Elementary Math Word Problem

Introduction to elementary math word problem:

In mathematics education, the term solving word problem is often used to refer to any mathematical exercise where significant background information on the problem is presented as text rather than in mathematical notation. As word problems often involve a narrative of some sort, they are occasionally also referred to as story problems and may vary in the amount of language used. In this article we shall discuss elementary math word problems. (Source: Wikipedia)

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Elementary math word problem examples


Here we are going to solve elementary math word problem with detailed solutions.

Example:

In an office there are 90 employees work. If the number of gents employees is 37, frame the equations and find how many number of ladies work in office.

Solution:

Let the number of ladies work in office be x.

The number of gents works 37.

Total number of worker 90.

Therefore simple equation is x+37 = 90

x =90 - 37

x = 53 ladies in office.

Example:

The 12 orange costs is `$` 125, find the total cost of 16 orange.

Solution:

Step 1:

Consider the given problem as If the 12 orange costs is 125. Find the cost of 16 orange?

Step 2:

12 orange cost =125

16 orange cost = `16/12 ` x125

=167

Answer:

Therefore the cost of 16 orange is `$ ` 167

Problem:

In a class room there are 60 students taking a math exam. 20 students get an average score of 70. The left over students get an average score of 75. Find the average score of the entire class?

Solution:

To find the average score of the entire class, we need to follow the following steps these steps very helpful to find the average.

Step 1:

First we need to find the sum of weighted terms and multiply each average value by the number of students in the entire class had that average and sums.

70 × 20 + 75 × 40 = 1400 + 3000 = 4400

Step 2:

Number of total terms = Number of students in the entire class = 60

Step 3:

Here we need using the formula for weighted average formula to find the average

Average = sum of average terms
Total number of term

=` 4400/60`

= 73.3

Answer:

The average mark of the entire class is 73.3


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Elementary practice math word problem


Problem:

In an office there are 70 employees work. If the number of gents employees is 27, frame the equations and find how many number of ladies work in office.

Answer:

43 ladies in an office

Problem:

The 13 orange costs is `$ `130, find the total cost of 17 orange.

Answer:

The cost of 17 orange is` $` 170

Solving Elementary Math Test

Introduction to solving elementary math test:

Mathematics is used for throughout the entire world used in many areas like, engineering, science, and medicine. In elementary school the students receive first level of education is called as primary education. Elementary mathematics includes topics from algebra, arithmetic, number system and geometry etc. In this article we shall discuss solving elementary math test example problem.

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Solving elementary math test example problem


Here we are going to solving the elementary math test example problem with detailed solutions. It is very helpful for elementary math students.

Example:

Solving the equation: x-15 = 35

Solution:

Given x-15= 35

x = 35 + 15 (-15 in the LHS becomes +15 when it comes to the RHS)

Therefore y = 50

Example:

The cost of 20 pens is `$` 420. Find the cost of each pen.

Solution:

Consider the cost of one pen be x

Therefore the cost of 20 pen is 20 × x = 20x

But the cost of 20 pen            = `$` 420

The simple equation is 20x         = $420

To get the cost of one pen, solving the equation

20x = 420

x = 420 x 1/20

= 21

The cost of each pen is `$` 21

Example:

Solving the equation 6x – 4 = 26

Solution:

Given 6x – 4 =26

6x = 26 +4

6x = 30

x = 30 x `1/6`

Therefore x = 5

Example:

Solve the expression 12x + 5y - 4 + 6x + 6y + 8

Solution:

Find the like terms in the expression and then group and combine like terms:

• +12x and +6x are like terms, and combined to get +18x,

• +5y and +6y combine all like terms to get +11y, and

• -4 and +8 combine all like term and get +4.

So after simplify, the expression:

18x + 11y + 4

Example:

The sum of two numbers is 25. If one number is 14, find the other number.

Solution:

Consider the unknown number be x.

The sum of two numbers = 25

One number is 14.

Therefore the simple equation is            x = 25 - 14

x = 25 -14

x = 11

The other number is 11.

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Elementary math test practice problem


Problem:

The cost of 25 pens is `$` 500. Find the cost of each pen.

