Most Common Number System (Nandan Nayak)

Introduction to most common number system:

In this we have most common number system. Most common system in math includes rational system, decimal numbers, fractional number, whole number, and so on. In this topic we will see some example problems for decimal number, fractional numbers, whole numbers, and so on. And also we have practice problems. Let us start to study about most common number system.

Example problems for most common number system:

Example problem 1: There is a population of 30,000 bacteria in a colony. If the number of bacteria doubles every 25 minutes, what will the population be 50 minutes from now?

Solution:

First, find out how many times the population will double. Divide the number of minutes by how long it takes for the population to double.

50 ? 25 = 2

The population will double 2 times.

Now figure out what the population will be after it doubles 2 times. Multiply the population by 2 a total of 2 times.

30,000 ? 2 ? 2 = 120,000

That calculation could also be written with exponents:

30,000 ? 22 = 120,000

After 50 minutes, the population will be 120,000 bacteria.

Answer: After 50 minutes, the population will be 120,000 bacteria.

Example problem 2: Preston bikes 0.4 kilometers each school day. How far in total will Preston bike over 14 school days?

Solution:

Multiply the kilometers biked each school day by the number of school days.

0.4 ?14 +40 = 56

Count the number of decimal places in the factors. There is 1 decimal place in 0.4.

56. => 5.6

Preston will bike 5.6 kilometers.

Answer: Preston will bike 5.6 kilometers.

Practice problems for most common number system:

Practice problem 1: Crystal is creating potpourri bowls using 18 bags of shredded bark and 15 bags of flower petals. If she wants to make all the potpourri bowls identical, containing the same number of bags of shredded bark and the same number of bags of flower petals, what is the greatest number of potpourri bowls Crystal can create?

Practice problem 2: There is a population of 10,000 bacteria in a colony. If the number of bacteria doubles every 19 minutes, what will the population be 38 minutes from now?

Practice problem 3: A restaurant chef made '1 2/3 ' pints of tomato soup. Each bowl of soup holds '5/6' of a pint. How many bowls of soup will the chef be able to fill?

Solutions for most common number system:

Solution 1: The greatest number of potpourri bowls Crystal can create is 3.

Solution 2: After 38 minutes, the population will be 40,000 bacteria.

Solution 3: The chef will be able to fill 2 bowls.

Processing ...

Five Number Summary Tutoring (Nandan Nayak)

Introduction to five number summary tutoring:

Five number summary is one of the important topics in mathematics. Five number summary is a sample from which they are derived from a particular group of individuals. Five number summary has a set of observations. In a single variable, it has a set of observations. Five number summary has a different statistics. Here we study about the different statistics involved in five number summary.The online tutoring for the five number summary will give the explanations to the students very interactively through the definitions, steps and examples problems. Therefore, students can learn from online.

Five number summary tutoring:

Different statistics are involved in five number summary are,

Minimum
Maximum
Median
Lower quartile
Upper quartile

Minimum:
Lowest value in the given set of numbers.

Maximum:
Largest value in the given set of numbers.

Median:
Middle value in the given set of numbers.

Lower quartile:
Number between the minimum and median.

Upper quartile:
Number between the maximum and median.

Five number summary tutoring - Steps to solve:

There are different steps to solve the five number summary are,

Observation can be arranged in the ascending order.
The lowest and largest value in the observation can be determined.
The median can be determined. When the observation has odd number of observation than the median is in middle of the observation. Otherwise it is an even number then the median is calculated by the average of the two middle numbers.
The upper quartile can be determined. When the observation minus one is divided by 4 means it is starting with the median and observations in the right side. Otherwise the observation is not divided by four means upper quartile is the median of the observation to the right of the location of overall median.
The lower quartile can be Determined. When the observation set minus one is divided by 4 then it is starting with the median and its observations in the left side. Otherwise the observation is not divided by four means lower quartile is the median of the observation to the left of the location of overall median

Five number summary tutoring - Example problem:

Example 1:

Find the five number summary for the given set of data

{535, 572, 534, 545, 529, 528, and 577}

Solution:

Given set of data

{535, 572, 534, 545, 529, 528, and 577}

{528, 529, 534, 535, 545, 572, 577} [Arrange the set in ascending order]

Minimum and Maximum values in the given set of data are 528 and 577.

Median:

Given observation is odd. So the median is middle of the observation then the median is 535.

Lower quartile:

Given observation is not divisible by four. So the lower quartile is {528, 529, and 534}

Upper quartile:

Given observation is not divisible by four. So the upper quartile is {545, 572, and 577}.

