Sixth Grade Math Word Problems

Introduction to Sixth Grade math word problems:

Word problem is one of the best ways to turn up children’s towards solving, thinking and analyzing problems. Word problems will enhance this kind of attitude from the childhood stage itself. Sixth grade level includes real numbers,decimal,fraction,charts, graphs, money and basic mathematics like addition,subtraction,multiplication,division .Sixth Grade math word  problems is very essential for the children’s whose age lies between 8-13years old .It will be so fitful ,let us enjoy it, Let us deal about worked problems. Having problem with What is a Trinomial keep reading my upcoming posts, i will try to help you.

Example 1-sixth Grade Math Word Problems

One cat can kill a 10 rat. Then a  how many number of cat can kill  1000 rat?

Given:

1 cat=10 rat

?=1000 rat

Solution:

Step 1:

To find out the no of cat needed to kill a 1000 rat, we have to divide the total no of rat by the no of rat can be killed by single cat.

Step 2:

Division operation is used

The no of cat needed to kill a1000 rat=`1000/10=100 ` cat

Example 2 -Sixth Grade math word problems

One child makes a building with 250 bricks. How many no of bricks needed to make a 5 building?

Given:

1 Building needed=250 bricks

5 Building needed=?

Solution:

Step 1:

To find out the no of bricks needed to make a 5 building, we have to multiply the no of bricks needed to make a one building with 5

Step 2:

Use multiplication

No of bricks needed for to make 5 Building=`5xx25` =1250 bricks

No of bricks needed is 1250 bricks

Please express your views of this topic how to subtract fractions with unlike denominators by commenting on blog.

Example 3 - Sixth Grade Math Word Problems

A man travels 3 km per hour .So after 5 hour the distance traveled by him?

Given:

Man covered a distance per hour=3 km

Solution:

Step 1:

To find out the distance covered by him, we have to multiply the distance covered in 1 hour with 5

Step 2:

Use Multiplication

The total distance covered in 5hour=`5xx3=15km`

Example 4 - Sixth Grade math word problems

A child has 100 Chocolates and the dog grabbed 20% of it, from the child. How much number of chocolates dog has?

Given:

The number of chocolates Child has at first=100

Grabbed by the dog=20%

Solution:

Step 1:

To find out the 20% of chocolates, multiply the given percent with number of chocolates

=20%of100

Step 2:

Consider % as 1/100

` =(20/100)xx100`

=20

Finally, the dog has 20 chocolates

Univariate Data

Introduction to uni variate data:

Univariate means to equation, expression, polynomial or function of exactly one variable. This term is commonly used in statistics, mean, arithmetic mean to differentiate a distribution of one variable from the distribution of many other variables. Although it could be applied in many other ways as well. Since it is the simpler way to distribute the values. Correspondingly, the “multivariate time series” refers us to the changing values over the time of several quantities. I like to share this Two Way Table with you all through my article.

Properties of Univariate Analysis:

Univariate analysis is been used primarily in descriptive purposes to represent the quantitative analysis and the statistical analysis. It is the easiest method to identify the attributes and the single variable.

Univariate analysis contrasts with the bivariate analysis because it cannot analyse two variables simultaneously – or do multivariate analysis – the analysis of the multiple variables are been done simultaneously.

Univariate analysis is been commonly used in many fields like the scientific research, medical field and in simple hand calculations. Please express your views of this topic free math help online now by commenting on blog.

Data Set (univariate Data):

In our day to day life there may be many simple values that we go across. In those simple values twe can come across problems with only one variable and also with a single column of the data set, these are represented as a list. Mathematically, in the univariate data set there cannot be any repetition (i.e) because it cannot repeat multiple times. In general the order of the univariate data set does not be considered, but collection of those values may be considered to be a multi set rather than the (ordered) list.

Generally, the values might be of any of the kinds described as a level of the measurement. For every variable, the values will be normally of the same kind or similar.  Uni variate data can be as real numbers or the integers. For example, representation of a building's height using the meters. This could also be represented as a nominal data. However, there could also be "missing values", and those values need to be indicated in some representation.