Answer:

The cost of each pen is `$` 20

Problem:

Solving the expression 8x + 6y - 5 + 6x + 6y + 10

Answer:

14x + 12y + 5

Problem:

The sum of two numbers is 22. If one number is 10, find the other number.

Answer:

The other number is 12.

4th Grade Math Expressions

Introduction to 4th grade math expressions:

4th grade math expressions deals with the simple  format of expressions containing variable, the variables are in the form of alphabetic, such as x, y, z, m, n… Using this we can create and expressions which is in the equation form and find the value of variables.

Addition, subtraction, division, and multiplication are called basic arithmetic operations of mathematics which are performed on 4th grade math expressions. This article shows the different operations performed on 4th grade math expressions.

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Examples problem for 4th grade math expressions:


1. Find the x value for given expression, x + 7.

Solution:

Given expression is,

x + 7 = 0

Both sides subtracting by -7,

x + 7 – 7 = -7

Simplify the values,

Then we get the answer is,

x = -7

The answer to variable x is -7.

2. Find the z value for given expression, z + 3.

Solution:

Given expression is,

z + 3 = 0

Both sides subtracting by -3,

z + 3 – 3 = -3

Simplify the values,

Then we get the answer is,

z = -3

The answer to variable z is -3.

3. Find the y value for given expression, y +17.

Solution:

Given expression is,

y + 17 = 0

Both sides subtracting by –17,

y + 17 – 17 = -17

Simplify the values,

Then we get the answer is,

y = -17

The answer to variable y is -17.


More examples problem for 4th grade math expressions:

4. Find the x value for given expression, x - 5 -13 + 4.

Solution:

Given expression is,

x - 5 -13 + 4 = 0

First combine the integers,

x - 5 -13 + 4 = 0                          (-5 -13 + 4 = -14)

x -14 = 0

Both sides adding by 14,

x - 14 + 14 = 14

Simplify the values,

Then we get the answer is,

x = 14

The answer to variable x is 14.

5. Find the y value for given expression, y - 2 - 3 + 4.

Solution:

Given expression is,

y - 2 - 3 + 4 = 0

First combine the integers,

y - 2 - 3 + 4 = 0                          (-2 -3 + 4 = -1)

y -1 = 0

Both sides adding by 1,

y - 1 + 1 = 1

Simplify the values,

Then we get the answer is,

y = 1

The answer to variable y is 1.

More examples problem for 4th grade math expressions:


6. Find the z value for given expression, z - 4 -10 + 24.

Solution:

Given expression is,

z - 4 -10 + 24 = 0

First combine the integers,

z - 4 -10 + 24 = 0                          (-4 -10 + 24 = 10)

z +10 = 0

Both sides adding by -10,

z + 10 - 10 = -10

Simplify the values,

Then we get the answer is,

z = -10

The answer to variable z is -10.

7. Find the x value for given expression, x - 25 -10 + 20.

Solution:

Given expression is,

x - 25 -10 + 20 = 0

First combine the integers,

x - 25 -10 + 20 = 0                          (-25 -10 + 20 = -15)

x -15 = 0

Both sides adding by 15,

x - 15 + 15 = 15

Simplify the values,

Then we get the answer is,

x = 15

The answer to variable x is 15.

Free 3rd Grade Math

Introduction for free 3rd grade math:

In algebra basic arithmetic operation (addition, subtraction, multiplication, and division) generally used in day to day life. In these articles we are going to discuss about free 3rd grade math. Addition (+) defined as adding the two numbers. Subtraction (-) defined as the inverse of addition.Addition is a mathematical process so as to represent combine collection of objects as one into a better collection. It is signifying by the plus sign (+). For example, there is 6 + 5 apple, 6 + 5 = 11. Subtraction is a mathematical process so as to inverse of addition. 6 – 3 apples, 6 – 3 = 3 apples (Source: Wikipedia)

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Free 3rd grade math - Addition and subtraction example problems:


Free 3rd grade math – Addition example problems:

Example 1:

Adding the given values

89775 – 16654

Solution:

89775

16654   (+)

-----------

106429

----------

So, the final answer is 106429

Example 2:

If there are 192 tickets in a box and Joshua puts 49 more tickets inside, how many tickets are in the box?

