Improper Fractions

Fractions form an integral part of our lives. Fraction is part of a whole. Hence, in a fraction we have two numbers. One on the top called numerator and the other on the bottom called denominator.
We classify fractions as proper fractions and improper fractions based on the values of numerator.

Improper fractions: 
Fractions with numerator greater than the denominator are called improper fractions.
Example: 13/4, 12/5
How to simplify improper fractions:
This is nothing but reducing improper fractions.
As the numerator is greater than the denominator in improper fractions, when we do the long division of this fraction, we will be getting a quotient greater than 1 and a remainder.
We can generalize the simplification by an algorithm:
Step 1: Perform the long division
Step 2:
Example: Simplify the improper fraction 18/7

Step 2:  Simplified form of the mixed fraction is


Improper fractions:

Improper fractions have two parts on simplification. The part which does not have denominator is called whole part and the part with denominator is called fractional part. The other name for the simplified improper fraction is mixed fraction.
Mixed fraction has both whole number part and a fractional part.

Adding improper fractions:
We adopt four steps to add improper fractions.
Step 1: Find the Least common multiple of the denominators
Step 2: Find the equivalent fractions of individual fractions such that the denominators of both the fractions are same.
Step 3: Add both the numerators and write the common denominator
Step 4: Simplify the improper fraction if need be
Example: 11/3 + 5/4
(11 x 4)/(3 x 4) + (5 x 3)/ (4 x 3)
= (44/12) + (15/12)
= 59/12
=4 11/12

Multiplying Improper Fractions
In this, the method adopted is as same as in multiplication of proper fractions. We follow three steps to evaluate the product of two improper fractions.
Step 1: Multiply both the numerators and write the result in numerator
Step 2: Multiply both the denominators and write the result in denominator
Step 3: Simplify if need be
Multiply 15/7 and 4/3
Step 1: Numerator = 15 x 4 = 60
Step 2: Denominator = 7 x 3 = 21
Step 3: Required product = 60/21 = 3 x 20/ 3 x7 = 20/7 = 2 6/7

Dividing Improper Fractions
In this as well, we follow the general rules of division of fractions.
Step 1: Write the first fraction
Step 2: Find the multiplicative inverse of the second fraction
Step 3: Multiply the results of steps 1 and 2 following the algorithm of multiplication of fractions.
Example:
Divide 15/ 7 by 4/3
Step 1: 15/7
Step 2: Multiplicative inverse of 4/3 is ¾
Step 3: 15/7 x 3/4 = (15 x 3)/ (4 x 7) = 45/28.
What is an improper fraction?
Improper fractions are those whose numerators are greater than denominators. The value of improper fractions is always greater than one.

Unit Conversion

Unit conversion is converting from one unit to another of the same quantity. Unit conversion is used when we have to compare or convert any quantity in any particular form. Unit conversion can be done for length, volume, time, temperature, area, energy etc. It is done using conversion factors.
For example: -
I kilogram = 1000 grams
1 foot = 12 inches
1 meter = 100 centimeters
1 minute = 60 seconds
1 day = 24 hours
What is the Metric Unit for Length?
The metric unit of length is meter.
Unit conversion length
1 meter = 1000 millimeter
1 meter = 100 centimeter
1 meter = 10 decimeter
1 meter = 0.001 kilometers
How to do unit conversions?
Unit conversions can be done by using the following steps: -
Write the given value.
For example: - Convert 582 cm to m.
Find conversion factor for the given and the desired units
In the above example the conversion factor is 100 cm = 1m.
Write it as a fraction with the given units as a denominator or in the opposite direction.
582 cm (1 m)/(100 cm)
Cancel the ‘like’ units that is cm in the numerator can be cancelled by cm in the denominator.
582 cm (1 m)/(100 cm )=582  (1 m)/100

Multiply odd units, we will be left with 582 times 1 m in numerator which gives 582 m and 100 in denominator which gives 582 m/100 = 5.82 m
5.82 m
For example: -
If we have to convert 12 millimeter to kilometer, then the steps would be: -
Convert 12 mm to km
Conversion factors are: -
1000 mm = 1 m
1000 m = 1 km
1.2 mm(1m/1000mm)((1 km)/(1000 m))
=0.0000012 km
This is how unit conversion is done when we have any quantity in a unit and we need to convert it in different unit.

