Dividing Rational Fractions

Introduction of fractions

A fraction (from the Latin fractus, broken) is a number that can represent part of a whole. The earliest fractions were reciprocals of integers: ancient symbols representing one part of two, one part of three, one part of four, and so on. A much later development were the common or "vulgar" fractions which are still used today (½, ?, ¾, etc.)                                  source wikipedia

Problems for Dividing Rational Fractions

Problem 1

For dividing the rational fractions, you will use the same method as you used for dividing the numerical fractions: when dividing by the fraction, we can to flip-n-multiply.:

Perform to the indicated operation:

`(4/3) / (9/6)`

To simplify in this division, we will convert it to multiplication by flipping what we dividing by; that is, we will switch from dividing by the fraction to multiplying by that fraction's reciprocal. Then we will simplify as usual:

`(4/3) / (9/6)`

To reciprocal the second term

`9/6` = `6/9`

= `(4/3) * (6/9)`

We get

= `24/27`

To simplified as the rational fraction

`8/9`

Problem 2

Dividing rational fractions

`(2x) / (x^2)`

To simplify as a numerical fraction, we would cancel off any common numerical factors. For this rational expression of this polynomial fraction, we can similarly cancel off any common numerical or variable factors.

The numerator of the factors are (2)(x); the denominator factors are (x)(x). Anything divided by it self is one, so we can cross out the any factors common to both the numerator and the denominator. Considering the factors are its particular fraction,

We get:

`(2x) / ((x^2))` = `(2*x) / ((x)(x))`

=`(x/x)(2/x)`

= 1`(2/x)`

= `2 / x`

Between, if you have problem on these topics find the prime factorization of 100, please browse expert math related websites for more help on substitution method for solving equations.

Another Problem for Dividing Rational Fractions

Problem 3

For dividing the rational fractions, you will use the same method as you used for dividing the numerical fractions: when dividing by the fraction, we can to flip-n-multiply.:

Perform to the indicated operation:

`(4/5) / (9/6)`

To simplify in this division, we will convert it to multiplication by flipping what we dividing by; that is, we will switch from dividing by the fraction to multiplying by that fraction's reciprocal. Then we will simplify as usual:

`(4/5) / (9/6)`

To reciprocal the second term

`9/6` = `6/9`

= `(4/5) * (6/9)`

We get

= `24/45`

To simplified as the fraction

`8/15`

Formula for Percent Change

Introduction to formula for percent change:

In math the percent raise and percent reduce are measures of percent change, which is the amount to which something gains or loses worth. Percent changes are very much helpful to people to understand changes in a price over time. Percentage Change is sued to find a company's income one annum to the next, a budget grows from quarter to quarter, population increase over a 10-year period. This article defines the formula for percent change and the example problem of percent change.

Formula for Percent Change:

The formula used to find the percent change is:

`"Percent change" = ("New value"-"Old value")/"Old value" xx100.`

Step 1: At first obtain the old value and subtract it from new value, then divide by old value.

Step 2: Find the product of step 1 result with 100. That number denotes the percent change.

Between, if you have problem on these topics free math equation solver, please browse expert math related websites for more help on solving equations online.

Example of Formula for Percent Change:

Example 1:

Fatima School had 20 teachers in 1999 and the next year, there were 25. Find the percent change from 1999 to 2000?

Solution:

From the given problem:

Old value = 20

New value = 25

Formula:

`"Percent change" = ("New value"-"Old value")/"Old value" xx100.`

Solve:

Percent change = ((25-20)/25)*100

= 20%.

Therefore, percent change of the number of teachers at Fatima school from 1999 to 2000 is 20%.

Example 2:

John works in a textile shop for 10.00 dollar per hour. If his pay is raised to 12.00 dollar, then what is his percent change in pay?

Solution:

From the given problem:

Old value = 10.00

New value = 12.00

Formula:

`"Percent change" = ("New value"-"Old value")/"Old value" xx100.`

Solve:

Percent change = ((12-10)/10)*100

= 20%.

Therefore, the percent change in John's pay is 20%.
Example 3:

At a supermarket, a certain thing gets increased from 80% per pound to 85% per pound. What is the percent change in the cost of the thing?

