Realworld Solving Problems

Introduction to real world solving problems:

In this we will see about real world solving problems. Real world problems include some real time example problems like as business problems, money calculation, sales problems, and so on. In this section we have example problems for real world solving problems. Let us see about real world solving problems. Having problem with Mixed Number to Improper Fraction keep reading my upcoming posts, i will try to help you.

Example Problems for Real World Solving Problems:

Example problem 1: Khalil and his classmates placed metal discs on a scale during a science lab. The orange disc weighed 9.5 pounds and the blue disc weighed 2.3 pounds. How much more did the orange disc weigh than the blue disc?

Solution:

Subtract the numbers of pounds.

Subtract: 9.5 – 2.3 = 7.2

The orange disc weighed 7.2 pounds more than the blue disc.

Answer: The orange disc weighed 7.2 pounds more than the blue disc.

Example problem 2: Coffee sells for 9 dollars per pound. If a farmer sells 5,000 pounds of coffee, how much money will the farmer make?

Solution:

There are 5,000 pounds, each of which sells for 9 dollars. Multiply 5,000 by 9 dollars.

First, multiply the non-zero parts of the numbers:

5 × 9 = 45 dollars

Now add back the zeroes at the end: 45,000 dollars

The farmer would make 45,000 dollars.

Answer: The farmer would make 45,000 dollars.Please express your views of this topic How to Find the Surface Area of a Pyramid by commenting on blog.

Practice Problems for Real World Solving Problems:

Practice problem 1: At an antique show, Emmanuel bought an old dresser for 773 dollars and a beautiful table for 589 dollars. How much did Emmanuel spend in all?

Practice problem 2: Addie buys 9 ice cream cones for 7.92 dollars. The ice cream cones all have the same price. What is the price of each ice cream cone?

Practice problem 3: A jewelry company ordered 9 boxes of glass beads. There were 1,991 beads in each box. How many glass beads did the jewelry company order?

Solutions for real world solving problems:

Solution 1: Emmanuel spent 1,362.00 dollars in all.

Solution 2: The price of each ice cream cone is 0.88 dollars.

Solution 3: The Company ordered 17,919 glass beads.

Equal Intervals

Introduction to equal intervals:

Generally interval in mathematics is defined as  difference between the two numbers, if that numbers are a, b means the interval will be denoted by a-b .Equal interval is applicable only for the set of numbers ,if a set contains the large number means  interval of each of the numbers must be equal, so it is called as equal interval, here we are using  formula for  equal given number will be divided by the equal interval. Is this topic The Perfect Number hard for you? Watch out for my coming posts.

Example Problems -equal Intervals:
Example problem 1:

If the number is 150, here we do the operation as equal interval

(I) 5 equal intervals

(ii) 10 equal intervals

(iii) 3 equal intervals

Solution:

(i)Here we are going to divide the number 150 into the 5 equal intervals it means we have to split the number,

150/5we get the answer is 30 ,

So 150 is divided into the 5 equal parts of 30

(ii)Here we are going to divide the number into the 10 equal intervals it means we have to split the number,

150/10 we get the answer is 15 ,

So 150 is divided into the 15 equal parts of 10

(ii)Here we are going to divide the number into the 3 equal intervals it means we have to split the number,

150/3 we get the answer is 50,

So 150 is divided into the 3 equal parts of 50

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Example Problem 2:

If the educated people in the city is 78%, split the people in the street wise with equal interval

(i) 2 equal intervals

(ii) 3 equal intervals

(iii) 6 equal intervals

Solution:

(I)Here we are going to divide 78% of the educated people with the equal interval of 2 it means we have to split percentage with the 2 equal intervals

78%/2 we get the answer is 39%,

So 78% of the educated people are separated with 2 equal intervals of 39%

(ii)Here we are going to divide78% of the educated people with the equal interval of 3 it means we have to split percentage with the 3 equal intervals

78%/3 we get the answer is 26%,

So 78% of the educated people are separated with 2 equal intervals of 36%

(iii)Here we are going to divide 78% of the educated people with the equal interval of 6 it means we have to split percentage with the 6 equal intervals

78%/6we get the answer is 13%,

So 78% of the educated people are separated with 6 equal intervals of 13%

Six Step Method Math

Introduction to six step method math:

Let us see about six step method math problems in this article. Six step method math problems are nothing but solving the particular problem by using six step procedures. These problem are easy when comparing to complex problems. We can use any math problem like algebra, geometry, trigonometry, fundamental math problems, etc, but the answer will be in six steps. Understanding Foil Method is always challenging for me but thanks to all math help websites to help me out.