Answer:

Minimum: 528

Maximum: 577

Median: 535

Lower quartile: {528, 529 and 534}

Upper quartile: {545, 572 and 577}

Example 2:

Find the five number summary for the given set of data

{36, 71, 33, 44, 22, 27, 55 and 76}

Solution:

Given set of data

{36, 71, 33, 44, 22, 27, 55 and 76}

{22, 27, 33, 36, 44, 55, 71, 76} [Arrange the set in ascending order]

Minimum and Maximum values in the given set of data are 22 and 76.

Median:

Given observation is even. So the median is median is calculated by the average of the two middle numbers

Median = (36 + 44)/2

= 80/2

Median = 40

Lower quartile:

Given observation is not divisible by four. So the lower quartile is {22, 27, 33 and 36}

Upper quartile:

Given observation is not divisible by four. So the upper quartile is {44, 55, 71 and 76}.

Answer:

Minimum: 22

Maximum: 76

Median: 40

Lower quartile: {22, 27, 33 and 36}

Upper quartile: {44, 55, 71 and 76}

Processing ...

Most Common Number System (Nandan Nayak)

Introduction to most common number system:

In this we have most common number system. Most common system in math includes rational system, decimal numbers, fractional number, whole number, and so on. In this topic we will see some example problems for decimal number, fractional numbers, whole numbers, and so on. And also we have practice problems. Let us start to study about most common number system.

Example problems for most common number system:

Example problem 1: There is a population of 30,000 bacteria in a colony. If the number of bacteria doubles every 25 minutes, what will the population be 50 minutes from now?

Solution:

First, find out how many times the population will double. Divide the number of minutes by how long it takes for the population to double.

50 ? 25 = 2

The population will double 2 times.

Now figure out what the population will be after it doubles 2 times. Multiply the population by 2 a total of 2 times.

30,000 ? 2 ? 2 = 120,000

That calculation could also be written with exponents:

30,000 ? 22 = 120,000

After 50 minutes, the population will be 120,000 bacteria.

Answer: After 50 minutes, the population will be 120,000 bacteria.

Example problem 2: Preston bikes 0.4 kilometers each school day. How far in total will Preston bike over 14 school days?

Solution:

Multiply the kilometers biked each school day by the number of school days.

0.4 ?14 +40 = 56

Count the number of decimal places in the factors. There is 1 decimal place in 0.4.

56. => 5.6

Preston will bike 5.6 kilometers.

Answer: Preston will bike 5.6 kilometers.

Practice problems for most common number system:

Practice problem 1: Crystal is creating potpourri bowls using 18 bags of shredded bark and 15 bags of flower petals. If she wants to make all the potpourri bowls identical, containing the same number of bags of shredded bark and the same number of bags of flower petals, what is the greatest number of potpourri bowls Crystal can create?

Practice problem 2: There is a population of 10,000 bacteria in a colony. If the number of bacteria doubles every 19 minutes, what will the population be 38 minutes from now?

Practice problem 3: A restaurant chef made '1 2/3 ' pints of tomato soup. Each bowl of soup holds '5/6' of a pint. How many bowls of soup will the chef be able to fill?

Solutions for most common number system:

Solution 1: The greatest number of potpourri bowls Crystal can create is 3.

Solution 2: After 38 minutes, the population will be 40,000 bacteria.

Solution 3: The chef will be able to fill 2 bowls.

Processing ...

Five Number Summary Tutoring (Nandan Nayak)

Introduction to five number summary tutoring:

Five number summary is one of the important topics in mathematics. Five number summary is a sample from which they are derived from a particular group of individuals. Five number summary has a set of observations. In a single variable, it has a set of observations. Five number summary has a different statistics. Here we study about the different statistics involved in five number summary.The online tutoring for the five number summary will give the explanations to the students very interactively through the definitions, steps and examples problems. Therefore, students can learn from online.

Five number summary tutoring:

Different statistics are involved in five number summary are,

Minimum
Maximum
Median
Lower quartile
Upper quartile

Minimum:
Lowest value in the given set of numbers.

Maximum:
Largest value in the given set of numbers.

Median:
Middle value in the given set of numbers.

Lower quartile:
Number between the minimum and median.

Upper quartile:
Number between the maximum and median.

