Solve Number Theory Test

Introduction to solve number theory test:

Solve number theory test includes convert between standard and scientific notation, prime or composite, prime or composite, identify factors, prime factorization, greatest common factor, least common multiple. Number theory helps students to learn about the number system with some basic knowledge. In below we have test questions with answer key in number theory. Let us see about solve number theory test.

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Test questions for solve number theory test:


Test question 1: Convert the following number from standard form in to scientific notation: 556.

Test question 2: Write the following scientific notation in to standard form 3.65 × 10^1

Test question 3: Identify the prime number from the following series: 100, 102, 103, 105, 200, and 250.

Test question 4: Calculate the prime factorization of 58.

Test question 5: Do the calculation to find the greatest common factor of 4 and 64.

Test question 6: Do the calculation to find the least common multiples 7 and 8.

Test question 7: Xavier is making stationery sets from 12 sheets of paper and 15 envelopes. If he wants all the sets to be identical without any paper or envelopes left over, find the greatest number of sets Xavier can make.

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Answer keys for solve number theory test:


Answer key 1: The scientific notation of the following standard form 556 is 5.56 × 10^2

Answer key 2: The standard form of the following scientific notation 3.65 × 101 is 36.5

Answer key 3: The prime number from the following series: 100, 102, 103, 105, 200, and 250 is 103.

Answer key 4: The prime factorization of 58 is 2 and 29.

Answer key 5: The greatest common factor of 4 and 64 is 8.

Answer key 6: The least common multiples 7 and 8 are 56.

Answer key 7: The greatest number of sets Xavier can make is 3.

Solve Help Percentages

Introduction – Solve help percentages:

In mathematics, a percentage is a way of expressing a number as a fraction of 100 (per cent meaning "per hundred" in French). It is often denoted using the percent sign, "%", or the abbreviation "pct". For example, 45% (read as "forty-five percent") is equal to 45/100, or 0.45. Let us see solve help percentages.

- Source from Wikipedia

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Example problems – Solve help percentages:


Problem 1:

How much is 9% of 1400 dollars?

Solution:

Since 1% is `1 / 100` * 1400 = 14 dollars, then 9% is 9 × 14 dollars = 126 dollars.

Problem 2:

A ice burg losses its weight from 140  to 125. What was its percentage weight loss?

Solution:

First, we have to find the absolute weight loss.

140 – 125 = 15 pounds

15 = (x) (140)

15 ÷ 140 = x

15 ÷ 140 = 0.10

Now we have to convert the decimal value as percent form.

To convert the decimal to percent form multiplies it by 100. That is 0.10*100 = 10.

Hence the ice burg losses its weight by 10%.

Problem 3:

Sham borrowed 950 dollars at 9% simple interest, for 3 years. How much did he have to pay back (principal + interest) after the 2 year period?

Solution:

The interest to pay is given by

Multiply the original amount by 9% and interest periods

Interest = 950 * `9 / 100` * 3 = 256.5 dollars

Total to pay back

950 + 256.5 = 1206.5 dollars.

After two years Sham has to pay 1206.5 dollars.

Problem 4:

A sales man sold his vehicle at 24% profit. Its original cost is 300 dollars. Find out the selling price.

Solution:

The gain is 24% of the 300 dollars cost, so the gain is:

`24 / 100 ` = (0.24) (300) = 72

Add the selling price percentage with original price

300 + 72 = 372

The vehicle sold at 372 dollars

Problem 5:

A person buys a laptop in a shop and paid 450 dollars for laptop and 15% for sales tax and 8% for accessories. How much did he pay for his laptop?

Solution:

He paid for laptop, sales tax and accessories, hence

Sales tax   = 15% = `15 / 100` * 450 = 67.5

Accessories           = 8% = `8 / 100` * 450 = 36

Total paid = 450 + 67.5 + 36 = 553.5 dollars.

Totally he paid 553.5 dollars for his laptop.

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Practice problems – Solve help percentages:


Solve help percentage practice Problem 1:

What is 68% of 840?

Answer:

= 571.2

Solve help percentage practice Problem 2:

The original price of a pen was 20 dollars. Now the price was decreased to 15 dollars. What is the percent decrease of the price of this pen?

Answer:

= 25%

Learn Types of Matrices

Introduction to learn types of matrices:

In mathematical matrix has a list of data. In math matrix elements are arranged in rectangular form. Elements are placed in row and column structure. In math matrix elements are put in the parenthesis or square brackets. Generally matrix is symbolized by capital letters. Many types of matrices are available in math. Let us see learn types of matrices in this article.


Learn types of Matrices:


Matrix:

Common representation of the word matrix is m`xx` n.

Where

Number of rows is represented by the variable ‘m’

Number of columns is represented by the variable ‘n’.

Example:

A = `[[a,b,c],[d,e,f],[g,h,i]]`

The above is 3`xx` 3 matrices.

Learn some other information about matrix:

We can perform addition, subtraction and multiplication process between matrices. But we cannot divide matrices.

