# 6TH GRADE MATH HELP - NUMBER OF SOLVED EXAMPLES AND EXERCISES

Algebra Word Problems before 6th Grade Math Help

if you have not already done so.

There we discussed The Method of Solving Word
Problems.That knowledge is a prerequisite here.

### Example 1 of 6th Grade Math Help

Solved Example 1 of 6th Grade Math Help :

One fifth of a number of butterflies in a garden are on jasmines
and one third of them are on roses. Three times the difference of
the butterflies on jasmines and roses are on lilys.If the remaining
one is flying freely, find the number of butterflies in the garden.

solution to Example 1 of 6th Grade Math Help :

Let x be the number of butterflies in the garden.
As per data,
Number of butterflies on jasmines = x⁄5.
Number of butterflies on roses = x⁄3
then
difference of the butterflies on jasmines and roses = x⁄3 - x⁄5
As per data
Number of butterflies on lilys = Three times the difference of
the butterflies on jasmines and roses
= 3(x⁄3 - x⁄5)
As per data,
Number of butterflies flying freely = 1.
∴ number of butterflies in the garden = x
= Number of butterflies on jasmines + Number of butterflies on roses
+ Number of butterflies on lilys + Number of butterflies flying freely
= x⁄5 + x⁄3 + 3 (x⁄3 - x⁄5) + 1.
x = x⁄5 + x⁄3 + 3 x x⁄3 - 3 x x⁄5 + 1.

This is the Linear Equation formed by converting
the given word statements to the symbolic language.

Now we have to solve this equation.
x = x⁄5 + x⁄3 + x - 3x⁄5 + 1
Cancelling x, which is present on both sides, we get
0 = x⁄5 + x⁄3 - 3x⁄5 + 1
L.C.M. of the denominators 3, 5 is 3 x 5 = 15.
Multiplying both sides of the equation with 15, we get
15 x 0 = 15 x x⁄5 + 15 x x⁄3 - 15 x 3x⁄5 + 15 x 1
⇒ 0 = 3x + 5x - 3 x 3x + 15.
⇒ 0 = 8x - 9x + 15 ⇒ 0 = -x + 15 ⇒ 0 + x = 15
x = 15.
Number of butterflies in the garden = x = 15. Ans.

Check:
Number of butterflies on jasmines = x⁄5 = 15⁄5 = 3.
Number of butterflies on roses = x⁄3 = 15⁄3 = 5.
Number of butterflies on lilys = 3(5 - 3) = 3(2) = 6.
Number of butterflies flying freely = 1.
Total butterflies = 3 + 5 + 6 + 1. = 15. Same as the Ans.(verified.)

### Example 2 of 6th Grade Math Help

Solved Example 2 of 6th Grade Math Help :

A man rowed upstream for 4 hours and returned to his starting point
in 2 hours. If he rowed at the rate of 5km/hr. in still water, what was
the rate of flow of the stream.

solution to Example 2 of 6th Grade Math Help :

Let xkm/hr. be the rate of flow of the stream.
Then the rowing rate of the man upstream
= rowing rate of the man in still water - the rate of flow of the stream.
= 5km/hr. - xkm/hr. = (5 - x)km/hr.
And the rowing rate of the man downstream
= rowing rate of the man in still water + the rate of flow of the stream.
= 5km/hr. + xkm/hr. = (5 + x)km/hr.
We know
distance = speed x time.
As per data, time for upstream rowing = 4 hrs.
And time for downstream rowing = 2 hrs.
∴ distance rowed during upstream rowing = (5 - x)km/hr. x 4 hrs.
= 4(5 - x)km.
and distance rowed during downstream rowing = (5 + x)km/hr. x 2 hrs.
= 2(5 + x)km.
But the two distances are equal.
∴ 4(5 - x)km. = 2(5 + x)km.

This is the Linear Equation formed by converting
the given word statements to the symbolic language.

Now we have to solve this equation.
⇒ 4 x 5 - 4x = 2 x 5 + 2x
⇒ 20 - 4x = 10 + 2x ⇒ -4x - 2x = 10 - 20 ⇒ -6x = -10
x = (-10)⁄(-6) = 5⁄3.
thus rate of flow of the stream = x = (5⁄3)km/hr. Ans.