Solution:

If there are 192 tickets in a box and Joshua puts 49 more tickets inside,

= 192 + 49

= 241 tickets

241 tickets are in the box.

Example 3:

Evelyn has 187 apples. Marvin has 125 apples. If Marvin gives all of his apples to Evelyn, how many apples will Evelyn have?

Solution:

Evelyn has 187 apples. Marvin has 125 apples. If Marvin gives all of his apples to Evelyn,

= 187 + 125

187

125   (+)

--------

312

----------

312 apples will Evelyn have,

Free 3rd grade math – Subtraction example problems:


Example 1:

Subtracting the given values

67484 – 45867

Solution:

67484

45867    (-)

-----------

21617

-----------

So, the final answer is 21617.

Example 2:

James reading a chapter book that has 872 pages. He has already read 246 pages. How many pages does he have left to read?

Solution:

James reading a chapter book that has 872 pages. He has already read 246 pages.

872

246   (-)

----------

626

----------

626 pages does he have left to read.

Example 3:

There are 659 employees working in an office building. 368 of them are about to leave to go home. How many employees will be left in the building?

Solution:

There are 659 employees working in an office building.

368 of them are about to leave to go home.

659

368   (-)

---------

291

---------

291 employees will be left in the building.

Elementary Math Area

Introduction For elementary Math Area:

Elementary math area consist of area for square, rectangle ,triangle it is a menstruation part it is interesting in finding area of shapes and measuring length for given shapes. In menstruation area is an essential part for measuring the shape length. Measurement math consists also volume, surface area such as in higher grade for elementary math we have only fundamental shapes.

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Elementary Math Area For Square:


Area of a Square:
We know  square is a like rectangle in which its Length = Breadth.
The area of the square
= Length `xx ` Length
= (Length)2 = (Side)2
= a × a
= a^2

Example 1:
Find area of a square whose side is 12 cm.

Solution :
Side of the square, a = 12 cm
Area of the square, A = a^2
= a × a
= 12 × 12
= 144 sq.cm (or 144 cm2)
Example 2:
Find area of a square whose side is 14 cm.

Solution :
Side of the square, a = 14 cm
Area of the square, A = a^2
= a × a
= 14 × 14
= 196 sq.cm (or 196 cm2)

Area of Rectangle:
Length `xx` Breadth

Example 1 :
Length and breadth of a rectangle are 15 cms and 13 cms respectively. find its area.

Solution:
= Length `xx` Breadth
= l `xx` b
= 15 cm. `xx` 13 cm.
= 195 Sq. cm.

Example 2:
Find the area  of a rectangle whose length is 2m and breadth is 70 cm.

Solution :
Length of the rectangle, l = 2 m or 200 cm
Breadth of the rectangle, b = 70 cm
Area of the rectangle, A = l × b
= 200 cm × 70 cm
Area = 14000 sq.cm.

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Elementary Math Area For Triangle:


Area of a  triangle:
`1/2` × base × height

Example 1 :
In a triangle the length of sides containing  angles are 20 cm and 21 cm. Find its area.

Solution :
Let b = 20 cm and h = 21 cm
Area of the right triangle, A =1/2 bh
= `1/2` × 20 cm × 21 cm
= 210 sq.cm

Example 2 :
In a right triangle the length of sides containing the right angles are 15 cm and 20 cm. Find its area.

Solution :
Let b = 15 cm and h = 20cm
Area of the right triangle, A = `1/2` bh
=`1/2` × 15 cm × 20 cm
= 150 sq.cm

Rules for Elementary Algebra

Introduction to rules for elementary algebra:

Algebra is a system of written calculations that help us reason about numbers. At the very first, we should realize that algebra is a skill. The initial thing to note is that, in algebra, we use letters as well as numbers.  But the letters represent numbers.  And the rules of algebra match to the rules of arithmetic, but we write those rules using letters. Rules for elementary algebra is very basic in algebra, Now we are going to see about the rules for elementary algebra.