Types of matrices

Column matrix
Row matrix
Square matrix
Diagonal matrix
Triangular matrix
Scalar matrix
Identity matrix
Zero matrixes
Equality of matrix


Learn definition for types of matrices:


Definition of column matrix:

Only one column is there in the column matrix.

Example:

A = `[[,a],[,b],[,c]]`

Definition of row matrix:

Only one row is there in the row matrix.

Example:

A = `[[a,b,c]]`

Definition of square matrix:

Square matrix has equal number of row and column.

Example:

A = `[[a,b],[c,d]]`

Definition of diagonal matrix:

Diagonal matrix has zero value (other than diagonal elements)

Example:

A= `[[a,0],[0,b]]`

Definition of triangle matrix:

Triangle matrix necessity is a square matrix. Every element in above the diagonal are zero means called as lower triangle matrix. Every element in below the diagonal is zero means called as upper triangle matrix.

Example for upper triangle matrix:

A = `[[a,b,c],[0,d,e],[0,0,f]]`

Example for lower triangle matrix:

A = `[[a,0,0],[b,c,0],[d,e,f]]`


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Definition of unit matrix:

Unit matrix necessity is a square and diagonal matrix. The diagonal elements are one and the other elements in the array is zero means called as unit matrix.

Example:

A = `[[1,0,0],[0,1,0],[0,0,1]]`

Hardest Math Problem to Solve

Introduction to hardest math problem to solve:

Learn and to solve the  hardest math problems involves the operations like addition, subtraction, multiplication and division and it be viewed as ( +,-,`xx` ,÷ ) .By solving the hardest math problems means  it helps in our daily life also without math there is no calculation involved and so every one is learning the math problems.The math problems helps  to increase our mental ability and to think and execute in some pressure situations with out any mistake. Here we are going to see about the article called hardest math problem to solve .


Solved hardest math problem


Math problem 1:

A ice cream manufacturing organization  produces an amount of 4357 ice cream product flavor  in a year. And that company produces three types of ice cream flavors of products like strawberry, Butterscotch, and chocolates. The amount of chocolates was 199 more than the flavors of Butterscotch. Then the strawberries flavor were made four times of the number of chocolates made in this year. Find the number of strawberry was produced by the company in this year?
Solution:

Let we denote as,

A = strawberry, B = Butterscotch, and C = chocolates.

Step 1:

From the given problem we can write as,

A + B+ C = 4357 (1) 

C = A + 199         (2)

B = 4A                   (3).

Step 2:

In step 2 denote the equations 2nd and 3rd in equation 1,

A+ 4A + A +199  = 4357

6A = 4158.

A = 693

So we get there are  693 strawberry  flavor were produced by the ice cream  company in this year.

Step 3:

Apply the value of A in equation 3 we get,

B = 4(693)

B =2772

So we get there are 2772 Butterscotch flavor were produced by the ice cream company in this year.

Step 4:

Apply the value of A and B equation 1 we get,

A + B + C = 4357

693+ 2772 + C =4357

3465+ C= 4357.

C = 892

So we get there are 892 chocolates flavor were produced by the ice cream company in this year.


One more solved hardest math problem


Math problem 1:

Solve the given problem 20(s – 99) – 87s - 18 = 191(s + 15)

The Solutions follows below:

Given expression is,

20(s – 99) – 87s `-` 18 = 191(s + 15)

Multiplying the integer terms

20s – 1980 – 87s – 18 = 191s + 2865.

Grouping the above terms

–67s –-1998= 191s + 2865

Add 1998 on both sides

–67s –1998+ 1998 = 191s + 2865  + 1998

Grouping the above terms

–67s = 191s +4863

Subtract 191s by on both sides

–67s – 191s = 191s – 191s + 4863

Grouping the above terms

–258s = 4863

S = `- 4863/258`

The required answers is 

S = `- 4863/258`

Nine Grade Math Slope

Introduction to nine-grade math slope:

Nine- grade math slope article deals with how to find the slope from the slope intercept from of the equation and from the two given points of the line. It includes the slope of the parallel and perpendicular line. We have the different formula to find the slope of the given line

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Formula related to nine grade math slope.

When two coordinate points on the line is given

Formula to find slope, m = `((y2-y1)/(x2-x1))`

When slope intercept form is given

The slope intercept form is y = mx+b

m = `((y-b)/x)`

Where m is the slope of the line

b is the y intercept.

When two lines are parallel to each other, the slope of the both lines is equal.

When two lines are perpendicular to each other, the product of slope is -1[ (m1*m2)= -1]

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Model problems for nine grade math slope


Example problems for nine grade math

Find the slope of the line whose coordinate points are (2, 3) and (4, 5).


