Algebra Game Math

Introduction to algebra games math:

In math, the numerical numbers are learnt by the algebra. Here we will see the simplest games of algebra. It is also used to study the polynomials and the equations etc. In this algebra having the quadratic equation, polynomial, algebraic expressions and algebraic identities. Here we will see about these explanation and example games.


Explanation about the algebra games math


Let us see about algebra games math:

Algebra math problem, the quadratic equation of the variable of A. An equation in the form xa2+yb+c=0.

A polynomial of quantity one is known as a linear polynomial.
Algebraic expressions are a partition of polynomial. It is indicated by a letters and exponent.
Algebraic identities are the form (x+y)^2=x^2+2xy+y^2.

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Some sample practice problem about algebra games math

Let us see about algebra games math:

Example 1:

To change the word of character by the same number to use the arithmetic operations are right.

SEND
MORE
---------
MONEY

Answer: 10652

Example 2:

To change the word of character by the same number to use the arithmetic operations are right.

SEVEN + SEVEN + SIX = TWENTY

Answer: 138214

Example 3:

To change the word of character by the same number to use the arithmetic operations are right.

SINUS
SINUS
KOSINUS
-------------
TANGENS

Answer: 4076175

Example 4:

John last birthday he weighed 125 pounds. After one year later he has put on x pounds. Which appearance gives he weight one year later?

Answer: x 125

Example 5:

If you multiply the square of a number n by 3 and then added 7 to the product, the sum is equal to 55. One of the terms is equals 55, which one is it?

Answer: 3n2 7

Example 6:

To change the word of character by the same number to use the arithmetic operations are right.

(J+O+I+N+T)*(J+O+I+N+T)*(J+O+I+N+T) = JOINT

Answer: 19683

Fact Family Math

Introduction to fact family math:

The fact family in math is nothing but the math equations or the numbers which can be operated and related within the operations such as addition, subtraction, division and multiplication. Using these operations the related numbers can be calculated. The fact family math can be learned easily with the help of the basic operations. Now we are going to see the fact family math with some examples. Understanding Vector Addition Problems is always challenging for me but thanks to all math help websites to help me out.


About fact family math:


The fact family math can be understands easily by following the basic operations. Let us learn the fact family math with some examples.

Example:

Write the fact family math for the numbers such as 5, 7 and 12.

Solution:

We know these numbers are related as the fact family and can be given as follows,

The number 7 and 5 added to give 12.

7 + 5 = 12

If we add the number 5 to 7 then also it will be 12.

5 + 7 = 12

The number 5 can be obtained by subtracting the number 12 and 7

12 – 7 = 5

The number 7 can be obtained by subtracting the numbers 12 and 5.

12 – 5 = 7

Thus, the given numbers can be obtained by using the operations. These can be called as the fact family because certain numbers can be obtained by repeating the numbers with different operations.

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Example for fact family math:

Find the family fact of the numbers such as 5 and 6 using multiplication and division?

Solution:

The family fact math numbers can be determined by using the multiplication and division numbers such as follows,

5 * 6 = 30

If we multiply 5 and 6 we get 30.

If we multiply the number 6 with number 5 again we get 30 only.

6 * 5 = 30.

The number 6 or 5 can be obtained again by dividing the numbers 30 by 5 to get 6.

` 30/5` = 6.

Now the number 5 can be obtained by dividing the numbers 30 by 6

`30/6` = 5.

The above are the facts of the numbers 5 and 6.

Radical Form in Math

Introduction to radical form in math:

Radicals is a form of symbol which is used in the mathematics. It is shown that the radical  symbol as  root "v". The number inside the radical symbol which is called as the radicand of the radical value, for example if the given value is square root of `sqrtx` . The x is called as the radicand which is the number inside the radical symbol root "v". There are more number of rooting methods available depending upon the value we have. The roots are square root `sqrtx` , cube root `root(3)(x)` , Fourth root `root(4)(x)` this up to nth root `root(n)(x)` . Here we are going to see about the radical form in math in different methods and the solved example problems on it.

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Radical form in math - Some Properties:

Radicals form - Representations:

Function `a^(1/n)` :

The radical exponent  `a^(1/n) = root(n)(a)`

If n has odd value then,

If a is positive value then the function  `a^(1/n)` is positive.

If a is negative value then the function `a^(1/n)` is negative.

If a is zero value then the function `a^(1/n)` is also zero

If n has even value then,

If a is positive value then the function `a^(1/n)` is positive.

If a is negative value then the function `a^(1/n)` is not a real number.

If a is zero value then the function`a^(1/n)` is also zero

Radical Expression:

`x^(1/n) = root(n)(x)`    it is n root of x value.

Relation between expression and Radical:

`(x^(1/n))^n`   is the relation between the expression and radical .

Radical Exponent of Product:

`root(n)(axxb) = (axxb)^(1/n) = root(n)(a) xx root(n)(b) = a^(1/n) xx b^(1/n) `

Radical for a quotient:

`root(n)(a/b) = (a/b)^(1/n) = root(n)(a)/root(n)(b) = a^(1/n)/b^(1/n)`

Radical of a fraction:

`msqrta^n = a^(n/m) `


Radical form in math - Example Problems:


Radical form in math -  Problem 1:

Solve the radical form for 16.