Solution:

From the given problem:

Old value = 80%

New value = 85%

Formula:

`"Percent change" = ("New value"-"Old value")/"Old value" xx100.`

Solve:

Percent change = ((85-80)/80)*100

= 6.25%.

There was an 6.25% increase in the cost of the thing.

Practice Problems of Formula for Percent Change:

Problem 1:

A class had 80 teachers in 2005 and the next year, there were 100. Find the percent change from 2005 to 2006?

Solution:

25

Problem 2:

Honey works in a textile shop for 15.00 dollar per hour. If her pay is raised to 24.00 dollar, then what is her percent change in pay?

Solution:

$60

Geometry Line Segment

Introduction For Geometry Line Segment

The term ‘Geometry’ means a study  properties of figures and shape diagrams and  relationship between them. Geometry is the important branches of a Mathematics. In a real life geometry plays an important role from the concept of geometry have begun from ancient times. Geometry gives idea for the various geometrical shapes and figures. A line segment which is a connected piece of  line. line segment has two endpoints and is named by its endpoints. Sometimes, the symbol – written on top of two letters is used to denote the segment.

Geometry Line Segment Problems:

Ex 1:
Find the point which divides line segment which  joins the point (–1, 2) and (4,–5) internally in the ratio 2:3.

Sol:
The required point is given by
` ((mx2+nx1)/(m+n),(my2+ny1)/(m+n))`

(x1,y1)=(-1,2) (x2,y2)=(4,-5)

m:n=2:3
=`((2xx4+3xx(-1))/(2+3),(2xx(-5)+3xx2)/(2+3))`
=`((8-3)/5,(-10+6)/5)`

=`5/5,-4/5`
=(1,-4/5)

Ex 2:
Find the point which divides the line segment joining the points (2,1) and (3,5) externally in the ratio 2:3.
Sol:
The required point is given by
` ((mx1-nx2)/(n-m),(my1-ny2)/(n-m))`
(x1,y1)=(2,1),(x2,y2)=(3,5) m:n=2:3
=`((3xx2 -2xx3)/(3-2),(3xx1-2xx5)/(3-2))`
=`(6-6)/1,(3-10)/1`

=(0,-7)

Ex 3:
Find the co-ordinates of the mid point of the line segment joining the points A(–3,2) and B(7,8)

Sol:
The required mid point is
(x1,y1)=(-3,2),(x2,y2)=(7,8)
Formula` ((x1+x2)/2,(y1+y2)/2)`

`((-3)+7)/2, (2+8)/2`

` (4/2,10/2)` =(2,5)

Ex 4:
Find the co-ordinates of the mid point of the line segment joining the points A(2,3) and B(4,5)
Sol:
The required mid point is   (x1,y1)=(2,3),(x2,y2)=(4,5)

Formula `((x1+x2)/2,(y1+y2)/2)`
=`((2+4)/2, (3+5)/2)`

=`(6/2,18/2) `

=(3,9)

Between, if you have problem on these topics solve my math problems for me, please browse expert math related websites for more help on math word problems for 5th grade.

Geometry Line Segment : Slope of Line Segment Problems:

Ex 1:
Find the slope of the line passing through (5,6) and (15,9)
Sol:
Take (5,6) as (x1, y1) and (15, 9) as (x2, y2).

m=`(y2-y1)/(x2-x1)`

=`(9-6)/(15-5)`

=`3/10`

Ex 2:
Find slope of line which passing through (-16, 29) and (40, -6)

Sol:
The slope of the line is
m=`(y2-y1)/(x2-x1)`

m =`(-6-29)/(40-(-16)) `
= `-35/56`

=`-5/8`

Number Theory Problems Help

Introduction for number theory problems help:
Number theory is one of the easiest chapter in the mathematics.  Number theory includes greatest common factor, least common multiple, prime factor, composite factor, etc.  In this article, we are discussing about the topic of “number theory problems help”.  Let us go to learn some problems and solutions in related given topic.

