63

By the geometric distribution, the probability for the success is calculated by using the formula

P(X =x) = q x p, the value of x is 0, 1, 2. . .

The target is destroyed at the third attempt, so x = 3.

P(X = 3) = (0. 63) 3 (0.37)

P(X = 3) = (0.25) (0.37)

P(X = 3) = 0.0925

The probability for destroying the target at the third trial is 0.0925.

Easy Way to Learn Statistics

Introduction to Easy Way to Learn Statistics

Statistics is the proper science of creating successful use of mathematical relating to groups of individuals or experiments. It deals with all features of this including not only the collection, analysis and interpretation of such data, but also the planning of the collection of data, in terms of the design of surveys and experiments. Now we will learn the statistics in easy way.

Examples for Easy Way to Learn Statistics

Example 1

What the mean, median,mode and range of the following group of numbers?

11,12,15,17,19.

Solution

The given numbers are 11,12,15,17,19.

Mean

We can find a mean in easy way. Mean is the average of the given number. So find the sum of the given numbers.

Sum of the given numbers are = 11+12+15+17+19

Now divided by 5 (Because 5 is the total given numbers) =74/5

=14.8.

Median

A middle value of the given number series is the median.

The number series is 11,12,15,17,19.

Here the center value is 15.

Therefore 15 is the median.

Mode

It is also very easy way to find. Mode is a duplicate value of the given number series. Here no duplicate value.

Therefore mode is empty or null.

Range

It can find in easy way. Range is the difference between maximum value and the minimum value of the given number series.

Range=19-11

=8.

Example 2

What is the mean, median of the following group in statistics?

14,16,18,20, 22.

Solution

The given numbers are 14,16,18,20 and 22.

Mean

We learn.mean is the average of the given number. We find the sum of the given numbers.

Sum of the given numbers are = 14+16+18+20+22

= 90.

Now divided by 5 (Because 5 is the total given numbers) = 90/5

= 18.

Median

We learn,a middle value of the given number series is the median.

The number series is 14,16,18,20, 22.

The middle value of the above series is 18.

Therefore 18 is the median.

These are the examples and find the solution in easy way.