Introduction to Trinomials

What is a trinomial?
To understand the concept of trinomial, we should know what a monomial is. A monomial is an algebraic expression that has only one term.

For example: - 2a, 4x, 6z are all monomials. A trinomial is a polynomial which consists of three monomial terms. For example: -
• 2a+3b-4c
• 4x-84-6z
They both are the examples of trinomials.
Factoring trinomials
Rules to factor trinomials: (how to factor trinomials)
A trinomial expression is an algebraic expression which has exactly three terms. Trinomials can either be quadratic equation or a higher order equation. In case it is a quadratic equation, it can be simplified either by factoring or using quadratic formula.

For example: - 2x^2-7x+6 can be written as 2x^2-4x-3x+6 which can be factored as (2x-3) (x-2) so this is how we factor trinomials if they are in quadratic form.
A higher order trinomial can be turned into a quadratic equation by factoring common terms and then can be factored again.

For example: - 6x^2y + 14xy + 4y
In this expression, we have 2y common in all terms, so we can take that common, so that becomes
2y (3x^2+7x+2)
And that can further be factored as 2x (3x+1) (x+2).
Following instructions should be followed for solving trinomials: -
• First, factor the common factors from all the terms. For example if we have 3x^2+24x+45 then we can take 3 common from all the terms and write the expression like this, 3(x^2+8x+15).
• Check the trinomial equation you are left with.
• If the highest power of the trinomial equation is 2, then it can be factored like a quadratic equation
• If the highest power is the higher degree, then we should look for a pattern that allows you to solve it like a quadratic equation.
• Solve the quadratic part of the equation and make the factors.

Applied Statistics

Applied Statistics is nothing but applying statistics in real life. There are different levels of measurement that are used in applied statistics. Below are few example:

Nominal
Interval
Ordinal
Ratio



For more help connect with an online statistics tutor and get your help. Not just statistics but you can get help from geometry tutors and so on as well.

Do post your comments.

Math online problems

Learning Geometry
Mutual geometry software (IGS, or propellant geometry environments, DGEs) are computer programs which figure one to create and then cook geometry tutor free, primarily in glide geometry.

In most IGS, one starts constituent by swing a few points and using them to delineate new objects such as lines, circles or additional points. You can also check geometry answers online.

After whatsoever thinking is through, one can act the points one started with and see how the construction changes. Also get information on geometry problem solver

Free math problem solver

Learn online calculus homework

After all, many professional engineers do not hesitate to admit their ignorance of the subject.
As a student you probably view calculus as another illogical memorization of equations that one needs to pass through school.The best engineers only need the number crunching to confirm what they think the result may be. Also get help with calculus answers solved

Multivariable calculus
A study of limits and continuity in multiple dimensions yields many counter-intuitive results not demonstrated by single-variable functions. More help with calculus problems solved. The multiple integral expands the concept of the integral to functions of many variables.

Understnading logical reasoning

Let us learn Logical reasoning test

Following are samples of logical test questions that are usually asked in entrance examinations, topics like logical puzzles, word problems, series completion, clocks problems, coding decoding all these are included under logical reasoning.

All the nine digits are arranged here so as to form four square numbers 9, 81, 324, 576 how would you put them together so as to form a possible square number and a single largest possible square number?
The lowest square number i can think of containing all the nine digits once and only once is 139854276 which is square of 11826 and the highest square number under the same conditions is 923187456 which is the square of 30384. Also get help with relatively prime
Hope you liked the above post, get more help with How to use a Protractor