Numerical Form

Introduction to numerical form:

Numerical form is nothing but the conversion of words into numbers. For example, one million can be expanded in numerical form as 1,000,000 or 106. Likewise, one billion can be expanded in numerical form as 1,000,000,000 or 109.  In this article numerical form, we are going to discuss about numerical form through example problems and practice problems. I like to share this Define Numerical Expression with you all through my article.

Example Problems for Numerical Form:

Example 1:

Write two and thirty five thousandths in numerical form.

Solution:

Step 1: thirty five thousandths can be written as .035

Step 2: Here, the whole number is two

Step 3: Hence, the numerical form is 2.035

Example 2:

Write thousand eight hundred million in numerical form.

Solution:

Step 1: one million is equal to 1000,000

Step 2: Thousand eight hundred million will be equal to 1,800,000,000

Step 3: Hence, the numerical form is 1,800,000,000

Example 3:

Write four and forty five thousandths in numerical form.

Solution:

Step 1: forty five thousandths can be written as .045

Step 2: Here, the whole number is four

Step 3: Hence, the numerical form is 4.045.

Example 4:

Write three thousand seven hundred million in numerical form.

Solution:

Step 1: one million is equal to 1000,000

Step 2: three thousand seven hundred million will be equal to 3,700,000,000

Step 3: Hence, the numerical form is 3,700,000,000

Example 5:

Write eight and eighty five thousandths in numerical form.

Solution:

Step 1: Eighty five thousandths can be written as .085

Step 2: Here, the whole number is eight.

Step 3: Hence, the numerical form is 8.085

Example 6:

Write two thousand four hundred billion in numerical form.

Solution:

Step 1: one billion is equal to 1000,000,000

Step 2: two thousand four hundred billion will be equal to 2,400,000,000,000

Step 3: Hence, the numerical form is 2,400,000,000,000


I have recently faced lot of problem while learning Number Line Template, But thank to online resources of math which helped me to learn myself easily on net.

Practice Problems for Numerical Form:

1) Write five and sixty five thousandths in numerical form.

Answer: Numerical form is 5.065

2) Write thousand hundred million in numerical form.

Answer: Numerical form is 1,100,000,000

3) Write four thousand five hundred billion in numerical form.

Answer: Numerical form is 4,500,000,000,000

Upper Limit Definition

Introduction to upper limit definition:

Real function: Let R be the set of all real numbers, and let X and Y be any two nonempty subsets of R.Then,a rule f which associates to each x ε X,a unique real number f(x) ε Y is called a real function from X to Y and we write, f : X ----> Y.f(x) is called the image of x or the value of the function at x.The sets X and Y are called the domain and co domain of f.Also,the set {f(x):x ε X} is called the range of f.

Limit : A function f(x) is said to tend to a limit L as x tends to 'a' if for every ε > 0,however small,there exists a corresponding positive  real number δ, such that

l f(x) − L l < ε, Whenever 0 < l x -a l < δ

This is denoted symbolically by        `lim_(x->a)` f (x) = L .

It implies that whenever the value of x lies in the open interval (a - δ , a + δ),for δ to be very small, then the value of the function f(x),lies in the open interval (L−ε , L+ε) on the y-axis.

Lower limit and Upper limit : In the limit of a function f(x), as x tends to a, x may approach a from lower side i.e, a < x or from upper side i.e, a > x.The limit of the function f(x),when 'x' tends to 'a' from lower side of a is called lower limit and when 'x' tends to 'a' from upper side of 'a' is called upper limit.

The upper limit and lower limit are represented as shown below.

Upper limit = `lim_(x->a+)` f(x),which implies that x tends to a from upper side of a,i.e, x > a.

lower limit = `lim_(x->a-)` f(x),which implies that x tends to a from lower side of a,i.e, x < a.

Fundamental Theorems of Limit Definition:

1) `lim_(x->a)` { f(x)+g(x)} = {`lim_(x->a)` f(x)} + {`lim_(x->a)` g(x)}.

2) `lim_(x->a)` { f(x)−g(x)} = {`lim_(x->a)` f(x)} − {`lim_(x->a)` g(x)}.