Solution:

Method 1: Finding the square root of 16 by long division method

_4__
2)16 (
16
0
The value for the `sqrt 16` is 4

Method 2:

`sqrt16` = `sqrt(4^2)`

=` (4^2)^2`

= `(4)^(2/2)`

= 4

Radical form in math - Problem 2:

Solve radical value for 435

Solution:

The root value 435 is nearly equal to the square values between 20 and 21, because 202 = 225 and 212 = 256

Step 1: Divide 435 by 20.

`435 / 20` = 21.75

Step 2: Take average for 21.75 and 20.

` (21.75+20)/2 ` = 20.87500

Step 3: Divide 255 by 16

`435/20.87500 ` =  20.8383234



Step 4: Take average for the 20.8383234 and 20.87500

`( 20.8383234 + 20.87500)/2` =  20.8566617

Step 5: Now check the above result by taking square

20.8566617 2 =  435.000337

This value is more or less equal to 435

If the value is not equal repeat the step 3 and step 4

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Radical form in math - Example Problems:


Problem 1:

Solve the radical value for 567

Answer: `sqrt 567` = 23.8117618

Problem 2:

Solve the radical val ue for 632

Answer: `sqrt 632` = 25.1396102

Student Problems in Math

Introduction to student problems in math:

Mathematics is the study of magnitude, structure, space, and modify. Mathematicians search for examples, formulate new inferences, and found truth by accurate deduction from correctly chosen theorems and explanation.

Students are allowed to solve the mathematics problems such as homework problems, practice problems and also providing the formulas and definitions. Homework problems are used to develop the knowledge of solving problems themselves. It includes algebra variant, geometry and so on...

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Example problems for students in math:


Student math problem 1:

A rectangular cabinet is of length 8 m and perimeter 22 m. Find the width of the cabinet.

Solution:

Length of cabinet, l   = 8m

Perimeter of cabinet = 22m

Width of cabinet       =w

Formula for perimeter of rectangle=2*(l + w).

Therefore we can substitute the value of l and p into the above formula,

2(l + w) =22

2(8 + w) = 22

Dividing by the value 2 on both sides,

8+w = 11

Subtracting the value 8 on both sides,

w =3

Therefore, width of rectangular cabinet is 3 m.

Answer: w= 3 m

Student math problem 2:

Solve the following equations using substitution method.

q = 2p

p + 2q = 5

Solution:

Step 1:

Given equations are q = 2p and p + 2q = 5.

The value of q is directly given in the first equation. So, substitute the value of q=2p in the second equation p + 2q = 5 and simplify.

Therefore, p + 2q = 5 becomes p + 2(2p) = 5.

p + 4p = 5

Add 4p and p.

5p = 5

Divide by the value 5 on both the sides to separate p.

p = 1

Step 2:

Substitute the value p = 1 to find the value of q.

Replace the value of p by 1 in the equation q=2p.

q = 2 (1)

q = 2

Step 3:

So, the solution of the given system of equations is (1, 2).

Answer: (1, 2)

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Practice problems for students in math:


1.  Solve the following equation using substitution method:

2p + q = 4

4p + 2q = 8

2. Find the area and perimeter of a rectangle whose length is 5 meter and width is 6 meter.

Answer for student problems:

1. Infinite many solutions

2.Area= 30 meter^2 and perimeter= 22 meter

Function in Math

Introduction for function in math:

Before giving the explanation of the function in math, we have to know, what is function in math? The function is nothing but the result of the given argument. The argument is also know as element of the function from the given set. Function is associated with domain and co domain. The element exists in domain which is also exactly one element in co domain.I like to share this Implicit Function with you all through my article.


Pre-requisite for function in math:


Constant and Variable:

The value will not be changed during the mathematical process is called constant. The value will be changed during the mathematical process is called variable.

Interval:

The subset of real number is called interval

Neighborhood:

In a number line the neighborhood of a real number is defined as a open interval of very small length.

Independent / Dependent Variable:

A variable is an independent variable when it has any arbitrary value. A variable is said to be dependent when its value depends on other variables.

Cartesian product:

The Cartesian product of the two sets A and B is denoted by A x B and is denoted as

Let A={ a1,a2,a3} B={b1,b2}

A x B={ (a1,b1),(a1,b2)(a2,b1)(a2,b2)(a3,b1)(a3,b2)}


Explanation of function in math:


A function is a special type of relation. If no two ordered pairs have same first element and different second element, the relation is called function. If two ordered pairs have same first element and different second element, the relation is called not a function. If the element x in the set A is associated with element x in the set B is called image of the function. The set of images is called range of the function. If the range of function in not equal to the co domain, those functions are called mapping.

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Types of function in math:


1. Identity function:

A function from a set A to the same set A is said to be an identity

2. Inverse of a function:

To define the inverse of a function f i.e. f−1 (read as ‘f inverse’), the

function f must be one-to-one and onto.

3. Constant function:

If the range of a function is a singleton set, the function is called a

constant function.

4. Linear function:

If a function f : R → R is defined in the form f(x) = ax + b then the function

is called a linear function. Here a and b are constants.

5. Polynomial function:

If f : R→R is defined by f(x) = an xn + an − 1 xn − 1+ …+ a1x + a0, where

a0, a1,…, an are real numbers, an≠0 then f is a polynomial function of degree n.