Five number summary tutoring - Steps to solve:

There are different steps to solve the five number summary are,

Observation can be arranged in the ascending order.
The lowest and largest value in the observation can be determined.
The median can be determined. When the observation has odd number of observation than the median is in middle of the observation. Otherwise it is an even number then the median is calculated by the average of the two middle numbers.
The upper quartile can be determined. When the observation minus one is divided by 4 means it is starting with the median and observations in the right side. Otherwise the observation is not divided by four means upper quartile is the median of the observation to the right of the location of overall median.
The lower quartile can be Determined. When the observation set minus one is divided by 4 then it is starting with the median and its observations in the left side. Otherwise the observation is not divided by four means lower quartile is the median of the observation to the left of the location of overall median

Five number summary tutoring - Example problem:

Example 1:

Find the five number summary for the given set of data

{535, 572, 534, 545, 529, 528, and 577}

Solution:

Given set of data

{535, 572, 534, 545, 529, 528, and 577}

{528, 529, 534, 535, 545, 572, 577} [Arrange the set in ascending order]

Minimum and Maximum values in the given set of data are 528 and 577.

Median:

Given observation is odd. So the median is middle of the observation then the median is 535.

Lower quartile:

Given observation is not divisible by four. So the lower quartile is {528, 529, and 534}

Upper quartile:

Given observation is not divisible by four. So the upper quartile is {545, 572, and 577}.

Answer:

Minimum: 528

Maximum: 577

Median: 535

Lower quartile: {528, 529 and 534}

Upper quartile: {545, 572 and 577}

Example 2:

Find the five number summary for the given set of data

{36, 71, 33, 44, 22, 27, 55 and 76}

Solution:

Given set of data

{36, 71, 33, 44, 22, 27, 55 and 76}

{22, 27, 33, 36, 44, 55, 71, 76} [Arrange the set in ascending order]

Minimum and Maximum values in the given set of data are 22 and 76.

Median:

Given observation is even. So the median is median is calculated by the average of the two middle numbers

Median = (36 + 44)/2

= 80/2

Median = 40

Lower quartile:

Given observation is not divisible by four. So the lower quartile is {22, 27, 33 and 36}

Upper quartile:

Given observation is not divisible by four. So the upper quartile is {44, 55, 71 and 76}.

Answer:

Minimum: 22

Maximum: 76

Median: 40

Lower quartile: {22, 27, 33 and 36}

Upper quartile: {44, 55, 71 and 76}

Processing ...

Number Sense Tutorial (Nandan Nayak)

Introduction to number sense tutorial:

In mathematics, number system is called as system of numeration. Number systems are used to express the quantities for counting, defining order, comparing the quantities, calculating numbers and denoting values. Number system includes natural numbers, integers, rational numbers, algebraic numbers, real numbers, complex numbers, p-adic numbers, surreal numbers and hyper real numbers.

Number sense is explained with examples and practice problems very interactively by tutorial. So students are getting number sense help by tutorial for their studies.

Examples to number sense tutorial:

Example 1:

Add the following decimal numbers 65.45 + 6.892

Solution:

Addition operation for decimal numbers is just like the integers addition. In this problem

65. 45 has two decimal place but 6.892 has three decimal place. Hence, we have to add 0 with the number 65.45, so we get 65.450

That is, 65.45+6.892 = 65.450+6.892

11 1
65.450
+ 6.892
72.342

Example 2:

Find the square root of the following numbers 'sqrt(289)' .

Solution:

'sqrt(189) ' = 'sqrt(17 xx 17)' = 17

Example 3:

Write the standard for the following number 69.089 'xx' '10^3'

Solution:

69.089 'xx' '10^3' which can be written as

69.089 'xx' 10 'xx' 10 'xx' 10

69.089 'xx' 1000 now we have to shift the decimal point to three decimal point. So that we will get

69089

Example 4:

Add the following mixed numbers '8 1/3' and '8 1/4' .

Solution:

We have to convert the following mixed numbers in to improper fraction. For this, denominators are multiplied with the whole number and then add the result of the product with numerator. So that, we will get the improper fraction.

'8 1/3' => '((8 xx 3) + 1)/3' => '(24 + 1)/3' => '25/3'

'8 1/4' => '((8 xx 4) + 1)' => '(32 + 1)/4' = '33/4'

Now we can add both improper fraction

'25/3' + '33/4' here, denominators are not same. So that, we have to find LCM. The LCM is 12

The denominator 3 from the fraction '25/3' is 4 times in the LCM. So we have to multiply the numerator 25 by 4. So we get '100/12'

The denominator 4 from the fraction '33/4' is 3 times in the LCM. So we have to multiply the numerator 33 by 3. So we get '99/12'

'(100 + 99)/12'

'199/12'

Practice Problems to number sense tutorial:

Problem 1:

Add the following decimal numbers 6.45 + 6.82

The answer is 13.27

Problem 2:

Find the square root of the following numbers 'sqrt(324)' .

