help with math word problems

Introduction to help with math word problem:

Math word problem is a real life problem put in words which has to be converted into mathematical form to solve it. Math word problems has to be solved by logically translating the problem to mathematical form. It requires understanding the mathematical concepts and its applications. I like to share this math tutoring free online with you all through my article.

To help with math word problems - examples

Math word problems help - example 1:

Jack has 21 bananas and 18 grapes . How many pieces of fruits does he have?

Solution:

We know that the sum of 21 and 18 is equal to the total sum of fruit. The total amount of pieces of fruit is unknown, so we will represent that sum with x.

Let x = Total Amount of Fruit from word given

The sum of 21 bananas plus 18 grapes is equal to the total amount of fruit. This can be used to explain the problem into an equation,

21 + 18 = x

By solving the last step equation.

Let x = Total Pieces of Fruit

Initial Equation     21 + 18 = x

After combining like terms 39 = x

The problems answer is then rewritten as a sentence.

There are 39 Total Pieces of Fruit

Math word problems  help - example 2:

Mike is twice as good as workman as Jones and therefore he is able to finish a job in 40 days less than Jones. Working together, they can do it in:

Solution:-

Given Mike is twice as good as work man as Jones.

Therefore the ratio of work done Mike and Jones is 1: 2

If difference of time is 1 days, Jones takes 2 days.

If difference of time is 40 days, Jones takes (2/1 x 40) = 80 days.

So, Mike takes 40 days to do the work.

so mikes one day work =  1/40

Jones one day work =  1/80

Now (mikes + Jones) one day work = ( 1/40 + 1/80 )

The LCM of 40 and 80 is 80.

Now take LCM and add we get

= 2 / 80 + 1/ 80

= (3)/ 80

Work done in one day=3/80

No. of days required to cover 80 portions of work=80/3

Mike and Jones together can do the work in 80 / 3 = 16.66 days. Understanding The Multiplication Table is always challenging for me but thanks to all math help websites to help me out.


More help with math word problems - practices


1. Math word problem help - practice 1:

Peter has 12 shirts and 7 T-shirts. How many of shirts does he have?

Answer: 19 Total number of shirts.

2. Math word problem help - practice 2:

The sum of thrice a number plus 8 is 62. Find the number.

Answer: The number is 18.

2. Math word problem help - practice 3:

Walker is thrice as good as worker as Kim and therefore he is able to finish a job in 40 days less than Kim. When they working  together, how long they can do it in?

Answer: 15 days.

Two Cents

Cents – Introduction:

In many national currencies, the cent is a monetary unit that equals 1/100 of the basic monetary unit. Etymologically, the word cent derives from the Latin word "centum" meaning hundred. Cent also refers to a coin which is worth one cent. In the America and Canada, the 1 cent coin is usually identified by the pet name penny, alluding to the British coin and unit of surname. In Ireland the 1cent coin is occasionally recognized as a penny in position to the Irish penny, worth 1/100 of the Irish pound swap by the euro.

Formula for converting the cents to dollars

1 U.S. cent = 0.01 U.S. dollars

Two Cents – Examples:

Two cents – Example 1:

Find how many dollars in the 2 cents also convert into the dollars

Solution:

Step 1:

Formula for converting cents to the dollars

X cents = x * 0.01 dollars

Step 2:

2 cents = 2 * 0.01 dollars = 0.02 dollars

Answer:

2 cents = 0.02 dollars

Two cents – Example 2:

Find how many dollars in the 102 cents also convert into the dollars

Solution:

Step 1:

Formula for converting cents to the dollars

X cents = x * 0.01 dollars

Step 2:

102 cents = 102 * 0.01 dollars = 1.02 dollars

Answer:

102 cents = 1.02 dollars

Two cents – Example 3:

Find how many dollars in the 22 cents also convert into the dollars

Solution:

Step 1:

Formula for converting cents to the dollars

X cents = x * 0.01 dollars

Step 2:

22 cents = 22 * 0.01 dollars = 0.22 dollars

Answer:

22 cents = 0.22 dollars

More Examples for Two Cents:

Two cents – Example 1:

Find how many dollars in the 32 cents also convert into the dollars

Solution:

Step 1:

Formula for converting cents to the dollars

X cents = x * 0.01 dollars

Step 2:

32 cents = 32 * 0.01 dollars = 0.32 dollars

Answer:

32 cents = 0.32 dollars

Two cents – Example 2:

Find how many dollars in the 42 cents also convert into the dollars

Solution:

Step 1:

Formula for converting cents to the dollars

X cents = x * 0.01 dollars

Step 2:

42 cents = 42 * 0.01 dollars = 0.42 dollars

Answer:

42 cents = 0.42 dollars

Solve Math Problems Fast

Introduction to solve math problems fast:

In this article we are going to discuss about the solve math problems fast. In the math problems have different types of topics. The level math problems has some of the followings numbers sets, logic, real number systems, functions and their graphs, probability and Statistics and some topics from algebra and geometry. The math  problems is more importance for all topics. Here we will see the example problems for solve math problems fast. Is this topic Conditional Probabilities hard for you? Watch out for my coming posts.

Example Problems for Solve Math Problems Fast:
Solve math problems fast – Example: 1

Solve `\int_1^2\int_1^x xy^2dx dy`

Solution:

`I=\int_1^2 \ [ \int_1^x xy^2 dy \ ]dx`

`\int_1^x xy^2dy=\ [ \frac{xy^3}{3}\ ]_{y=1}^{x}=\frac{x^4}{3}-\frac{x}{3}`

Therefore,`I=\int_1^2 \ [ \frac{x^4}{3}-\frac{x}{3} \ ]dx`

` =\int_1^2\frac{x^4}{3}dx-\int_1^2\frac{x}{3}dx`

`=\ [ \frac{x^5}{15} \ ] _1^2- \ [ \frac{x^2}{6} \ ]_1^2`

`=\ [ \frac{32}{15}-\frac{1}{15} \ ]-\ [\frac{4}{6}-\frac{1}{6}\ ]`

` =\frac{31}{15}-\frac{3}{6}`

` =\frac{31}{15}-\frac{1}{2}`

`=\frac{62-15}{30}=\frac{47}{30}`

Solve math problems fast – Example: 2

Determine the unit vector perpendicular to both the vectors `2\bar{i}+\bar{j}+3\bar{k},\bar{i}-2\bar{j}+\bar{k}`

Solution:

Let a,b be the given vectors `2\bar{i}+\bar{j}+3\bar{k},\bar{i}-2\bar{j}+\bar{k}`

`\bar{a}\times\bar{b} =` `[[i,j,k],[2,1,3],[1,-2,1]]`

which is equal to `\bar{i}(1+6)-\bar{j}(2-3)+\bar{k}(-4-1)=7\bar{i}+\bar{j}-5\bar{k}`

Therefore unit vector perpendicular to both the vectors is `\pm\frac{\bar{a}\times\bar{b}}{|a||b|}=\pm\frac{7\bar{i}+\bar{j}-5\bar{k}}{\sqrt{49+1+25}}=\pm\frac{1}{5\sqrt{3}}(7\bar{i}+\bar{j}-5\bar{k})`

Solve math problems fast – Example: 3

Evaluate `\nabla^2(\frac{x}{r^2})`

Solution:

`\nabla^2(\frac{x}{r^2})=\sum \frac{\partial^2}{\partial x^2}[\frac{x}{r^2}] --(1)`

Now,`\frac{\partial}{\partial x}(\frac{x}{r^2})=\frac{1}{r^2}-\frac{2x}{r^3}\frac{\partial r}{\partial x}=\frac{1}{r^2}-\frac{2x}{r^3}[\frac{x}{r}]=\frac{1}{r^2}-\frac{2x^2}{r^4} --(2) [ r^2=x^2+y^2+z^2 and \frac{\partial r}{\partial x}=\frac{x}{r}]`