Example 1: Six Step Method Math:

Find the volume of the cube whose side a is 8

Solution:

Step 1: In this given side a is 8

Step 2: Formula for find the volume of the cube is the a^3.

Step 3: a^3 means a`xx` a`xx` a

Step 4: substitute the a values for the above formula.

Step 5: 8^3 = 8`xx` 8 `xx` 8 = 512.

Step 6: Volume of the cube is 512.

Example 2: Six Step Method Math:

Work out the problem using short division method: `355/5`

Solution:

Step 1: Number 350 is divided by number 5

Step 2: Dividend number is 350 and the divisor number is 5

Step 3: Dividend number 3 is not divided by the divisor number 5 so take the next digit

Step 4: The next number is 5. Number 35 is dividing by 5 the remainder is 0, result is 7

Step 5: Take the next number 5. Number 5 is divided by 5. The remainder is 0 and the result is 1.

Step 6: Answer for this problem is 71

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Example 3: Six Step Method Math:

To solve: 2x + 3y + 6z + 5 = 4y + 6z + 10

Solution:

Step 1:

Given: 2x + 3y + 6z + 5 = 4y + 6z + 10

Step 2:

Take the terms on the right side to the left side of the equation, before the equal sign.

2x + 3y + 6z + 5 - 4y - 6z – 10 = 0

Step 3:

Grouping the terms:

2x + 3y - 4y + 6z - 6z + 5 – 10 = 0

Step 4:

Grouping the variable terms:

2x - y + 5 - 10 = 0

Step 5:

Grouping the number terms:

2x - y - 5 = 0

Step 6:

Answer for this problem is 2x - y - 5 = 0

Solving Applied Math Problems

Introduction to solving applied math problems:

Mostly college level students are using the applied mathematics problems. Applied mathematics is very helpful for students for learning about math. Applied math is a division of math that concerns itself with the mathematical techniques typically used in the application of math knowledge to other domains. The following topics are covered in applied mathematics; they are functions of a complex variable, calculus, ordinary differential equations, partial differential equations and the calculus of variations.

Example Problems for Solving Applied Math Problems:

Solving applied math problems – Example: 1

Transform the BVP to an integral equation: `(d^2 y)/(dx^2) + y = x, y(0) = 0,` `y'(1) = 0.`

Solution:
First, integrate both sides from x to 1 (so that the boundary condition `y'(1) = 0 ` can be applied). This gives

`y'(1) - y'(x) + int_x^1 y(u) du = int_x^1 y(u)du = int_x^1 udu = (u^2)/(2)|_x^1 = 1/2 – (x^2)/(2)`
Applying the condition` y'(1) = 0 ` and multiplying both sides by (-1) results in

`y'(x) - int_x^1 y(u)du = (x^2)/(2)- 1/2`

Next, integrate both sides from 0 to x:

`(y(x) - y(0)) - int_0^x int_z^1 y(u)dudz = int_0^x (u^2)/(2) - 1/2 du = ((u^3)/(6) - (u)/(2))|_0^x = (x^3)/(6) - (x)/(2)`

or, applying the condition y(0) = 0,

`y(x) - int_0^x int_z^1 y(u) dudz = (x^3)/(6) - (x)/(2)`

We see that the region must be split into two pieces, and a separate integral written for each piece:

`int_0^1 int_z^1 y(u)dudz = int_0^x int_0^u dz y(u) du + int_x^1 int_0^x dz y(u) du`

or after doing the trivial z-integration,

`int_0^1 int_z^1 y(u)dudz = int_0^x u y(u) du + int_x^1 x y(u) du`

The desired integral equation, then, is

`y(x) - int_0^x u y(u) du - int_1^x xy(u) du = (x^3)/(6) - (x)/(2)`

Such an integral equation is often written in the form

`y(x) - int_0^1 k(x, u) y(u) du = (x^3)/(6) - (x)/(2)`

where

k(x, u) = `{ u, 0 < u < x`

`{ x, x< u < 1`

`Answer: k(x, u) = { u, 0 < u < x`

`{ x, x< u < 1`

Solving applied math problems – Example: 2

If `f(t) = ti + (t^2 - 2t)j + (3t^2 + 3t^3)k` , find `int_0^1 f(t)dt.`

Solution:

`f(t) = ti + (t^2 - 2t)j + (3t^2 + 3t^3)k`

` = i int_0^1 tdt + j int_0^1 (t^2 - 2t)dt + k int_0^1 (3T2 + 3t^3)dt`

`= i[(t^2)/(2)] + j[(t^3)/(3) - t^2] + k[t^3 + (3t^4)/(4) at (0,1)`

`= i[1/2 + j[1/3 - 1] + k[1 + 3/4]`

`= 1/2 i - 2/3 j + 7/4 k`

`Answer: 1/2 i - 2/3 j + 7/4 k`

Practice Problems for Solving Applied Math Problems:

1. Solve:  `g(s) = f(s) + lambda int_0^(2 pi) sin(s) cos(t)g(t) dt`

`Answer: g(s) = f(s) + lambda sin(s) int_0^(2 pi) cos(t)f(t) dt`

2. If  `f(t) = (t - t^2)I + 2t^3 j - 3k,` Find i) `int f(t) dt ` ii) `int_1^2 f(t) dt`

`Answer: (i) i[(t^2)/(2) - (t^3)/(3)] + (t^4)/(2) j - 3tk + c`

` (ii) - 5/6 I + 15/2 j - 3k`

Solve Mean Average Deviation

Introduction to Solve mean average deviation :

Statistics is one of the part in the mathematics and it is a tool that is used to analyze the data. The data values should be in either numeric in origin or it can be transformed from other form into numbers of data. The statistics is used to measure the average, middle value, repeated values, mean difference, mean deviation, variance and also finds the standard deviations in the given data set. Here we are going to see about the solve mean average deviation with some example problems and practice problems on it. I like to share this Mean Deviation with you all through my article.

Definition of Statistics Mean Deviation:

Mean Deviation of the statistics is used to measure of the difference between the given data set and mean value of the given data set and the square of those mean difference.

Steps to calculate mean average deviation:

Step 1: Find the mean for a given set of data.

Step 2: Calculate the difference between the given set of values and with the step 1 result individually.

Step 3 : Now squaring all the values individually.

Step 4: Summing up all the values of step 3.

Step 5: Calculate the average for a result of step 4.

Step 5 is the final result.

For calculating the mean deviation initially we have to measure the mean,

Formula for finding the mean is given by,

` barx`  =  ` (sum_(k=1)^n (x_k)) /N `

where as

`barx` is the symbol for the mean

`x_k` is the given set of values in the data set limits from `sum_(k=1)^n`

` N` is the total number of values in the data set.

Using the mean value mean deviation have to be found Formula for mean deviation is,

Mean Deviation  =`sum_(k=1)^n` `(x_k-barx)^2 / N`

Please express your views of this topic Dividing complex numbers by commenting on blog.

Solve Mean Average Deviation - Example Problems:

Solve mean average deviation - Problem:

Solve the mean deviation statistics of the given data set. 13, 17, 15, 14, 16, 15.