3) `lim_(x->a)` {c . f(x)}  = c. {`lim_(x->a)` f(x)}, where c is constant.

4) `lim_(x->a)` {f(x) . g(x)}  = {`lim_(x->a)` f(x)} . {`lim_(x->a)` g(x)}.

5) `lim_(x->a)` `(f(x))/(g(x))` = `(lim_(x->a)f(x))/(lim_(x->a)g(x))` , where `lim_(x->a)` g(x) ≠ 0.

6) If f(x)≤ g(x) for all x then `lim_(x->a)` f(x) ≤ `lim_(x->a)` g(x).

Example Problems of Upper Limit

Ex 1:  Find the upper limit of  `lim_(x->3 )` `(x^2-9)/(x-3) ` ?

Sol : `lim_(x->3+)` `(x^2-9)/(x-3)` = `lim_(x->3+)` `((x-3)(x+3))/(x-3)`

=  `lim_(x->3+)` `(x+3)`

= ` 6`

Ex 2:  Find the upper limit of `lim_(x->1)` `(x^2-4x+3)/(x-1)` ?

Sol : `lim_(x->1+)` `(x^2-4x+3)/(x-1)` = `lim_(x->1+)` `((x-1)(x-3))/(x-1)`

= `lim_(x->1+)` `(x-3)`

=   ` -2`


Is this topic derivative of cotx hard for you? Watch out for my coming posts.

Practice Problems of Upper Limit

Pro 1:  Evaluate `lim_(x->1+)` `(6x^2-4x+3)`

Ans: 5

Pro 2:  Evaluate `lim_(x->7+)` `(x^2-49)/(x-7)`

Ans:   14

Pro 3:  Evaluate `lim_(x->0+)``{(x-2)^2+6}`

Ans: 10

Polygon with all Sides and Angles Congruent

Introduction of polygon with all sides and angles congruent:

Polygon is one of the important shapes in geometry generally; there are two types of polygon. They are regular polygon and irregular polygon,in regular polygon as closed shape the sides of the regular polygon are equal, and the angles are also equal. But in the irregular polygon both angle and sides are not equal. In this article, we have to discuss about polygon with all sides and angles congruent.

Polygon with all Sides and Angles Congruent:

Regular Polygon consist of several types. They are,

Triangle
Square
Pentagon
hexagon
heptagon
octagon
nonagon
decagon
hendecagon, and
dodecagon.


Types of Regular polygon Table:

Description of Polygon with all Sides and Angles Congruent

Triangle:

The equilateral triangle is one of the types of regular polygon because it has three sides, and three angles congruent. The each side of interior and exterior angles is 60o.

Square:

The square is one of the types of regular polygon because it has four sides and four angles are congruent. The each side of interior and exterior angles is 90o

Pentagon:

The pentagon is one of the types of regular polygon because it has five sides and five angles  congruent. The each side of interior and exterior angles is 108o

Hexagon:

The hexagon is one of the types of regular polygon because it has six sides and six angles congruent. The each side of interior and exterior angles is 120o

Is this topic Circle geometry hard for you? Watch out for my coming posts.

Heptagon:

The heptagon is one of the types of regular polygon because it has seven sides and seven angles congruent. The each side of interior and exterior angles is 128.571o

Octagon:

The octagon is one of the types of regular polygon because it has eight sides  and eight angles congruent. The each side of interior and exterior angles is 135o

Nonagon:

The nonagon is one of the types of regular polygon because it has nine sides and nine angles congruent. The each side of interior and exterior angles is 144o

Decagon:

The decagon is one of the types of regular polygon because it has ten sides and ten angles congruent. The each side of interior and exterior angles is 140o

Hendecagon:

The hendecagon is one of the types of regular polygon because it has eleven sides and eleven angles congruent. The each side of interior and exterior angles is 147.273o

Dodecagon :

The dodecagon is one of the types of regular polygon because it has twelve sides and twelve angles congruent. The each side of interior and exterior angles is 150o