The answer is 18

Problem 3:

Write the standard for the following number 675.89 'xx' ' 10^3'

The answer is 675890

Problem 4:

Add the following mixed numbers '1 5/3' and '2 6/4' .

The answer is '22/12'

Processing ...

Number Theory Homework Tutoring (Nandan Nayak)

Introduction to number theory homework tutoring:

In this article we will see about number theory homework tutoring. Number theory homework tutoring is nothing but it is also the basic chapters of mathematics. The number theory problems will be simple and easier. Number theory homework tutoring is done by the tutors in online process. Below are some of the solved example problems under this topic of number theory. Number theory homework tutoring will include the problems on the topics like scientific notation, prime factorization etc.

Number theory homework tutoring

Homework tutoring is done by the tutors of tutor vista. There are many tutors of high qualification are always ready to provide tutoring for the students.

Solved problem 1: Write standard form of the given scientific notation 3.432 ? 102

Solution:

Given 3.432 ? 102

To find the standard form just multiply the scientific notation by 10.

10 are raised with the powers of 2. So shift the decimal point two places to the right side. 3.432 --> 343.2

3.432 ? 102 = 343.2

Solved problem 2: Find the least common multiple of 3 and 8

Solution:

Given 3 and 8

To find the least common multiple (LCM), we have to list out the multiples of 3 and 8.

Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30

Multiples of 8: 8, 16, 24, 32, 40, 48

The least common multiple of 3 and 8 is 24. Since 24 is the least common number that comes first in the multiples of both 3 and 8

Solved problem 3: Find the prime numbers in the given series of numbers 14, 16, 19, 21, 25, 29

Solution

Prime numbers are divisible only by 1 and the number itself. It does not have any other multiples. Here we check the given numbers

Multiples of 14 = 1, 2, 7, 14

Multiples of 16 = 1, 2, 4, 8, 16

Multiples of 19 = 1, 19

Multiples of 21 = 1, 3, 7, 21

Multiples of 25 = 1, 5, 25

Multiples of 29 = 1, 29

So here 19 and 29 are the prime numbers of the given series of numbers.

Number theory homework tutoring

Below are some of the practice problems about number theory homework tutoring.

1. Find the prime numbers of the series given below

35, 37, 39, 41, 45

2. Find the LCM of 7 and 9

3. Write the standard form of the scientific notation given 5.243x 102

4. Find the LCM of 11 and 6

5. Find out the prime numbers of the given 42, 63, 70,71

Answer

1. 37, 41

2. 63

3. 524.3

4. 66

5. 71

A number is a mathematical object used in counting and measuring. A notational symbol which represents a number is called a numeral, but in common usage the word number is used for both the abstract object and the symbol, as well as for the word for the number. In addition to their use in counting and measuring, numerals are often used for labels (telephone numbers), for ordering (serial numbers), and for codes (ISBNs).Let us see about the articles is solving math number problems.

Processing ...

is a repeating decimal a rational number (dave hook)

Introduction - Is a repeating decimal a rational number?

In math a rational number is a number that can be articulated as a ratio of 2 integers, which is in the form of 'p/q' where p and q are integers and q should not be equal to zero. Likewise, any repeating or ending decimal represents a rational number. In this article we shall argue is a repeating decimal a rational number.

Examples of rational numbers:

The following are the examples of rational numbers:

'1/4' is a rational number (1 divided by 4, or the ratio of 1 to 4)

The decimal 0.5 is a rational number ('1/2' )

1 is a rational number ('1/1' )

4 is a rational number ('4/1' )

The decimal 3.14 is a rational number ('314/10' )

The decimal 1.13 is a rational number ('113/100' )

The negative decimal -3.3 is a rational number ('-33/10' )

The repeating decimal 1.1212121212... is a rational number.

The repeating decimal 1.3333333333... is a rational number.

Is a repeating decimal a rational number?

Yes a repeating decimal is a rational number. Because the decimal extension of a rational number always either terminates after finitely many digits or begins to replicate the same series of digits more and more. Therefore any repeating decimal is a rational number.