Solution:

Mean :

Formula for calculating the mean  is given by,

` barx` =  ` (sum_(k=1)^n (x_k)) /N `

=  13 + 17 + 15 + 14 + 16 + 15
6
= ` 90/6`

`barx`=  15

Average Deviation = `(sum_(k=1)^n (x_k-barx)^2) / N`
=  4 + 4 + 0 + 1 + 1 + 0
6
= `10/6`

Average Deviation = 1.66666667

Hence the average deviation is founded out from the average daviation formula.

Solve Mean Average Deviation - Practice Problems:

Problem 1:

Calculate the mean deviation statistics of the given data set.  565, 566, 568, 564 , 562, 567, 568.

Answer: Mean deviation = 4.28571429

Problem 2:

Calculate the mean deviation statistics of the given data set. 93, 91, 92, 93, 95, 94 .

Answer: Mean Deviation = 1.66666667.

Average and Range Method

Introduction for average and range method

An average, central tendency of a data set is a measure of the "middle" or "expected" value of the data set. the average is calculated by combining the values from the set in a specific way and computing a single number as being the average of the set. Understanding Newton S Method Calculus is always challenging for me but thanks to all math help websites to help me out.

-   Source Wikipedia

The range is subtracting least number from greatest number.

Examples for Average and Range Method:

Example 1 for average and range method:

Find the average and range for the given number set. 6, 2, 5, 3, 7, 4

Solution:

First we have to arrange the numbers in ascending order, so we get,

2, 3, 4, 5, 6, 7

Range = greatest number – least number.

Range = 7 – 2

Range = 5

Average = `"sum of the numbers" / "count of the numbers"`

Average = `(2 + 3 + 4 + 5 + 6 + 7) / 6`

Average = `27/6`

Average = 4.5

Example 2 for average and range method:

Find the average and range for the given number set. 16, 12, 15, 13, 17, 14

Solution:

First we have to arrange the numbers in ascending order, so we get,

12, 13, 14, 15, 16, 17

Range = greatest number – least number.

Range = 17 – 12

Range = 5

Average = `"sum of the numbers" / "count of the numbers"`

Average = `(12 + 13 + 14 + 15 + 16 + 17) / 6`

Average = `87/6`

Average = 14.5

Example 3 for average and range method:

Find the average and range for the given number set. 26, 22, 25, 23, 24

Solution:

First we have to arrange the numbers in ascending order, so we get,

22, 23, 24, 25, 26

Range = greatest number – least number.

Range = 26 – 22

Range = 4

Average = `"sum of the numbers" / "count of the numbers"`

Average = `(22 + 23 + 24 + 25 + 26) / 5`

Average = `120/5`

Average = 24

Example 4 for average and range method:

Find the average and range for the given number set. 36, 32, 35, 33, 34

Solution:

First we have to arrange the numbers in ascending order, so we get,

32, 33, 34, 35, 36

Range = greatest number – least number.

Range = 36 – 32

Range = 4

Average = `"sum of the numbers" / "count of the numbers"`

Average = `(32 + 33 + 34 + 35 + 36) / 5`

Average = `170/5`

Average = 34


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Practice Problems for Average and Range Method:

Problem 1 for average and range method:

Find the average and range for the given number set. 47, 42, 45, 43, 44

Range = 5

Average = 44.2

Problem 2 for average and range method:

Find the average and range for the given number set. 56, 52, 55, 53, 54, 51

Range = 5

Average = 53.5

Additive Inverse of Complex Numbers

Introduction to Complex numbers:

Complex number is said to be the sum of whole numbers and imaginary numbers. The imaginary numbers can be denoted as in numbers in form of ‘’i’’, where the value of I is `sqrt(-1)` . In this article, we see about the additive inverse of complex numbers. The additive inverse of the any number is the changing the sign of the number. That is instead –ve sign is positive and vice versa.

Additive Inverse of Complex Numbers:

We know that the sum of any number and its additive inverse of that number is zero.