Study of Errors in Measurement

Any number when expressed in the form of percentage conveys lot of meaning. Percentage is nothing but a number being expressed as a part of 100. This can be ratio of 100 or also can be termed as fraction. Percentage can be denoted by the symbol % and is very commonly used. Many measurements are made in the real world. So, there can be errors also. When there is deviation from the desired measurement error is obtained. It has to be measured to ascertain its cause and also to seek its remedy. At first the absolute is calculated. This is done by subtracting the value of the measurement obtained and the standard value. This will always be a positive number as absolute value of a number will always be positive. Once the absolute value is obtained the next step is to find the relative error which can be found if the value of the standard measurement is known. The relative error formula is quite simple. It is obtained by dividing the absolute error by the true value. If it has to be found in percentage then the answer obtained is multiplied by 100. So, the relative error equation is absolute error being divided by original value and multiplied by 100. The final answer is obtained in percentage.

This error is very significant and can be very helpful. It can be very useful in making a comparison between two measurements. The symbol percent is very important. One must not forget to write this after the answer is obtained as the answer obtained is in percentage. Also while rounding off the digits it has to be seen that the numbers do not lose their values. The terms relative error and absolute error are inter-related.


Understanding coordinate transformation is always challenging for me but thanks to all math help websites to help me out.

To calculate the former one first the latter one has to be calculated. So, the calculation of absolute error is very important and no mistake must be done while finding it out. To calculate the absolute value the standard value is required. This has to be available and if it is not then the term absolute error cannot be found out and the process cannot be completed. Error occurs in the real world as the instruments used cannot give 100% accuracy. So, the errors cannot be eliminated but they can only be reduced. When an error occurs it means there is deviation from true value.

Smoothing Function in Math

Introduction for smoothing function in math:

In smoothing function in math, let f(x) be a real-valued function of a real variable x and let a be some fixed point in the domain of f. The number L is the limit of f (x) as x approaches a if, given any positive number `epsi`, we can find a positive number `delta` such that f (x) is in the range

|f(x) – L| `<` `epsi`

Whenever x is in the domain

0 `<` |x – a| `<` `delta`

We write

`^lim_(x -> a)` f(x) `=` L

More about for Smoothing Function in Math:

In smoothing function in math, the notation

`^lim_(x -> a)` f(x) `=` L

is read “the limit of F(x) as x approaches a is L.

f(x) `->` L  as x `->`a;

This is read as “f(x) approaches L as x approaches a” or “f(x) goes to L as x goes to a”. I like to explain limits by writing

f(x) `~~` L when x `~~`a (but x `!=` a).

The notation A `~~` B means A is approximately equal to B. In ? We will study a limit

f’(a) `=` `^lim_(x -> a)` `(f(x)-f(a))/(x-a)`

called the derivative. The derivative is a limit, but the concept of limit is more general. Note that in the definition of limit we consider values of x close to a but never plug in x = a. In the interesting examples (like the derivative) setting x = a in f(x) leads to something undefined like `0/0` for smoothing function in math. Is this topic 8th grade math practice problems hard for you? Watch out for my coming posts.

Example for Smoothing Function in Math:

In smoothing function in math,

`^lim_(x -> 1)` 4x `-` 2 `=` 2

`^lim_(x -> 1)` `x^2` `+` 3 `=` 12

Some limits are more difficult to find if they contain a denominator that goes to zero as x `->` a. These limits must be treated carefully using, for example, L Hopitals rule.

Proof that a limit exists requires manipulation of inequalities to determine the relationship between `epsi` and `delte`. It is also necessary to verify that the inequalities |f(x) `-` L| `<` `epsi` and 0 `<` |x `-` a| `<` `delta` are satisfied as required by the definition of a limit.

Suppose we have the limits

`^lim_(x -> a)` f(x) `=` L

And

`^lim_(x -> a)` g(x) `=` M

Then

`^lim_(x -> a)` [ f(x) `+` g(x)] `=` L + M

That is, the limit of the sum of two functions is the sum of the limits.

`^lim_(x -> 1)` [`x^2` `+` 3 `+` 4x `-` 2 ] `=` 2 `+` 12

Answer is     `^lim_(x -> 1)` [`x^2` `+` 4x `+` 1 ] `=` 14