Let us discuss the properties of rational numbers

Commutative property a+b = b+a

Associative property (a+b)+c = a+(b+c)

Additive identity a+0 = a

Multiplicative identity a (1) = a

Additive inverse a+ (-a) = 0

Multiplicative inverse (1/a) =1

Multiplication property of zero a(0)=0

Distributive property a(b+c) = ab + ac

Example problems for rational number:

Identify the rational numbers from the following.

5, 78, 5.6, 784, 0.55, 6.57575757..., 3.645548349... , 'sqrt2' , 'sqrt3' , 'pi'

Solution:

5 can be written as a ratio of 5 and 1, which is '5/1' where 1 and 5 are integers.

78 can be written as a ratio of 78 and 1, which is '78/1' where 1 and 78 are integers.

5.6 can be written as a ratio of 56 and 10, which is '56/10' where 10 and 56 are integers.

0.55 can be written as a ratio of 55 and 100, which is '55/100' where 100 and 55 are integers.

6.57575757... has a repeating decimal 5 and 7 therefore it is a rational number.

3.645548349... has a repeating decimal 3 therefore it is a rational number.

sqrt2 is equal to 1.4142135.. is not a rational number because the decimal is not repeating.

sqrt3 is equal to 1.732050.. is not a rational number because the decimal is not repeating.

'pi ' is equal to 3.14159265.... is not a rational number because the decimal is not repeating.

Here in this page we are going to discuss about operations with rational numbers. In abstract algebra, the concept of a polynomial is extended to include formal expressions in which the coefficients of the polynomial can be taken from any field. In this setting given a field F and some indeterminate X, a rational expression is any element of the field of fractions of the polynomial ring F [X].

Source: Wikipedia

Operations on rational numbers

Rational number is the quotient of two integers. Therefore, a rational number is a number that can be write in the form 'w/x', where w and x are integers, and x is not zero. A rational number written in this way is commonly called a fraction.

'w/x'

Where

w 'rArr' an integer

x 'rArr' a nonzero integer

'17/15', '(14)/(9x)' 'rArr' Rational numbers

An integer can be marking it as the quotient of the integer and 1, every integer is a rational number.

Note : A rational number written as a fraction can be written in decimal notation.

Examples

Below are the examples on operations with rational numbers -

Example 1:

Write '48/4' as a decimal.

Solution:
12 'rArr' This is called a terminating decimal.
4 | 48
4
08
8
0'rArr' The remainder is Zero.

'48/4' = 12

Adding operations with same denominators:

Example 2:

'8/2' + '4/2' = ?

Solution:

'8/2' + '4/2' = '8/2' + '4/2'

= '(8+4)/2'

= '(12/2)'

= '6'

Adding operations with different denominators:

Just as we add fractions, rational numbers with different denominators can also be extra. By finding out the LCM, we can take the denominators to the same number.

Example 3:

'4/3' + '3/6'

Solution:

= '4/3' + '3/6'

6 is the LCM of 3 and 6.

= '8/6' + '3/6'

= '(8+3)/6'

= '11/6'

= '11/6'

Subtraction operations with same denominators:

Just as we subtract fractions, we can subtract rational numbers with same denominator.

Example 4:

'5/6' - '2/6' = ?

Solution:

= '5/6' - '2/6'

= '(5-2)/6'

= '4/6'

= '2/3'

Subtraction operations with different denominators:

Just as we subtract fractions, rational numbers also can be taken off with different denominators. The common denominator is achieved by finding out the LCM.

Example 5:

'-5/12' + '2/6'

Solution:

= '-5/12' + '2/6'

= '-5/12' + '4/12'

= '(-5+4)/12'

= '-1/12'

Multiplication operations with same denominators:

Just alike the multiplication of whole numbers and integers, multiplication of rational number are also repeated addition.

Example 6:

'5/4*10/5'

Solution:

= '5/4*10/5'

= '(5*10)/(4*5)'

= '50/20'

= '5/2'

Multiplication operations with different denominators:

Example 7:

'5/2*10/3'

Solution:

= '5/2*10/3'

= '(5*10)/(2*3)'

= '50/6'

Practices problems

Problem 1:

'2/6+1/3' = ?

Answer: '2/3'

Problem 2:

'2/5' + '1/5'

Answer: '3/5'

Problem 3:

'7/5' - '5/5'

Answer: '2/5'

Problem 4:

'30/3' -('5/5')

Answer:'135/15' or '9'

Problem 5:

'5/3*2/3'

Answer:'10/9'

Problem 6:

'2/5*4/2'

Answer:'4/5'

Processing ...