To find: Additive Inverse of the Complex Numbers:

Let take the complex numbers Z = X + iy and its inverse be Z-1 = a + ib

Step 1: Now add the Z and Z-1, we get

Z + Z-1 = (X + iy) + (a + ib) = 0

Step 2: Combine Like term, we get

(X + a) + i (y + b) = 0

Step 3: By using zero product property, we can equating as

X + a = 0 and i (y + b) = 0

X = -a and y = -b

Thus the additive inverse of the complex numbers X + iy = -X – iy

Example Problems – Additive Inverse of Complex Numbers:

Example 1:

Choose the correct option - The additive inverse of the complex number 5 + 6i

Option:

a)     5 – 6i

b)    -5 + 6i

c)     -5 – 6i

d)    -11i

Solution:

Given: 5 + 6i

Formula: The additive inverse of X + iy = - X – iy

5 + 6i = -5 – 6i

Answer: Option c

Example 2:

What is the value of the sum of the complex number 4 + 8i and its additive inverse?

Solution:

Given: The sum of 4 + 8i and its additive inverse

The additive inverse of 4 + 8i = -4 – 8i

4 + 8i – 4 -8i = (4 -4) + i (8 -8) = 0

Answer: 0

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Practice Problem – Additive Inverse of Complex Numbers:

Problem 1;

What is the additive inverse of the complex numbers 7 – 9i?

Answer: -7 + 9i

Problem 2:

What is the sum of any complex numbers and its additive inverse?

Nine Tenths of a Whole Number

Introduction to nine tenths of a whole number:

Decimals are a technique of writing fractional numbers devoid of writing a fraction containing a numerator and denominator. The fraction `9/10` should be written as the decimal 0.9 .The decimal point shows that it is a decimal. The decimal 0.9 possibly will be pronounced as nine tenths. In this article we shall discuss nine tenths of a whole number.

Nine Tenths of a Whole Number :

9 tenths means how many tenths in 9.We can write 9 tenths as follows:

9 tenths =` 9 xx (1/10)`

= `9/10`

= 0.9

Therefore 9 tenths can be written as 0.9 in decimal.

Let us take a whole number 10.

We are going to calculate the nine tenths of a whole number.

We have to multiply the whole number 10 by 0.9

That is, `10 xx 0.9` = 9.

Therefore  9 tenths of a whole number 10 is equal to 9. Please express your views of this topic greatest common denominator by commenting on blog

Example Problems for Nine Tenths of a Whole Number:

Example 1:

Find 9 tenths of a whole number 100

Solution:

The given whole number is 100.

We are going to calculate the nine tenths of a whole number 100.

We know that nine tenths is equal to 0.9

We have to multiply the whole number 100 by 0.9

That is, 100 x 0.9 = 90.

Therefore  9 tenths of a whole number 100 is equal to 90.

Example 2:

Find 9 tenths of a whole number 50

Solution:

The given whole number is 50.

We are going to calculate the nine tenths of a whole number 50.

We know that nine tenths is equal to 0.9

We have to multiply the whole number 50 by 0.9

That is, 50 x 0.9 = 45.

Therefore  9 tenths of a whole number 50 is equal to 45.

Example 3:

Find 9 tenths of a whole number 110

Solution:

The given whole number is 110.

We are going to calculate the nine tenths of a whole number 110.

We know that nine tenths is equal to 0.9

We have to multiply the whole number 110 by 0.9

That is, 110 x 0.9 = 99.

Therefore  9 tenths of a whole number 110 is equal to 99.

Example 4:

Find 9 tenths of a whole number 11

Solution:

The given whole number is 11.

We are going to calculate the nine tenths of a whole number 11.

We know that nine tenths is equal to 0.9

We have to multiply the whole number 11 by 0.9

That is, 11 x 0.9 = 9.9.

Therefore  9 tenths of a whole number 11 is equal to 9.9

Convert decimal to fraction

How do you Change a Decimal to a Fraction
Numbers that are not whole numbers or integers are expressed in two forms. One is called fraction form and the other is decimal form. The fraction form of a number tells you what parts are considered out of the total equal parts to indicate the value. But with the advancement in communication or working with numbers, we needed a form that will suit. That form is the decimal form which implicitly uses the powers of 10 as the number of equal parts. The numbers of considered parts are written as digits after a dot ‘·’, called as decimal point.