Integers and Math

Introduction to integers and math:
In mathematics, integer is one interesting topics in number representation. Integer has a set of numbers in which there are two difefrent types of integers that are non negative integers and negative integers. Integers have complete entity or unit. No fractional part in integers. Integers perform different arithmetic operations such as addition, subtraction, multiplication and division. Let us solve some example problems in integers and math.

Example for integers:

1254, -5365, 0 etc,

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Example problems for integers and math:


Example 1:

Perform arithmetic operation addition for the given two integer numbers

875 + 432

Solution:

Given two integer numbers are

875 + 432

Both are two positive integers so, the result is also a positive numbers

Here we add 875 into 432, and then we get the result

875 + 432

1307

Solution to the given two integers is 1307.

Example 2:

Perform arithmetic operation subtraction for the given two integer numbers

1024 and 827

Solution:

Given two integer numbers are

1024 - 827

Here we subtract 1024 into 827, and then we get the result

1024 - 827

197

Solution to the given two integers is 197.

Example 3:

Perform arithmetic operation multiplication for the given two integer numbers

1524 × 1028

Solution:

Given two integer numbers are

1524 × 1028

Both are positive integers so, the result is also a positive numbers

Here we multiply 1524 into 1028, and then we get the result

1524 × 1028

1566672

Solution to the given two integers is 1566672.

Example 4:

Perform arithmetic operation division for the given two integer numbers

6000/ 150

Solution:

Given two integer numbers are

6000 / 150

Both are positive integers so, the result is also a positive numbers

Here we divide 6000 by 150, and then we get the result

6000/ 150

40

Solution to the given two integers is 40.

Example 5:

Perform arithmetic operation addition for the given two integer numbers

- 728 + 206

Solution:

Given two integer numbers are

- 728 + 206

- 728 is negative number and 206 is positive number

Here we add - 728 into 206, and then we get the result

- 728 + 206

- 522

Solution to the given two integers is - 522.

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Practice problems for integers and math:


Perform arithmetic operation for the given two integers and math are,

i). 3286 + 7025

ii). 5021 – 2856

iii). 481 × 200

iv). 540 / 20

v). – 258 + 625

vi) – 286 × 85

Solution:

i). 10311

ii). 2165

iii). 96200

iv). 27

v) 367

vi) – 24310

Word Problems Second Grade Math

Introduction to word problem:
In mathematics, especially in the area of abstract algebra known as combinatorial group theory, the word problem for a recursively presented group G is the algorithmic problem of deciding whether two words represent the same element. Although it is common to speak of the word problem for the group G strictly speaking it is a presentation of the group that does or does not have solvable word problem. (Source: Wikipedia)

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Example of word problems second grade math


Math second grade word problem: 1

There are 109 boxes in the store. We bought 42 more boxes for the store. How many boxes are there in the store now?

Solution:

In 109 boxes in the store

And then we bought 42 boxes in the store

109 + 42 = 151

Therefore 151 boxes in the store now.

Math second grade word problem: 2

A fruit wholesaler had 128 grapes. He sold 52 grapes. How many grapes did he have left?

Solution:

Wholesaler 128 grapes

Sold 52 grapes

Left grapes =?

So, 128 – 52 = 76

He had totally 76 grapes left.

Math second grade word problem: 3

There are 11 pine apples in each box. How many are there in 8 boxes?

Solution:

In one box = 11 pine apples

In 8 boxes =?

11 * 8 = 88

There are 88 pine apples in 8 boxes.

Math second grade word problem: 4

Andrew bought a sack of 62 kg of flour. He packed the flour equally into 8 bags. How many kilograms of flour in the each bag?

Solution:

In one sack = 62 kg

Then 3 bags =?

64 ÷ 8 = 8

There were 8 kg of flour in each bag.

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Practice - word problems second grade math


1. There are 1238 erasers in the store. We bought 53 more erasers for the store. How many erasers are there in the store now?

[Answer: 1291 erasers in the store now]

2. A vegetables seller had 563 potatoes. He sold 154 potatoes. How many potatoes did he have left?

[Answer: He had 162 oranges left]

3. There are 5 pine apples in each box. How many are there in 9 boxes?

[Answer: 45 pine apples in 9 boxes]

4. Arnold bought a sack of 90 kg of flour. He packed the flour equally into 10 bags. How many kilograms of flour in the each bag?

[Answer: 10 kg of flour in each bag]

Matrices in Math

Introduction to matrices in math:

In order to locate the position of a particular element of a matrix. We have to specify  the number of the row and that of  the column in which the element occurs. An element occurring in the ith row and jth column of a matrix A will be called the (i,j)th element of A , to be denoted by aij .

In general ,an m x n matrix A may be written as ,

A     =     `[[a_11,a_12,...,a_1n],[a_21,a_22,...,a_2n],[...,...,...,...],[a_m1,a_m2,...,a_mn]]`

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Types of matrices:


Row matrix:

Row matrix is a matrix that contain only one row or a row vector.

Example :

(i) A = [aij]1 × 3 = [1 6 5] is a row matrix of order 1 × 3.

(ii) B = [bij]1 × 2 = [0  1] is a row matrix of order 1 × 2

(iii) C = [cij]1 × 1 = [1] is a row matrix of order 1 × 1

Column matrix:

A colum matrix is a matrix that contain  only one column  or a column vector.

