Mixed Numbers and Define Numbers

Mixed Numbers in the number system are basic numbers which involves different types of number which are defined as below.

Hope the definition of numbers will help you to know the terminologies of different kinds of numbers.

Natural numbers : The numbers 1, 2, 3, 4 …. are called as natural numbers or positive numbers

Whole numbers : The numbers 0, 1, 2, 3, 4 ….. are called as whole numbers. whole numbers include “0” also

Integers : The numbers …. -3, -2, -1, 0, 1, 2, 3 …… are called as integers .

Rational number : Any number which is positive or negative integer or fraction ,or zero is called a rational number . A rational number is one which
can be written in “p/q”form where “p” and “q” are positive or negative integers.

Irrational number : An infinite non recurring decimal number is know as an irrational number , these numbers can not be expressed in the from of proper fraction.

Prime number : Those numbers which are divisible only by themselves and by “1” are called as prime number.

How to check whether a given number is prime or not

– If a number has no factor equal to or less than its square root than the given number is a prime number co – prime — two number as called as co-prime if they do not have any factor in common other than 1
composite — a number which has factors other than it self and 1 is called as composite number.

Surd : Any root of a number which can not be exactly found is called as surds.

Real numbers :  A number which is either rational or irrational is called as real number.

Complex numbers : A number which is not real is a complex number or numbers of the type “a+ib” where “i” is square root of “-1”

Mixed numbers is a number form by the combination of any of the above type of numbers.

 

A set theory problem

Set theory is the branch of mathematics that studies sets, which are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics.In set theory, the union (denoted as ∪) of a collection of sets is the set of all distinct elements in the collection. The union of a collection of sets gives a set .the intersection (denoted as ∩) of two sets A and B is the set that contains all elements of A that also belong to B (or equivalently, all elements of B that also belong to A), but no other elements.These both can define us what is Universal Set U .The language of set theory is used in the definitions of nearly all mathematical objects, such as functions, and concepts of set theory are integrated throughout the mathematics curriculum. Elementary facts about sets and set membership can be introduced in primary school, along with Venn and Euler diagrams, to study collections of commonplace physical objects. elementary algebra practice such as set union and intersection can be studied in this context. More advanced concepts such as cardinality are a standard part of the undergraduate mathematics curriculum.Let’s see an example from free math answers

S ∩ B U M = n(S)+n(B)+n(M) – n(S∩B) – n(B∩M) – n(M∩S)+n(S∩B∩M)+vehicle investment

275 = 145+90+72+-47-40-39+x+75

275 = 307-126+75+x

x = 19

number of employees invested in all three = 19

 

A word problem on Linear Equations

Equations play a crucial role in modern mathematics and form the basis for mathematical modeling of numerous phenomena and processes in science and engineering.
It also outlines some methods for solving equations,like linear equations ,includes interesting articles, gives links to mathematical websites and software packages, lists useful handbooks and monographs, and refers to scientific publishers, journals, etc. The website includes a dynamic section Equation Archive which allows authors to quickly publish their equations (differential, integral, and other) and also exact solutions, first integrals, and transformations.An equation is a mathematical statement, in symbols, that two things are exactly the same (or equivalent). Equations are written with an equal sign,Lets see how to solve equations for a given word problem from 8th grade math word problems.

Question:-

Two brothers are saving money to buy tickets to a concert .their combined savings is $55.one brother has $15 more than the other .
How much has each saved?

Answer:-

Let the saving by the first brother be $x

the saving by other is $x+15

according to the question

x+x+15=55

2x+15=55

subtract 15 on both sides

2x = 40

divide with 2 on both sides

x=20

So the brothers have saved $20 and $35 respectively…

 

Algebraic Equation with Variables

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and (the first power of) a single variable.

Linear equations can have one or more variables. Linear equations occur with great regularity in applied mathematics. While they arise quite naturally when modeling many phenomena, they are particularly useful since many non-linear equations may be reduced to linear equations by assuming that quantities of interest vary to only a small extent from some “background” state.We have linear equations explained with one variables and linear equations with two variables ..so on.We follow different methods based on the number of variables present in a linear equation.

Question:-

Solve (4w-28)+(11w+13)=180

Answer:-

(4w-28)+(11w+13)=180

Re arrange the equation ,by writing like terms together.

(4w+11w)+(-28+13)=180

15w – 15 = 180

add 15 on both sides

We get 15w = 195

Now divide with 15 on both sides

We get w=13

Similarly we get answers to algebra equations  with variable terms on both sides

 

How to find the missing angle in a Triangle.

Trigonometry is a branch of mathematics that studies triangles, particularly right triangles. Trigonometry deals with relationships between the sides and the angle of triangles and with the trigonometric functions, which describe those relationships, as well as describing angles in general and the motion of waves such as sound and light waves.If we have a right angle triangle which will have a hypothesis .We can see more hypothesis examples. Similarly we can find the adjacent angles as well.
Trigonometry is usually taught in secondary schools either as a separate course or as part of a precalculus course. It has applications in both pure mathematics and in applied mathematics, where it is essential in many branches of science and technology. A branch of trigonometry, called spherical trigonometry, studies triangles on spheres, and is important in astronomy and navigation.We can find the volume of a triangle by using volume formula.