Solution:

(x1,y1) = (2, 3)

(x2,y2) = (4, 5)

Formula:

Formula to find slope, m = `((y2-y1)/(x2-x1))`

= `((5-3)/ (4-2))`

= `(2/2)`

= 1

The slope of the line is 1

2.find the slope of the line whose slope intercept form is 3y = 6x +9

Solution:

The slope intercept form is y= mx+b

The given equation is 3y= 6x +9
rewrite the equation of the line

y= `(6/3)x+(9/3)`

y= 2x+3

Now it is in the standard form.

Therefore, the slope of the line is 2

3. Line AB and CD are perpendicular to each other, find the slope of the line CD when the two points on the lineAB is (2, 7) and (6, 4)

Solution:

(x1,y1) = (2, 7)

(x2,y2) = (6, 4)

Formula:

Formula to find slope, m = `((y2-y1)/(x2-x1))`

= `((4-7)/(6-2))`

= `((-3)/4)`

= `(-3/4)`

The slope of the line is `(-3/4)`

Since AB and CD are perpendicular to each other.

so, the slope of the CD =` (- 1/"slope of AB")`

= `(-1/ ((-3/4)))`

= `(4/3)`

Slope of the line CD is `(4/3)`

4th Grade Learning Math

INTRODUCTION TO FOURTH GRADE LEARNING MATH

Fourth grade learning math is the learning basic of some more brief of mathematics that was learned in third grade. Fourth grade learning math is the learning based on topic such as addition, subtraction, multiplication, division, equations and variables. Fourth grade learning math consists of chapters like algebra, charts, graph, fractions, decimals and geometry. Fourth grade learning math work consists of more subtopic under each chapter. Here we can learn some of the fourth grade math on some chapters. Fourth grade learning math is advance of third grade learning math.

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FOURTH GRADE LEARNING MATH


1.    Add 7 2 1 0 + 2 4 2 5

Solution

7 2 1 0

2 4 2 5 +

-------------

9 6 3 5

-------------

2.  Subtract 9 7 5 3 – 2 6 3 0

Solution

9 7 5 3

2 6 3 0 –

-------------

7 1 2 3

-------------

3.  Tony had 15 biscuit packets. Each packet consists of 7 biscuits. How many biscuits totally he had?

Solution

Number of biscuits in one packet = 7 biscuits

So 15 biscuit packets consists = 15 x 7= 105 biscuits.

4. Add the decimal value 75. 36 + 23.21

Solution

75. 3 6

23. 2 1 +

-----------

98. 5 7

------------

5. Subtract decimal value given 54.34 – 24.51

Solution

5 4.3 4

2 4.5 1   -

-------------

2 9.8 3

----------------

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MORE PROBLEM OF FOURTH GRADE LEARNING MATH


6.   Solve the equation 5x + x = 24

Solution

5x + x = 24

6x = 24

Divide 6 on both sides

x = 4



7. Add `3/11` +`6/11`

Solution

Here the denominators are same. So just add the numerator alone

` (3+6)/11`

`9/11` is the answer.

8. Subtract `8/9` – `4/9`

Solution

Here the denominators are same. So just subtract the numerator alone.

`(8 - 4)/9`

`4/9`

9. Multiply` 3/5` * `3/ 4 `

Solution

`3 / 5 ` * `3 / 4`

3* 3 / 5* 4

= `9 / 20 `

10. Convert 100 centimeter =? Meter

Solution

100 centimeter = 1 meter.

Commission Math Problems

Introduction to commission math problems:

Commission math problems article deals with the definition of the commission and the math problems related to the commission.

Definition of commission math problems:

This math problems deals with the rate of money, which we can earn by selling some product or doing the work behind the target fixed.This is very important things in selling and buying the products and it is used to find the commission amount.

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Formula to commission math problem


In these problems the commission rate r % is fixed, by multiply the commission rate with the original cost of the product, we can get the commission amount on that particular product,

Commission amount = r% *(original cost of the product).

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Model problems to the commission math problems:


Find the monthly income of the john if his monthly salary is $2000 and he gets 4% of commission if he sells a car of cost about $4500.
Solution:

The monthly salary of the john is $2000

The commission rate is r= 4%

Commission amount = r% *(original cost of the product).

= 4 %*( 4500)

= (4/100)*(4500)

=(0.04)*(4500)

= $180

Commission amount is 180 $

The monthly income of the john = monthly income +commission amount

= $ 2000 +$180

= $2180

The monthly income of the john is $2180.

2.Find the income of the sam if his daily salary is $200 and he gets 3% of commission if he sells the product amount morethan $500.

Solution:

The daily salary of the john is $200

The commission rate is r= 3%

Commission amount = r% *(500).

= 3 %*( 500)

= (3/100)*(500)

=(0.03)*(500)

= $15

Commission amount is $15

The daily income of the john = daily income +commission amount

= $ 200 +$15

= $215

The monthly income of the john is $215.

3.Find the commission price of the product of cost $700 and the tax commission is 6%.

Solution:

The tax commission is 6%

The cost of the product is $700

Commission amount = r% *(original cost of the product).

= (6/100)*700

= (0.06)*700

= 42

commission amount is $42.