Example :

1)[aij]mxn =`[[2],[4],[6]]` is a column matrices of order 3 x1

2)[aij]mxn =`[[0],[1]]` is a column matrices of order 2 x1

3)[aij]mxn =[45] is column matrices of order 1 x1

Square matrix:

A square  matrix is a matrix in which the elments in rows and columns are equal and a  matrix of order n × n is also known as a square matrix of order n.

Example :

1) `[[4,5],[5,4]]` is the square matces of order 2 x2

2) `[[1,2,3],[4,5,6],[7,8,9]]` is the square matrix of order 3 x3

3) `[[0,1,2,3],[2,1,4,5],[3,4,6,7],[0,6,7,8]]` is the square matrix of order 4 x4.

Diagonal matrix:

Diagonal matrix means  a  square matrix A = [aij]n × n is said to be a diagonal matrix if aij = 0 when i ? j. In a diagonal matrix all the entries except the entries along the main diagonal are zero.

Example :

1) `[[1,0,0],[0,2,0],[0,0,3]]` is the diagonal matrix of order 3 x3

2) `[[3,0],[0,7]]`   is the diagonal matrix of order 2 x2.

Zero matrix or null matrix or void matrix:

All the entries are zero in the given matrix then the matrix is said ti be a zero  matrix .

Example :

A = `[[0,0,0],[0,0,0],[0,0,0]]` is the null matrix  or zero matrix of order 3 x 3

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Operation on Matrices in math:


Basic operation involved in matrix:

Addition of two matrices in math
Subtraction of matrices in Math
Multiplication of matrices in math.
Let  us discuss about the  operation of matrices in math.

1)Addition of matrices.

Let us consider the two different matrices of order 2 x2

A=`[[3,5],[4,7]]` and B= `[[1,8],[4,7]]`

A+B = `[[3+1,5+8],[4+4,7+7]]`

A+B =`[[4,13],[8,14]]`

Subtraction of two matrices:

Let us consider the two different matrices of order 2 x2

X= `[[4,6],[3,5]]` and Y =`[[5,7],[3,4]]`

X-Y =`[[4-5,6-7],[3-3,5-4]]`

X-Y =`[[-1,-1],[0,1]]`

Multiplication of two matrices:

Let us consider the two different matrices of order 2 x2

P = `[[4,5],[3,2]]` and Q =`[[2,3],[2,1]]`

PQ =`[[4*2 +5*2,4*3+2*1],[3*2+2*2,3*3+2*1]]`

PQ =`[[8+10,12+2],[6+4,9+2]]`

PQ =`[[18,14],[10,11]]`

6th Grade Math Probability

Introduction to 6th grade math Probability:

Probability is a way of expressing knowledge or belief that an event will occur or has occurred. In mathematics the concept has been given an exact meaning in probability theory, that is used extensively in such areas of study as mathematics, statistics, finance, gambling, science, and philosophy to draw conclusions about the likelihood of potential events and the underlying mechanics of complex systems. (Source: Wikipedia)


Example problems for 6th grade math probability:


Example: 1

Two dice are rolled. A is the event that the sum of the numbers shown on the two dice is 5, and B is the event that at least one of the dice shows up a 3. Are the two events

(i) Mutually exclusive

(ii) Exhaustive? Give the arguments in support of your answer.

Solution:

When two dice are rolled, we have n(s) = (6 x 6) = 36.

Now, A = {(1, 4), (2,3),(4,1),(3,2)} and

B = {(3,1), (3,2), (3,3), (3,4), (3, 5), (3,6), (1,3), (2,3), (4,3), (5,3), (6,3)}

(i) A`nn`B = {(2,3), (3,2)} `!=` `phi` .

(ii) Also, A`uu`B `!=` s

Therefore A and B are not exhaustive events.

Example: 2

Two dices are rolled. Let A, B, C  be the event getting a sum of 2, a sum of 3 and a sum of 4 respectively. Then, show that

(i)    A is a simple event

(ii)   B and C are compound events

(iii)  A and B are mutually exclusive

Solution:

Clearly we have

A  = {(1, 1), B = (1,2),(2,1) and c = (1,3),(3,1),(2,2)}

(i) Since A consists of a single sample point, it is a simple event.

(ii) Since both B and C contain more than one sample point, each one of them is compound event.

(iv) Since A`nn` B =`phi`, A and B are mutually exclusive.

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Practice problems for 6th grade math probability:


1. From a well-shuffled deck of 52 cards, a card is drawn at random. Find the probability that the card drawn is

(i) red and a  king

(ii) Either red or a king

[Answer: (i) 1/26

(ii) 7/13]

2.The odds in favour of occurrence of an event are 5:12. Find the probability of the event.

[Answer: 5/17]

Answer Math Problems For You

Introduction to answer math problems:

Mathematics is the study of quantity, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions. I like to share this Small Sample Size Statistics with you all through my article.

Applied mathematics, the branch of mathematics concerned with application of mathematical knowledge to other fields, inspires and makes use of new mathematical discoveries and sometimes leads to the development of entirely new mathematical disciplines, such as statistics and problems of game theory.