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Rules for elementary algebra part - I:


Property of zero

0 · x = 0
0 + x = x

Property of One

1 + x = 1
1. x = x

Identity Property

x · x = x
x + x = x

Redundancy Property

x · ( x + y ) = x
x + ( x · y ) = x

Commutative property

x · y = y · x
x + y = y + x

Associate Property

x · ( y · z ) = ( x · y ) · z
x + ( y + z ) = ( x + y ) + z

Distributive Property

x · ( y + z ) = ( x · y ) + ( x · z )
x + ( y · z ) = ( x + y ) · ( x + z )


Rules for elementary algebra part - II:


Properties of negation

a ( -1 ) = -a

-( -a ) = a

( -a ) b = - ( ab ) = a ( -b )

( -a ) ( -b ) = ab

-( a + b ) = ( -a ) + ( -b )

Properties of equality

If a + c = b + c, then a = b

Word Problems Elementary Level

Introduction:

The term word problem refers to the math exercise which has information about the problem in words rather than text. It is hard to translate the words into mathematical expression or equations. When it is done, then it is easy to solve those problems. But translation of those words to mathematical symbols or equation is hard. Understanding the given condition or situation in the word problem is more important than solving it. Without understanding the math word problems the solving work can’t be done. Elementary level word problems are easy to solve. The elementary level word problems involve basic arithmetic operations only. Those elementary level problems are not much complicated.

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Elementary level Word problems:


Example 1:

A fish tank contains 30 fish of which 5 are stationary. How many fish in the tank are moving?

Solution:

Here the total number of fish = 30

Number of stationary fish = 5

Numbers of moving fish = 30 – 5

= 25 fish

The answer is 25 fish.



Example 2:

A zoo has 18 Thailand elephants and 6 Indian elephants. How many elephants are there in the zoo?

Solution:

Number of Thailand elephants = 18

Number of Indian elephants = 6

Total number of elephants = 18 + 6

= 24 elephants.

The answer is 24 elephants.



Example 3:

Raja sent invitations to 60 relatives for a family get-together. Only 35 relatives came to the function. How many relatives did not come?

Solution:

Total number of invitations send = 60

Number of relatives came to function = 35

Number of relatives did not come = 60 – 35

= 25

The answer is 25.

More elementary level word problems:


Example 4:

Lokesh had brought 17 flowers from a Park last time. His mom wants Lokesh to bring 4 times as many this time. How many flowers will Lokesh bring this time?

Solution:

Number of flowers Lokesh bought last time = 17

He bought 4 times as many flowers this time,

Hence,

Number of flowers Lokesh bought this time = 17*4

= 68

The answer is 68 flowers.



Example 5:

There are 60 apple trees planted in 5 rows. How many apple trees are there in each row?

Solution:

Total number of trees planted = 60

Total number of rows = 5

Number of apple trees peer row = 60/5

= 12 trees

The answer is 12 trees.

5th Grade Math Variables

Introduction to 5th grade math variables:

In mathematics, 5th grade math variables are using addition and subtraction operation with variables. Single-symbol are called for variables are the normal, with x, y, and z being most common using in variables problem. Constants are generally denoted as a, b, c. In mathematics, constants and variables are usually set in an italic typeface.

Specific branches and applications of mathematics regularly have specific naming conventions for variables.

Meanings or variables with similar roles are regularly assigned consecutive letters. For example, x, y, and z is the three axes in 3D coordinates space are conventionally.

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Examples problems for 5th grade math variables:


1. Find the x value, for the given for single variable expressions.

18x + 2 = 38

Solution:

18x + 2 = 38

Subtract (2) with both sides,

18x + 2 – 2 = 38 – 2

18x = 36

Divide (18) with both sides,

18x / 18 = 36 / 18

x = 2.

The solution to the given expression in single variable x = 2.

2. Find the y value, for the given for single variable expressions.

4y + 4 = 20

Solution:

4y + 4 = 20

Subtract (4) with both sides,

4y + 4 – 4 = 20 – 4

4y = 16

Divide (4) with both sides,

4y / 4 = 16 / 4

y = 4.

The solution to the given expression in single variable y = 4.


More examples problems for 5th grade math variables:


3. Find the z value, for the given for single variable expressions.

5z + 5 = 30

Solution:

5z + 5 = 30

Subtract (5) with both sides,

5z + 5 – 5 = 30 – 5

5z = 25

Divide (5) with both sides,

5z / 5 = 25 / 5

z = 5.