But when some quantity is expressed in fraction form or decimal form has to possess the same value. Even these days many understand the fraction form better. Therefore it is imperative to know how to convert decimals to fractions. That is, if you know the measure of a quantity in decimal you must be able to convert decimals to fractions.

Let us now study how to change a decimal to a fraction. As we mentioned earlier, the digits after the decimal point represent the number of parts out of the total number of parts. The total number of parts is the same as 10 to the power of number of digits.  That is 0.2536 in fraction form is (2536)/(10000). In many cases, this fraction can be simplified to the lowest possible terms. Thus, this is the method of how to turn a decimal into a fraction.

There are certain tricky cases in converting decimals to fractions. Some decimals may have non terminating decimal terms. That is, there may be endless number of digits after the decimal point. Again there are two cases with non-terminating decimal terms. The digits of the terms may show a pattern or there may not be any pattern. If there is no pattern then the decimal terms beyond a predetermined decimal place may be ignored and the last digit to be considered may be suitably rounded. With this rounding, the decimal number can be changed into a fraction as per the method explained. Please express your views of this topic GCF Word Problems by commenting on blog.

How to Convert Decimal to Fraction if the non-terminating terms show a pattern? There is an interesting algebraic method is there to do that. The following is an example. How do you convert 0.23232323…. to a fraction?
Let x = 0.23232323….
So, 100x = 23 + 0.23232323…., which is 100x = 23 + x, which means 99x = 23 or x = (23)/(99)
Therefore, 0.23232323…. = (23/99)!

Dividing mixed numbers

Here in this page we are going to discuss aboout the concept of Dividing mixed numbers .The division of mixed number is same as the division of improper fractions. The reciprocal function of the mixed numbers is called as the division of mixed numbers.  For example, 2  `(5)/(6)`  is known as mixed number example. In this article, we are going to see about how to divide mixed numbers with example problems and also with brief explanation. Understanding Dividing Monomials is always challenging for me but thanks to all math help websites to help me out.

How to Divide Mixed Numbers

The explanations given below ,

Step 1: For dividing the given mixed number, the given improper fraction are converted into the proper fraction.

Step 2: Then in the next step, we have to take reciprocal function for the second term and put the multiplication sign.

Step 3: Then, normal multiplication of mixed number operation is performed.

Examples

Let see some solved problems on Dividing mixed numbers-

Problem 1: How to divide following mixed number, 4 `2/3` and  5 `4/3` .

Solution:

Step 1: Given:

4 `2/3` and  5 `4/3` .

Step 2: Solve:

4 `xx` 3 = 12 and 5 `xx` 3 = 15

12 + 2 = 14 and 15 + 4 = 19

`15/3`   `-:`   `19/3`

Step 3: Now we are taking reciprocal to the above functions, we get

= `15/3`  `xx`  `3/19`

= `15/19`

Result: Division of mixed numbers = `15/19`

Therefore, this is the required answer for solving the division of mixed numbers.

Problem 2: How to divide following mixed number, 3 `4/6` and  6 `5/7` .

Solution:

Step 1: Given:

3 `4/6` and  6 `5/7` .

Step 2: Solve:

3  `xx`  6 = 18 and 6 `xx` 7 =42

18 + 4 = 22  and 42 + 5 = 47

`22/6`   `-:`   `47/7`

Step 3: Now we are taking reciprocal to the above functions, we get

= `15/3`  `xx`  `7/47`

= `105/141`

Result: Division of mixed numbers = `105/141`

Therefore, this is the required answer for solving the division of mixed numbers. Is this topic Finding the Mode hard for you? Watch out for my coming posts.

Practice Problems

Here are the Practice problems to how to divide mixed numbers-

Problem 1: How to divide following mixed number, 2 `1/3` and  3 `1/4` .

Answer: `28/39`

Problem 2: How to divide following mixed number, 3 `2/3` and  4 `2/5` .

Answer: `5/6`