SOURCE: WIKIPEDIA


Examples of answer math problems:


Math problem 1:

Solve the equation 5(-3y - 2) - (y - 3) = -4(4y + 5) + 13

Solution:

Given the equation 5(-3y - 2) - (y - 3) = -4(4y + 5) + 13

First we can multiply the factors for both left hand side and right hand side.

-15y - 10 - y + 3 = -16y - 20 +13

Here we can group the like terms on both sides. Then we get.

-16y - 7 = -16y – 7

Add 16y+7 on both sides. Then we get the final answer.

0=0

Therefore all real numbers are possible solution to the given equation.

Math problem 2:

Solve p: 2p – 4q = 9

Solution:

Given 2p– 4q=9

If we can find p intercept value we set the q=0.

Then we can find the p value.

Substitute the value of q (q=0) into the above equation.

2p– 4(0) =9

2p– 0=9

2p=9

Divide by the value 2 on both sides. Then we get the final answer.

`(2p)/2` =`9/2`

p=`9/2`

Answer: `9/2`

Math problem 3:

Find the area of following figure:

Solution:

Given length= 15 ft and width= 7 ft

We can find the area of rectangle by using the following formula:

Area A= length*width or (l*w)

Substitute the value of l and w into the above formula and then we get the final answer.

Area A= 15*7

= 105 ft2

Answer: 105 ft2

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Practice problems of math:


Problems:

Solve x: 10+5x=50
Solve y: 2y+3x=5
Find the perimeter of square with the side value 5 cm.
Answer key:

x= 8
y=`5/2`
20 cm

Superstar Math Answers

Introduction to superstar answers:

The fundamental concepts of algebra, number, measurement, and geometry. Simple addition, subtraction, multiplication, and conservation are performed in the number. The Superstars program is to provide extra challenge that self- motivated to the students. More number of way to solve any problem. But student wants to know the shortcut methods. This shortcut method is one of the best way to study the math’s and easily understand the concept.


Math superstar answers:


Superstar math problem 1:

Rohit saw 4 cow and 2 dogs outside. How many legs did he see?

Solution:                          4 cow = 16 legs

2 dogs = 8 legs

8 + 16 = 24 legs

Answer:  24 legs

Superstar math problem 2:

Nijam have 5 nickel and 3 pennies, how much money do he have all together?

Solution:                   1 nickel = 5 pennies

So, 5 nickel = 25 pennies

Total = 25 + 3 = 28 pennies

Answer:  28 pennies

Superstar math problem 3:

Reena saw eight triangles, how many sides are there all together on eight triangles?

Solution:                                 1 triangle has 3 sides

8 triangle has 8 × 3 = 24 sides

Answer:  24 sides

Superstar math problem 4:

There are 5 cars and 6 tricycles in the neighbor's garage. How many wheels are there in all? Forget about any "spare tires"!

Solution:             20 wheels on the 5 cars,  and 18 on the 6 tricycles

Total = 20 + 18 = 38

Answer:  38wheels

Superstar math problem 5:

Martin has 16 balls, half of them are red. How many are Red?

Solution:                                  Total balls = 16

Half of ball = `16/2` = 8

Answer: 8 Red balls

Superstar math problem 6:

If the 22th day of the month falls on Thursday, on what day did the 11th fall?

Solution:   The calendar or make a chart with “Su, M, T, W, Th, F, Sa” at the top and begin numbering

backward putting 24 under Saturday. The date 17th and 10th must be fall on Saturdays and count Forward one

from the 10th.

Answer:  Sunday

Superstar math problem 7:

The sum of 3 consecutive numbers is 555. What are the numbers?

Solution:   We can use guess-check-revise method. Some students know that the numbers they seek are about `1/3`

of the total, and approximate the numbers by dividing 555 by 3. This gives 185, which is the middle number.

Answer:  184, 185, 186

Superstar math problem 8:

How many corners are on 3 triangles and 2 rectangles?

Solution:                                      1 triangle = 3 corners

1 rectangle = 4 corners

So, 3 triangle and 1 rectangle = (3 * 3) + (2 * 4) = 9 + 8 = 17 corners

Answer: 17 corners

Superstar math problem 9:

Together, 12 cars and 6 bikes weigh 1050 pounds. The bikes all weigh the same -- x pounds. Each cars weighs 55 pounds.

What is the  weigh of one bike?

Solution:      First finding the total weight of the 12cars: 12 × 55 = 660 pounds. Then they

will calculate 1050 - 660 = 390 pounds, the weight of the 6 bikes = 390 pounds.

So weight of one bike = ` 390 / 6` = 65 pounds per bike

Answer:  65pounds

Superstar math problem 10:

Find the side of the square if the perimeter of square is 20 m.

Solution:            The perimeter formula for square = 4a

4a = 20

a = ` 20/4` = 5 m

Answer: The side of the square 5m

I Need a Math Function

Introduction to math function:

The mathematical concept of a function expresses the intuitive idea that one quantity (the argument of the function, also known as the input) completely determines another quantity (the value, or the output). A function assigns a unique value to each input of a specified type.(source : wikipedia)

An example, the function f(x) = 5x, which assigns to all real number the real number that is three times as big. In this case, we can write f (3) = 15. Please express your views of this topic Types of Functions by commenting on blog.