Therefore,`\frac{\partial^2}{\partial r^2}=\frac{\partial}{\partial x}[\frac{\partial}{\partial x}(\frac{x}{r^2})]=\frac{\partial}{\partial x}[\frac{1}{r^2}-\frac{2x^2}{r^4}],` by using (2)

`=-\frac{2}{r^3}\frac{\partial r}{\partial x}-[\frac{4x}{r^4}-\frac{8x^2}{r^5}\frac{\partial r}{\partial x}]=-\frac{2}{r^3}(\frac{x}{r})-\frac{4x}{r^4}+\frac{8x^2}{r^5}\frac{x}{r}`

Therefore,`\frac{\partial^2}{\partial x^2}[\frac{x}{r^2}]=\frac{8x^3}{r^6}-\frac{6x}{r^4} --(3)`

Now,`\frac{\partial}{\partial y}(\frac{x}{r^2})=-\frac{2x}{r^3}(\frac{y}{r})`

`\frac{\partial^2}{\partial y^2}=\frac{\partial}{\partial y}[-\frac{2xy}{r^4}]`

`=-2x[\frac{1}{r^4}-\frac{4y}{r^5}\frac{\partial r}{\partial y}]=-2x[\frac{1}{r^4}-\frac{4y^2}{r^6}]=\frac{8xy^2}{r^6}-\frac{2x}{r^4} --(4)`

Similarly,`\frac{\partial^2}{\partial z^2}[\frac{x}{r^2}]=\frac{8xz^2}{r^6}-\frac{2x}{r^4} --(5)`

Adding (3),(4),(5), we have

`\sum \frac{\partial^2}{\partial x^2}=\frac{8x}{r^6}[x^2+y^2+z^2]-\frac{10x}{r^4}=-\frac{2x}{r^4}`

`or \nabla^2[\frac{x}{r^2}]=-\frac{2x}{r^4},` by using (1)


I have recently faced lot of problem while learning Sum of Uniform Random Variables, But thank to online resources of math which helped me to learn myself easily on net.

Practice Problems for Solve Math Problems Fast:

1. Find a vector of the magnitude 3 and that which is the perpendicular to both of the vectors `3\bar{i}+\bar{j}-4\bar{k},6\bar{i}+5\bar{j}-2\bar{k}`

`Answer: \pm (2\bar{i}-2\bar{j}+\bar{k})`

2. Solve `\int_1^2\int_3^4 \frac{1}{(x+y)^2}dx dy`

`Answer: log\frac{25}{24}`

Revise Maths

Introduction to Revise maths:
In this article we are discussing about basic maths revise exam problems in which tutor helps the students to get the solutions. Basic maths revise exam problems can solve problems with step by step solutions for all problems. The maths basic problems involved topics such that algebra, geometry, polynomials, trigonometry, data handling and calculus. Let us solve some basic maths revise exam problem with step by step solutions and practice problems are given below. I like to share this Practice Math Problems with you all through my article.

Revise Maths – Example Problems:

Example 1:

John purchased 2 kg 351g apples, 3 kg 800 g mangoes and 1 kg 450 g bananas. What is the total weight of fruits purchased?

Solution:

Weight of apples:        2kg 351 g

Weight of mangoes:    3 kg 800 g

Weight of bananas:    (+) 1 kg 450 g

Total weight: 7k 601 g

Thus, jack purchased 7 kg 601 g fruits.

Example 2:

Find the volume of cuboids of length (l) 5 cm, breadth (b) 2.5 cm and height (h) 3.2 cm

Solution:

Here, length = 5cm

Breadth = 2.5 cm

And height = 3.2 cm

We know that v = l x b h

Hence, v= 5 x 2.5 x 3.2 cu.cm

= 40cu.cm

Example 3:

Find the volume of cubical box of side 5.2 cm.