Example Problems – Number Theory Problems Help

Example problem 1 – Number theory problems help

In an industry, the manager needs to separate the employees into two groups equally as 12 men and 20 women.  Each of men and women with the same combination and nobody left out.  What is the largest number of groups that can be formed?

Solution:

We need to find the largest number of groups.  The largest common factor is the largest whole number that is a factor of each of more than one number.

First we need to find out the factors of 12

Factors of the number 12:  12, 6, 4, 3, 2, 1

Now, we need to find out the factors of 20

Factors of the number 20:  20, 10, 5, 4, 2, 1

The largest common factor of 12 and 20 is 4.  The largest number of groups that can be formed as 4.

Answer:  4



Example problem 2 – Number theory problems help

Find out the prime factorization of the number 16.

Solution:

We need to find the prime factorization of the number 16.

Writing a number as the product of prime factors is called prime factorization.

Divide by prime factors until the quotient is 1.

16 ÷ 2 = 8

8 ÷ 2 = 4

4 ÷ 2 = 2

2 ÷ 2 = 1

The prime factorization of the number 16 is:

16 = 2 × 2 × 2 × 2

Answer:  2 × 2 × 2 × 2



Example problem 3 – Number theory problems help

Find out the least common multiple of 5 and 6?

Solution:

Given,

The value 5 and 6

We need to find the least common multiple of 5 and 6

The number 5’s multiplies:  5, 10, 15, 20, 25, 30

The number 6’s multiplies:  6, 12, 18, 24, 30

The least common multiple of 5 and 6 is 30

Answer:  30

Between, if you have problem on these topics math solver word problems, please browse expert math related websites for more help on physics problem solvers.

Practicing Problems – Number Theory Problems Help
Practicing problem 1 – Number theory problems help

Find out the prime factorization of the number 10.

Answer:  2 × 5

Practicing problem 2 – Number theory problems help

Find out the least common multiple of 2 and 6.

Answer:  6

The Product of Two Consecutive Integers

Introduction :

Consecutive integer is the number after the same number. Let take the a number a  and its consecutive number can be said as      a + 1.  

Example: (4,5), (6,7) (5,6), (21, 22)

Product of two consecutive integers is nothing but multiplication of the number and its consecutive number. Thus the result of the multiplication of the number and its consecutive is called as product of two consecutive integers. In this article, we see about the product of two consecutive integers.

Product of Two Consecutive Integers:

Formula: multiplication of integer and its consecutive

Let take the number as ‘’a’’ and its consecutive is ‘’a + 1’’.

Step 1: Multiplication of the number ‘’a’’ and its consecutive

a * (a + 1) = a + a²

Thus the product of the integer and its consecutive is equal to the sum of the integer and its square of the same integer.

 My forthcoming post is on how do i factor polynomials, how to simplify mixed fractions will give you more understanding about Algebra.

Example Problems – Product of Two Consecutive Integers:

Example problem 1:

What is the product of the integer 10 and its consecutive?

Solution:

Formula: a * (a + 1) = a + a²

Here a = 10

10 * (10 + 1) = 10 + 10²

Square of 10 =100

10 + 100 = 110

Answer: 110

Check the answer:

Step 1: The consecutive integer of 10 is 11

10 * (11) = 110

Therefore the answer is correct.

Example 2:

The product of two consecutive positive integers is 420. Find the integer and its consecutive integer.

Solution: Let take the integer as ‘’a’’ and its consecutive is ‘’a + 1’’

Formula: a * (a + 1) = a + a²

 a * (a + 1) = a + a² =  420

a² + a - 420 = 0 --- > equation 1

Step 1: Factoring the equation1, we get the integer.

a² + a - 420 = 0

a² -20a + 21a - 420 = 0

a (a - 20) + 21 (a - 20) = 0

(a -20) (a + 21) = 0

Possibilities of ‘’a’’ value is

a = 20

a = -21

Note: in given problem the integer is positive. Hence the value of the integer is 20 and its consecutive is 20 +1 = 21

Answer: 20 and 21

Practice Problem – Product of Two Consecutive Integers:

1. What is the product of the integer -5 and its consecutive?

Answer: 20

2. What is the product of the integer 5 and its consecutive?

Answer: 30