Examples problem for math function:


1. Add the two function for given functions, f (x) = 6x + 6 and g (x) = 2x + 5 when x = 4 find f (4) + g (4).

Solution:

Given function is f (x) = 6x + 6 and g (x) = 2x + 5

Add the two functions,

f (x) + g (x) = 6x + 6 + 2x + 5

Combine the terms,

= 6x + 2x + 6 + 5

Add the terms,

= 8x + 11

f (x) + g (x) = 8x + 11

When x = 4,

Find the f (4) + g (4),

f (4) + g (4) = 8x +11

Plug x = 4 in the equation,

= 8 (4) + 11

= 32 + 11

= 43

The solution of f (4) + g (4) is 43.

2. Subtract the two function for given functions, f (x) = 3x + 15 and g (x) = 9x + 5 when x = 3 find f (3) + g (3).

Solution:

Given function is f (x) = 3x + 15 and g (x) = 9x + 5

Subtract the two functions,

f (x) + g (x) = 3x + 15 - 9x - 5

Combine the terms,

= 3x - 9x + 15 - 5

Subtract the terms,

= -6x + 10

f (x) + g (x) = -6x + 10

When x = 3,

Find the f (3) + g (3),

f (3) + g (3) = -6x + 10

Plug x = 3 in the equation,

= -6 (3) + 10

= -18 + 10

= -8

The solution of f (3) + g (3) is -8.

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More examples problem for math function:


3. Multiply the two function for given functions, f (x) = x + 5 and g (x) = 2x + 2 when x = 5 find f (5) + g (5).

Solution:

Given function is f (x) = x + 5 and g (x) = 2x + 2

Multiply the two functions,

f (x) + g (x) = (x + 5) × (2x + 2)

Multiply the terms,

= 2x2 + 10x + 2x + 10

Combine the terms,

= 2x2 + 12x + 10

f (x) + g (x) = 2x2 + 12x + 10

When x = 5,

Find the f (5) + g (5),

f (5) + g (5) = 2x2 + 12x + 10

Plug x = 8 in the equation,

= 2(52) + 12 (5) + 10

= 50 + 60 + 10

= 120

The solution of f (5) + g (5) is 120.

How to do Probability Math

Probability Math

In mathematics, probability means likelihood of the outcome of an event of a particular experiment. The probability of event E is written P(E). Probabilities are occurs always numbers between 0 and 1. The set of all possible outcomes of a particular experiment is referred to as sample space. For example, the probability of getting a tail when tossing a coin is 1/2. Please express your views of this topic Continuous Random Variable by commenting on blog.


Probability Math - Example Problems


Example 1:

25 tokens numbered from 1 to 25, two tokens are drawn simultaneously. Find the probability that:

a) Both the tokens drawn have prime number

b) None of the tokens drawn have a prime number

Solution:

We want to select 2 tokens from 25 tokens.

n(S) = 25C2 = 25! / (2! x 23!)

= (25 x 24) / 2

= 300

a) Let A = Event that both the tokens have prime numbers.

Prime numbers between 1 to 25 are: 2, 3, 5, 7, 11, 13, 17, 19, and 23.

Total Numbers = 9.

We have to select 2 numbers from these 9 numbers.

n(A) = 9C2 = 9! / (2! x 7!)

= (9 x 8) / 2

= 36

P(A) = `(n(A)) / (n(S)) `

=` 36/300 `

= `3/25`

b) Non prime numbers between 1 to 25: 25 - 9 = 16

Let B = Event that both the tokens have non-prime numbers.

Now we have to select 2 numbers, from 16 numbers.

n(B) = 16C2 = 16! / (2! x 14!)

= (16 x 15) / 2

= 120

P(B) = n(B) / n(S)

= 120 / 300

= 2/5

Example 2:

A bag contains 5 mangoes and 5 oranges. Two fruits are taken at random. Find the probability that both will be of the same kind.

Solution:

Let S = Sample space

A = the event of taking 2 mangoes.

B = the event of taking 2 oranges.

(A or B) = The event of taking 2 mangoes or 2 oranges.

i.e. the event of taking 2 fruits of same kind.

n(S) = 10C2 = 10! / (2! x 8!) = 10 x 9 / 2= 45

n(A) = 5C2 = 5! / (2! x 3!)

= 5 x 4 / 2

= 10

n(B) = 5C2 = 5! / (2! x 3!)

= 5 x 4 / 2

= 10

P(A) = n(A) / n(S)

= `10/45`

= `2/9`

P(B) = n(B) / n(S)

= `10/45`

= `2/9`

P(A or B) = P(A) + P(B)

=`2/9+2/9`

= `4 / 9`

P(A or B)  = 4/9

I have recently faced lot of problem while learning hard 5th grade math problems, But thank to online resources of math which helped me to learn myself easily on net.

Probability Math - Practice Problems


Problem 1:

10 tokens numbered from 11 to 20, two tokens are drawn simultaneously. Find the probability that both the tokens drawn have prime number

Answer: 2/15

Problem 2:

2 dice are thrown simultaneously. What is the probability of getting an odd number as the sum?