Solution:

Length of the side of the cube = 5.2 cm

We know that the volume V of the cube = l x l x l

= 5.2 x 5.2 x 5.2cm3

=140.608cm3


Understanding hard math problems for 8th graders is always challenging for me but thanks to all math help websites to help me out.

Revise Maths – Practice Problems:
Problem 1: John purchased 3 m 25 cm cloth for the suit, 2 m 80 cm for the shirt and 2m 20 cm for the trouser. Find the total length (l) of the cloth purchased.

Problem 2: Find the volume of cuboids of (l) length 5 cm, breadth (b) 5 cm and height (h) 2 cm

Problem 3: Find the volume of cubical box of side 3 cm.

Revise maths – answer key:

Problem 1: 8 m 25 cm

Problem 2: 50cm3

Problem 3: 27cm3

Postulate Math

Introduction to postulate math:

In general, math postulates are nothing but the math statements, which are assumed as real without any proofs. Math postulates help to understand various concepts involved in the field of mathematics and also useful for the preparation of exam   In this article postulate math, we are going to study few math postulates which will be helpful for the students. Please express your views of this topic Difference of Cubes Formula by commenting on blog.

Math Postulates:
If the two straight lines cross each other, they cross at only one point.

In general, if perpendicular lines cross, four right angles will be formed.

Consider that equal quantities are added to equal quantities, and then their sums will be equal. Likewise, if similar quantities are subtracted to similar quantities, their differences will be equal.

A square is nothing but a parallelogram having four congruent sides and also four right angles.

A rectangle is nothing but a parallelogram having four right angles.

If same quantities are multiplied by same quantities, the products will be equal.

If the two geometric shapes are said to be congruent, then their area must be same.

The addition of the areas of its non-overlapping parts is referred as the area of section.

The addition of the lengths of any two sides of a triangle will be bigger than the length of the third side.

Is this topic Covariance Statistics hard for you? Watch out for my coming posts.

Additional Math Postulates:

All right angles are said to be congruent according to the Euclid’s postulate.

The addition of interior angles of any triangle will always measure 180 degrees.

Trapezoid is nothing but a quadrilateral, which has single pair of parallel sides.

In general, each and every segment has a single midpoint.

The quotients will be equal if same quantities are divided by equal nonzero quantities.

In general, a line segment can be extended for an indefinite period along a line.

The intersection of planes will be a line, if two planes intersect

If two triangles have equal angles to one another, then the two triangles are similar.

Definition of Slides in Math

Introduction for Math Slides:

Math slides is a transformation which has a plane figure or move across a line. Moving a shape without rotating or flipping is known as slides (translation). A math slides is also known as translation. If any student wants to know about the definition of math slides, they can refer the below examples with definitions Let us see some of the definition and examples for math slides. I like to share this Properties of Exponents with you all through my article.

Definition of Slides in Math – Explanations:

These are the explanations of slides in math with definition and example figure.

Slides are one of the transformations which can translate the image from original direction A, B, C, D and E to other direction as shown.

This means, they can translate the same image to other side A', B', C', D', and E' as shown.

The image of the angle, length and size are not change in them.

The image of the figure translation is its mirror of the image or their translation plane.

Every point in the translation is same distance from the center of the line as shown.

This center line is known as the mirror line.

It has the same size and length from the original image.

The translating image in the opposite side will be always same as the original image as shown in the example figure.

Each point of translation can be marked in them to shows the image length and their sides.

We can show the translation from one place to another in the following example figure.


Please express your views of this topic solved sample papers for class 12 by commenting on blog.

Definition of Slides in Math – Example Figure:

These are the example figure for the definition of slides (translation) in math.

Slides in Math:

The example figure below shows the slides in math with the shape of an object.

Elementary Column Operations

Introduction on elementary column operations:

According to the term elementary Column operation are found to be one of the parts in matrix. Elementary is found be defined as Elementary matrix is found to be defined as a simple matrix where it represented in different identity matrix form. Elementary column operation is the operation that is done by post or right multiplication. I like to share this Complex Fractions with you all through my article.