The solution to the given expression in single variable z = 5.

More examples problems for 5th grade math variables:


4. Find the x value, for the given for single variable expressions.

6x - 2 = -38

Solution:

6x - 2 = -38

Add (2) with both sides,

6x - 2 + 2 = -38 + 2

6x = -36

Divide (6) with both sides,

6x / 6 = -36 / 6

x = -6.

The solution to the given expression in single variable x = -6.

Elementary Set Theory

Introduction to elementary set theory:

A set theory is a collection of elements or the items can be considered as a whole. If the set contains only a few items or elements, then the set can be defined by listing them in braces. For example: A = {1,2,3}. Now we are going to see about the elementary set theory.

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Elementary set theory:


Now we are going to see about the elementary set theory as follows,

Set and Sample Space:

The sets are the important part and the basic concepts in mathematics and probability. Sets are usually consists of collection of some elements.

Example of sample spaces:

Pick a card from a pack of 52 cards:

Sample space = {1, 2 ...52}, which is a infinite sample space.

Subset:

A subset is can be defined by some property of its elements.

For example, let P = {1,2,3,4}, and let Q = {2,}. Then Q can be defined as the set of all elements of P which are even, or in symbols:

Q ={x  `in` A |  x is even}.

The operation properties are given as follows,

The intersection operation has the properties are given as,

Commutative: A `nn` B = B `nn` A.

Associative: (A `nn` B) `nn` C = A `nn` (B `nn` C).

The union operation has several properties

Commutative: A `uu` B = B `uu` A.

Associative: (A `uu` B) `uu` C = A `uu` (B `uu`C).

Ordered pairs:

An ordered pair contains set of two elements that are arranged in a specified order. An ordered pair is usually written as (x, y).

Relations:

A relation R is on a set A, where A is simply a set of ordered pair of element of A.

Functions:

A function ‘f’ from the set X to the set Y is a rule given any element x of A, This concept is often expressed symbolically as f: X--->Y

Problems for elementary set theory:


Example 1:

A = {1, 2, 3, 4, 5, 6, 7, 8, 11, 12} B = {9, 10, 11, 12, 13). Determine the union and intersection of set A and B.

Solution:

The union of set is nothing but including both the set elements in a single set

(B `uu` C) = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}, (B ∩ C) = {11, 12}.

Example 2:

P = {f, g, h, i, j, k, l} Q = {g, j, l, m, n}. Determine (P – Q) and compliment of C related to Q.

Solution:

The difference of the two sets P and Q are given as,

(P – Q) = {f, h, I, k}, Cc = {m, n}

Study Elementary Probability

Introduction to study elementary probability:

The elementary probability theory condition for all probability mass function (pmf) there is functions which give the probability in a divide random variable which is accurately corresponding to some of the value recognized. A pmf differs as of a common probability density function (pdf) in the values of a pdf, defined for the permanent random variables and not the probabilities as such desired.


How to study elementary probability:


The study of elementary probability function always defines as known in the relationship among the two such variables in a probability distribution function which is named as the "Probability Function". An elementary probability function assumes that the "variable" which indicates the values within the given range of such a random variable at its independent variable and "probability" defined as the dependent variable.

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Study the representation of probability function for elementary type:


An elementary probability function which relates the break up random variable is recognized as the "Probability Mass Function". In the sequence of a random variable the value of "X" assumes that the distinct set of values `x_1, x_2, x_3, ... x_n,` then the function "f" is defined by the f(xi) = P(X = xi) and that is called as the "Probability Function" or "Probability Mass Function". The pmf assigns a value for the required probability [P(X = xi)] in each of the possible values [xi] of the variable.

That gives the study of elementary probability value and the variable which represents the sequence of the distinct random variable which equals to some value. A study of discrete probability function f(x) defines the following properties.

f (xi) ≥ 0 is given by the probability for the variable to carryover a particular value which is always a positive real number.

Σ f (xi) = 1 [i = 1, 2, 3, ... ∞] The sum of the corresponding probabilities of all the given possible values and that suits the variable which represents the range of all the discrete random variable which may carry the value equal to One.