Check:
upstream distance = 4(5 - x)km = 4(5 - 5⁄3) = (4⁄3)(5 x 3 - 5)
= (4⁄3)(15 - 5) = (4⁄3)(10) = (40⁄3) km.
downstream distance = 2(5 + x)km = 2(5 + 5⁄3) = (2⁄3)(5 x 3 + 5)
= (2⁄3)(15 + 5) = (2⁄3)(20) = (40⁄3) km.
Both distances are equal. (verified.)

Great Deals on School & Homeschool Curriculum Books

Here is a collection of proven tips,
tools and techniques to turn you into
a super-achiever - even if you've never
thought of yourself as a "gifted" student.

and remember large chunks of information
with the least amount of effort.

If you apply what you read from the above
collection, you can achieve best grades without
giving up your fun, such as TV, surfing the net,
playing video games or going out with friends!

Know more about the Speed Study System.

### Exercise on 6th Grade Math Help

Solve the following problems on 6th Grade Math Help.

1. In a stream the current flows at the rate of 4 km/hr.
For a boat the time taken to cover a certain distance
upstream is 5 times the time it takes to cover the same distance
downstream. Find the speed of the boat in still water.
2. In a stream whose current flows at the speed of 3km/hr,
a man rowed upstream and returned to his starting point
in 6.25 hours. If the man rows at a speed of 5 km/hr. in still water,
how long did he row upstream ?

## Progressive Learning of Math : 6th Grade Math Help

Recently, I have found a series of math curricula
(Both Hard Copy and Digital Copy) developed by a Lady Teacher
who taught everyone from Pre-K students to doctoral students
and who is a Ph.D. in Mathematics Education.

This series is very different and advantageous
over many of the traditional books available.
These give students tools that other books do not.
Other books just give practice.
These teach students “tricks” and new ways to think.

These build a student’s new knowledge of concepts
from their existing knowledge.
These provide many pages of practice that gradually
increases in difficulty and provide constant review.

These also provide teachers and parents with lessons
on how to work with the child on the concepts.

The series is low to reasonably priced and include

Elementary Math curriculum

and

Algebra Curriculum.

of the exercise given above, are given below.

1. 6 km/hr
2. 5 hrs.

## Research-based personalized Math Help tutoring program : 6th Grade Math Help

Here is a resource for Solid Foundation in
Math Fundamentals from Middle thru High School.
You can check your self by the

### FREE TRIAL.

Are you spending lot of money for math tutors to your
child and still not satisfied with his/her grades ?

Do you feel that more time from the tutor and
more personalized Math Help to identify and fix
the problems faced by your child will help ?

Here is a fool proof solution I strongly recommend
and that too With a minuscule fraction of the amount
you spent on tutors with unconditional 100% money
back Guarantee, if you are not satisfied.

### SUBSCRIBE, TEST, IF NOT SATISFIED, RETURN FOR FULL REFUND

It is like having an unlimited time from an excellent Tutor.

It is an Internet-based math tutoring software program
that identifies exactly where your child needs help and
then creates a personal instruction plan tailored to your
child’s specific needs.

If your child can use a computer and access
the Internet, he or she can use the program.
And your child can access the program anytime
from any computer with Internet access.

### Unique program to help improve math skills quickly and painlessly.

There is an exclusive, Parent Information Page provides YOU
with detailed reports of your child’s progress so you can
monitor your child’s success and give them encouragement.
These Reports include

• Time spent using the program
• Assessment results
• Personalized remediation curriculum designed for your child
• Details the areas of weakness where your child needs additional help
• Provides the REASONS WHY your child missed a concept
• List of modules accessed and amount of time spent in each module
• Quiz results
• Creates reports that can be printed and used to discuss issues with your child’s teachers
These reports are created and stored in a secure section
of the program, available exclusively to you, the parent.
The section is accessed by a password that YOU create and use.
No unauthorized users can access this information.

### Personalized remediation curriculum designed for your child

Thus The features of this excellent Tutoring program are

• Using detailed testing techniques
• Identifing exactly where a student needs help.
• Its unique, smart system pinpointing precise problem areas -
• slowly and methodically guiding the student
• raising to the necessary levels to fix the problem.

### Not a “one-size-fits-all” approach!

Its research-based results have proven that
it really works for all students! in improving
math skills and a TWO LETTER GRADE INCREASE in
math test scores!,if they invest time in using
the program.

Proven for More than 10,000 U.S. public school
students who increased their math scores.