Rules Based on Elementary Column Operations:

Rule 1: To find the sum given, of elementary column operator, the identity matrix operation is applied.

Rule 2: The post multiplication has to be done for carry out elementary column operations.

Rule 3: The column operator is created from multiplying “column * column"

Representation of Column in Matrix:

The column is represented in matrix as :  `[[a],[b],[c]]`

Example Problems Based on Elementary Column Operations:

Example 1:

Elementary column operation on the term “A”, where the identity used in matrix   `A= [[1,6], [4,1], [0,1]]` and identy matrix `x = [[1,0], [0 ,1]]`

Solution:

Given: Identity matrix `x = [[1,0], [0 ,1]]`

`A= [[1,6], [4,1], [0,1]]`

Step 1:  The given identity matrix x is interchanged of fist and second column and the finding result is named it   (x1).

Step 2: To do the elementary column operation on given `A= [[1,6], [4,1], [0,1]]`

Step 3: The operation in matrix is done by [row *column]

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

The first and second column is interchanged and the result is,

`X1= [[0,1], [1,0]].`

Now, the found X1 is calculated with given “A”

`A= [[1,6], [4,1], [0,1]]`

`X1= [[0,1], [1,0]]`

`A*X1` for calculation elementary column operation on

`A*X1`

` [[1,6], [4,1], [0,1]] * [[0,1], [1,0]]`

` [[1*0+6*1 , 1*1+6*0],[4*0+1*1 , 4*1+1*0],[0*0+1*1, 0*1+1*0]]`

`[[0+6, 1+0], [0+1,4+1], [0+1, 0+0]]`

`[[6,1],[1,4],[1,0]]`

Hence ,the elmentary column operation for the given value `A=[[6,1],[1,4],[1,0]]`

Example 2:Based on elementary column operations

Elementary column operation on the term “D”, where `D= [[1,2],[1,1],[0,0]] ` the identity used in matrix   `"x= [[1,0],[0,1]] `

Solution:

Given: Identity matrix `x = [[1,0], [0 ,1]]`

`"D= [[1,2], [1,1],[0,0]], `

Step 1:  The given identity matrix x is interchanged of fist and second column and the finding result is named it   (x1).

Step 2: To do the elementary column operation on given `D=[[1,2],[1,1],[0,0]]`

Step 3: The operation in matrix is done by [row *column]

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

The first and second column is interchanged and the result is,

`"X1= [[0,1],[1,0]]`

Now, the found X1 is calculated with given “A”

`D= [[1,2], [1,1], [0,0]]`

`X1= [[0,1], [1,0]]`

`D*X1` for calculation elementary column operation on

`D*X1`

`[[1,2], [1,1], [0,0]]*[[0,1], [1,0]]`

`[[1*0+2*1 , 1*1+2*0],[1*0+1*1 , 1*1+1*0],[0*0+0*1, 0*1+0*0]]`

`[[0+2, 1+0], [0+1,1+0], [0+0, 0+0]]`

`[[2,1],[1,1],[0,0]]`

Hence ,the elementary column operation for the given value `D=[[2,1],[1,1],[0,0]]`

Understanding free help with math word problems is always challenging for me but thanks to all math help websites to help me out.

Problems to be Solved Based Elementary Column Operations:

Elementary column operation on the term “S”, where  `S ` =  `[[6,2],[2,1],[9,4]]` the identity used in matrix `X` =  `[[1,0],[0,1]] `
Answer: The elementary column operation of  `S` =`[[2,6],[1,2],[4,9]]`

Elementary column operation on the term “Z”, where `Z` =`[[2,1],[3,2],[6,3]]`   the identity used in matrix  `X` = `[[1,0],[0,1]] `

Answer: The elementary column operation of    `Z` =`[[1,2],[2,3],[3,6]]`