Question:-

How to find an angle in a triangle, when two angles are given as 55 and 75 degrees.

Answer:-

We know that sum of the 3 angles of a triangle is 180 degrees

one angle = 55

second angle = 75

Let the third angle = x

55+75+x = 180

130+x = 180

x = 180 – 130

x = 50

So the third angle = 50 degrees

 

A Solved Example on Fractions and Equation Fractions

Fraction is defined as a number which represent the part of a whole. Here is one such fractions help which helps you to better understand how to do fractions and calculating fractions in equations.

Below is a simple solved example and a simple help with equations with fractions

Solve : 8/2 – 15/3 + 18/4 = 7/2

Solution :

8/2 – 15/3 + 18/4

=  (48 – 60 + 54)  / 12

=  (102 – 60) / 12

= 42 / 12

= 21 / 6

= 7 / 2

Hope the above steps explained, how to simplify the fraction

and is a problem help with equations with fractions.

 

Types of Fractions in algebra

In algebra answers , earliest fractions were reciprocals of integers, symbols representing one half, one third, one quarter, and so on. A much later development were the common or “vulgar” fractions which are still used today, and which consist of a numerator and a denominator, the numerator representing a number of equal parts and the denominator telling how many of those parts make up a whole. An example is 3/4, in which the numerator, 3, tells us that the fraction represents 3 equal parts, and the denominator, 4, tells us that 4 parts make up a whole.Let’s see the types of fractions from Online Tutoring for Grade 3

1).Proper Fractions

When a fraction’s numerator is lesser than the denominator, this fraction is a proper fraction.

Below are some examples:

5/20 , 3/8 , 7/8

2).Improper Fractions

A fraction is considered as an improper fraction when its numerator is greater or equals to the denominator.

Below are some examples:

8/7, 2/1 , 20/6 , 5/5

3).mixed fraction
A mixed number has a part that is a whole number and a part that is a fraction.

We can see more 4th grade math algebra word problems with solution for fractions.

 

problem on functions like y=f(x)

function in mathematics, a relation f that assigns to each member x of some set X a corresponding member y of some set Y ; y is said to be a function of x, usually denoted f ( x ) (read “f of x ” ). In the equation y = f ( x ), x is called the independent variable and y the dependent variable. In practice, X and Y will most often be sets of numbers, vectors, points of some geometric object, or the like. For example, X might be a solid body and f ( x ) the temperature at the point x in X ; in this case, Y will be a set of numbers. The formula A =π r ² expresses the area of a circle formula as a function of its radius. A function f is often described in terms of its graph, which consists of all points ( x,y ) in the plane such that y = f ( x ). Although a function f assigns a unique y to each x, several x ’s may yield the same y ; e.g., if y = f ( x )= x ² ( x is a number), then f (2)= f (-2). If this never occurs, then f is called a one-to-one, or injective, function.

Question:-

If  x³-kx²+2x-4  leaves no remainder when divided by (x-2),find k.

Answer:-

Let’s see the solution from answers to math problems

Let f(x)=x³-kx²+2x-4

If it is divisible by (x-2),f(2)=0

Therefore,

2³-k.2²+2.2-4=0

8-4k+4-4 = 0

8-4k = 0

4k = 8

k=2 is the answer

 

How to find the volume of a rectangle

Question:- Find the area of the following figure

Solution:-

This math answers will gives the solution for the above problem

we have two rectangles….
One AGHD (the bigger one )
And one BEFC the smaller one
The area of the requited figure is
Area of bigger rectangle minus area of the smaller rectagle
Also side GH = AB+ BC + CD
= 2 + 6 + 2 =10 CM
So area of bigger rectangle AGHD = length x width
Length (GH)= 10, width (AG) = 5
Area of AGHD = 10 x 5 = 50 cm²
Area of smaller rectangle(BEFC) = length x width
Length (BE)=3 , width(EF)=6
Area of smaller rectangle(BEFC)= 3 x 6 = 18 cm²
Area of required figure = Area of AGHD minus Area of BEFC
= 50 – 18 = 32 cm²

This kind of problems are from 10 grade math geometry

 

How to find compound interest

Compound interest is the concept of adding accumulated interest back to the principal, so that interest is earned on interest from that moment on. The act of declaring interest to be principal is called compounding (i.e., interest is compounded). A loan, for example, may have its interest compounded every month: in this case, a loan with $100 principal and 1% interest per month would have a balance of $101 at the end of the first month.

Question:-

Find the amount at compound interest on $3500 for 2years at 12%.

Solution:-

Principal = $3500, Rate = 12%, Time = 2years.
                          3500 * I * 12
Interest for I year =  ---------------------   = 35*12= $420
                              100
Amount at the end of first year = Principal + Interest
= $3500 + $420
= $3920
$3920 become principal for 2 nd year.
Principal = $3920, Rate = 12%, Time = 1 year.
                            3920 *1* 12
Interest for 2 nd  year = -----------------    = 39.2 * 12 = $470.4
                                100
Amount at the end of Second year = Principal + Interest
= $3920 + $470.4
= $4390.4

For more help on this ,you can reply me.