Answer: 1/2

Basic Laws of Math

Introduction to basic laws of math:
Mathematics contains the some basic laws. The basic laws are used to calculate the mathematical problems easily. Following are the basic laws of arithmetic: Addition, Subtraction, Multiplication, and Division. The addition is identifying as the grouping of numbers. ‘+’ sign used for represent the addition. The subtraction is identifying as the difference of numbers. ‘-’ sign used for represent the subtraction. The multiplication is identifying as the product of numbers. ‘× ’ sign used for represent the multiplication. The division is identifying as the opposite method of multiplication. ‘/’ sign used for represent the multiplication. Mathematics has the other important law is exponent. The exponent of a number defined as how many times to we can utilize the number in a multiplication. For example: 43 = 4 × 4 × 4= 64.

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Basic laws of math:


Basic laws in math:

Addition

Subtraction

Multiplication

Division

Exponent

Basic laws of addition:

Commutative law:

Let us consider the two variables a and b we can written the commutative law of addition in the following way

a + b = b + a

Associative law:

Let us consider the three variables a, b and c we can written the associative law of addition in the following way

a + (b + c) = (a + b) + c

Basic laws of multiplication:

Commutative law:

Let us consider the two variables a and b we can written the commutative law of multiplication in the following way

a × b = b × a

Associative law:

Let us consider the three variables a, b and c we can written the associative law of multiplication in the following way

a(bc) = (ab)c

Distributive law:

Let us consider the three variables a, b and c we can written the distributive law of multiplication in the following way

a(b + c) = ab + ac

Subtraction:

Subtraction is the inverse method of addition.

Example:

10 - 2 = 8

Division:

Division is the inverse method of multiplication.

Example:

`12/6 = 2`

Laws of Exponents:

Assume two variables a and b

a0=1

a1= a

a-1=`1/a`

` (a^(x))/(a^y)` =ax-y

ax ay=ax+y

(ax)y = ax y

(ab)x= ax bx


Examples for basic laws of math


Example 1:

Solve: 14 + 8 = ? + 14

Solution:

Given: 14 + 8 = ? + 14

By the commutative law of addition,

a + b = b + a

14 + 8 = ? + 14

The missing value is 8

Example 2

Solve: 4 (5 + x) = 40

Solution:

Given: 4 (5 + x) = 40

By the distributive law of multiplication,

4 (5 + x) = 40

4 (5) + 4(x) = 40

20 + 4x = 40

4x = 40 - 20

4x = 20

x = `20/4`

x = 5

Example 3

Prove: 4 +(6 + 7) = (4 + 6) + 7

Solution:

Given: 4 +(6 + 7) = (4 + 6) + 7

4 + (13) = (10) + 7

17 = 17

Therefore, the given statement is true. Understanding Partial Derivative Calculator is always challenging for me but thanks to all math help websites to help me out.


Practice problems for basic laws of math:


Problem 1:

Find the value of x: 6 (4 + x) = 48

Answer: x = 4

Problem 2:

Prove: 10 +( 5 + 8) = (10 + 5) + 8

Anti X Math

Introduction to anti x math:

In this article we are going to see anti x math. We know that math is large volume that used to resolve and discover so many things in the world. In math, variable is an most important part that used to get a input values. Most commonly we use x as a variable for most of the problems. Here we are going to see how to find anti(inverse) x of the variable x.

Anti x can be called as inverse of x or reciprocal of x . The reciprocal of the variable x can be find by interchanging the numerator and its denominator. The inverse of the function can be find by solving for x from y. Every function has its inverse. But not  every inverse function has function


Problems on anti x math:


Problem 1:

The variable `x = 12 / 5` . Find the value of anti x.

Solution:

Given , x = `12 / 5`

We need to find the anti x.

In this problem anti x mean that the multiplicative inverse or reciprocal.

To find the reciprocal, change the numerator into denominator and vice verse.

`x = 12/5`

Taking reciprocal on both sides,

`1/x = 5/12`

We can write `1/x = x^(-1)`

`x^(-1) = 5/12`

Answer: `x^(-1) = 5/12`

Problem 2:

Find the inverse of the function y = 5x - 8

Solution:

Given, y = 5x - 8

We need to find the the inverse of the given function.

To find the inverse of the function we need to solve for x.

y = 5x - 8

Add 8 on both sides,

y + 8 = 5x - 8 + 8

y + 8 = 5x

Divide by 5 on both sides,

`( y + 8 ) / 5` = 5x / 5

`( y + 8 ) / 5` = x

x = `( y + 8 ) / 5 `

Answer: x = `( y + 8 ) / 5 `

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Practice problems on anti x math :


Problems:

1. Find the anti x of  x = 54 / 67

2. Find the inverse of the function f(x) = 9x - 6

Answers:

1. `x^(-1) = 67/54`

2. `f^(-1)(x) = (x+6) / 9`

Math For All Seasons

Introduction of math for all seasons:

The math for all seasons is nothing but the ways for solving the problem solving to children. It helps you to get the idea how to find the solution for the particular problem. The children can develop their ideas on grouping for the arithmetic operations like addition and subtraction. Also we give the idea to find the way to save the time on the particular problem. Please express your views of this topic Solving Equations Using Addition and Subtraction by commenting on blog.


Math for all seasons:


The children can have the idea to solve the pattern and symmetric problems. These topics give the various types of problems which makes you excel in each topic. Hence the math for all seasons gives you ideas for solving all the subtopics in math.


Example for math for all seasons:


Example 1: Compute the math partial sums of (355 +565).

3 6 6

4 8 5

Add 100s                  7 0 0

Add 10s                     1 4 0

Add 1s                       1 1

Add partial sums    8 5 1

Step 1: first sum up the place value of hundred = 700.

Step 2: Then sum up the ten place values = 140.

Step 3: Then sum up the one place values = 11.

Step 4: Finally sum up all the partial values to compute the solution = 851.

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Example 2: Compute the math partial sums of (243 + 134).

2 4 3

1 3 4

Add 100s                3 0 0

Add 10s                   7 0 0

Add 1s                     7 0 0

Add partial sums 3 7 7

Step 1: First sum up the place value of hundred = 300.

Step 2: Then sum up the place value of tens = 700.

Step 3: Then sum up the place value of ones = 700.

Step 4: Then sum up all the partial values to compute the solution = 377.

Example: What is +4+ (+2)?

From above: + (+) becomes a positive sign.

+4+ (+2) = +4 + 2

Start at +4 on the number line, move forward 2, and you end up at 6

Answer: 4+ (+2) = 6

Example: Find out the place value and the face value of the each digit in the number 78,234,543.

Solution:         Face value (digit)                                Place value (digit)

7                                                            70,000,000

8                                                                8,000,000

2                                                                   500,000

3                                                                      30,000

4                                                                         4000

5                                                                           500

4                                                                             40

3                                                                              3

The above sequence of number can be written as “seven eighty million two hundred and thirty four thousand and five hundred and forty three”.

Math Partial Sums

Introduction of math partial sums:

The math partial sums deal with the numerical values and their operations on math. This system involves natural numbers, integers. The arithmetic operations which deals with positive numbers and negative numbers. The natural numbers which includes all the whole numbers. The natural numbers sets are denoted as N. The number systems have the ability to count. The collections of some features are termed with number systems.


Math partial sums:


The math partial sums includes the two stages in which the first stage looks at the columns present, works from left to right and we should sum up the place values of the digits present in the particular column. The negative number systems are the one which is lesser than the zero.

The negative numbers are followed by the sign (-). The negative number systems are also denoted as the inverse of the number. The positive number systems are which are larger than zero. It is the most used number systems found in our day to day life. The second stage of the math partial sums includes the place values sum up together. Please express your views of this topic An Odd Number by commenting on blog.


Examples for the math partial sums:


Ex 1: Compute the math partial sums of (355 +565).

3 6 6

4 8 5

Add 100s                  7 0 0

Add 10s                     1 4 0

Add 1s                       1 1

Add partial sums    8 5 1

Step 1: first sum up the place value of hundred = 700.

Step 2: Then sum up the ten place values = 140.

Step 3: Then sum up the one place values = 11.

Step 4: Finally sum up all the partial values to compute the solution = 851.



Ex 2: Compute the math partial sums of (243 + 134).

2 4 3

1 3 4

Add 100s                3 0 0

Add 10s                   7 0 0

Add 1s                     7 0 0

Add partial sums 3 7 7

Step 1: First sum up the place value of hundred = 300.

Step 2: Then sum up the place value of tens = 700.

Step 3: Then sum up the place value of ones = 700.

Step 4: Then sum up all the partial values to compute the solution = 377.

Learn Math Facts Fast

Introduction to learn math facts fast:
A fact is a group of a declaration of each of which stand for the same meaning. All the declaration has the same meanings. Addition and subtraction facts contain 2 or 3 numbers. The types of facts operations are addition and subtraction facts, multiplication and division facts. In here we shall discuss about learn math facts fast. Having problem with Decimal to Percent Calculator keep reading my upcoming posts, i will try to help you.

Addends:

The facts being added in an addition operation like 7 and 4 in 7 + 4 = 11 or 4 + 7 = 11.

Reverse operation:

Reverse of a process is call as inverse operation of addition and subtraction.


Sample problem for math facts fast learn:


First we take an addition operation like 3 + 5 = 8.

In the next operation the addends are reversed like 5 + 3 = 8.

Now we can write the inverse operations of the above values both.

8 - 5 = 3

8 - 3 = 5

Addition and subtraction math facts fast learn:

Example 1:

What are the members of the fact family of 11 + 9 = 20?

Solution:

11 + 9 = 20

Reversing the addends:

9 + 11 = 20;

Inverse operations:

20 - 9 = 11;

20 - 11 = 9;

When we are modify the order to addition, then answer will be based on the numbers which we in use to do the addition process.

Example 2:

Write the facts of the family with numbers 9, 5 and 14.

Solution:

9 + 5 = 14;

5 + 9 = 14;

14 - 9 = 5;

14 - 5 = 9;

When 2 of the numbers are same, then we have only 2 facts. Because, the 1st two and last two fact values are same. Please express your views of this topic Cone Volume Formula by commenting on blog.


Division and multiplication math facts fast learn :


Example 1:

Write the facts of the family with numbers 11, 5 and 16.

Solution:

In the problem we find the facts value for division and multiplication.

11 * 5 = 55

5 * 11 = 55

55 / 11 = 5

55 / 5 = 11

When 2 of the numbers are same, then we have only 2 facts. Because, the 1st two and last two fact values are same

Example 2:

Write the four facts of the family with numbers 2, 7 and 9.

Solution:

7 * 2 = 14

2 * 7 = 14

14 / 2 = 7

14 / 7 = 2

When 2 of the numbers are same, then we have only 2 facts. Because, the 1st two and last two fact values are same