Proportions

In algebra proportion is define as the special form used for comparison of two ratios . When we talk about the ratios it define as relationship between two or more things. But when we talk about the proportion it is the method of setting two ratios equal. We can say it in other words as when two ratios are equal to each other then their proportion are also equal. It is explained as 1 / 2 is equal to the 2 / 4 or 14 / 28.

Proportions is used when there is one part is missing in the given ratio as if a ratio is equal to other ratio means there proportion are equal then we can easily find the missing value. (want to Learn more about Proportions, click here),

As if there are two ratios a / b that is equal to x / y then these are stated as

a / b = x / y means these ratios have same proportions.

Sometimes values are missing from ratios but having the same proportion as x / 10 and 1 / 2 have these ratios are stated as x / 10 = 1 / 2, so for finding the value of x we use the proportion as

x = 10 * 1 / 2

x = 10 / 2 = 5.

We can also depict the proportion as the comparison that shows the relative relation between two or more things in terms of quantity , quality and any other sort of measurement.

Topic on How to Graph a Circle will describe all the methods of graphing a circle in easy manner.

icse sample paper that is provided by the icse board that helps the students to understand the pattern of paper come in the exam and In the next session we will discuss about How to Find Percentage. 

Proportions

Here we are going to learn about Proportions (some portion of this topic taken from ICSE class 10 syllabus).
When any two ratios are equal, we say that the two ratios are in proportion. It is the relationship between two ratios whose output is same and constant.
It is represented by a/b  :: c/d
or
a : b :: c : d
Here the ratio of a: b is proportion to c: d. Both symbols :: and = are used to represent the proportionality of two ratios.
If we have a : b : : c : d , it is read as a is to b as  c is to d
In the above statement we have 'a' as First  term, 'b' as second term , 'c' as third term and  'd' as the fourth term.
In this a and d are called extreme terms or extremes and b and c are middle terms and are also called means
If the given four numbers are in proportion, then the product of means is equal to the product of extremes.
In order to check that the two ratios are in proportion, we simply check if the product of extremes and the product of means are equal.
Let us see how to solve proportion with the help of an example:
Example: solve Proportion problem  60 : 105  :: 84 :147 .
Sol: We first take the product of means ie 105 * 84 = 8820
now we take the product of extremes i.e. 60 * 147 = 8820
Here we observe that the product of means = product of extremes. So the two ratios are in proportion.
This can also be checked by converting both ratios in lowest terms, if both the values are same, they are in proportion
Let us try it for the same data:
60 / 105  ,we divide numerator and denominator by 5 and get
= 12 /21 , again dividing by 3 we get
= 4 / 7
Similarly we write 84/147 , dividing & multiplying  by 3 we get
= 28 / 49
Now dividing & multiplying by 7 we get
= 4 /7
So they are in proportion.

In next post we will talk on Estimation of Solutions in Grade VI. For more information on Substitution Method, you can visit our website

Ratio and Proportion in VI Grade

Hello friends! Welcome back to another important session for enhancing your knowledge of sixth grade math of Tamilnadu education board. In previous article we had discussed the whole syllabus of grade 6 math which student needs to learn throughout this course and from today we are going to start explaining each and every topic of this syllabus in total demonstrative way that will help students to solve the relative problems in their exams. So, topic for the day is Ratios and proportions along with some percent problems. This content is included in your first unit of grade VI math as Algebra.
Let’s start with the short introduction of ratios, nothing much needed to be explained about this because students are getting through this topic since their previous classes. Still; Ratio is a kind of presentation that includes division or ‘:’ between two numbers as:
A:B = A/B Ratio is also called the fraction , where upper part of division is numerator and lower one is denominator. A ratio is a pair of numbers that compares two quantities or describes a rate. In general Ratio can be represented in three manners as:
When explained in words then as: 2 to 3
By using a colon: 2:3
Similarly it can be represented as a fraction: 2/3

There are some conditions where equal ratios are used; equal ratios make same comparisons and to determine the equal ratios. Both terms of ratios are multiplied or divided by same number. Let us take an example to find equal ratios of any given one:

If given ratio is 10/12 then

Divide both terms by 2 as
10 ÷ 2/ 12 ÷ 2 = 5/6
 Now by multiplying 2 in both terms
10 X 2/ 12 X 2 = 20/24
Various more can be determined in similar ways.

Now let us take one more example and see the word problems of ratios:
Example: if the ratios of boys to girls is 4 to 3 where there are total 35 students in the class then how many boys are there in class?

Solution; suppose boys as B and girls as G so given is that
4:3 = B:G
Also given in question that B + G = 35
So if we take the ratio of boys to total students then it is as:
4/7 = B / 35
Now implement cross multiplication
B = 4/7 X 35
B = 4 X 5
B = 20
So, there are 20 boys among 35 students in the class.

This is how any ratio problem is solved but as done in the above problem, every time the use of proportion and cross multiplication is needed to implement while solving the query. So let’s elaborate about these terms in detail. Starting with proportions:

A proportion is a representation of two equal ratios. Any proportion shows that numbers in different ratios. Those numbers related by proportion are compared to each other in same manner.

For example, 2/3 = 10 /15
Now it can be said as “2 is to 3 as 10 is to 15”.
In general to present proportion, a double colon symbol is used as;
2/3 = 10 /15 also can be represent as 2:3 :: 10:15

While solving proportions, the use of cross multiplication is often used because it is equal. Every proportion includes two terms as means and extremes. In proportion 2/3 = 10 /15, 3 and 10 are means and 2, 15 are extremes.

So when cross multiplication is done the next equation includes:
Product of means = product of extremes
3 X 10 = 2 X 15
This phenomenon is really useful when in any proportion in which one of the terms is unknown. Let us take an example of solving proportion:

A is a product that is preferred by 9 out of 10 people., if this statement is true then how many people in  numbers out of 250 should prefer A?

Solution:  suppose ‘n’ is the number of peoples who prefers A among 250 people. Then set up the appropriate proportion as:

n / 250 = 9 /10
use the cross multiplication
Product of means = product of extremes
250 X 9 = n X 10
10 n = 2250
n = 2250/10
n= 225


So, 225 out of 250 peoples should prefer product A.

There is a useful application existing for proportions and that is Unit Pricing. The Unit price of any product is the price of per unit measure. To calculate the unit price students need to implement the proportion as follows

Total price paid/ quantity bought in units = unit price/1 unit
Because the denominator of LHS is one the proportion remains as:
Unit price = (Total price paid)/ (quantity bought in units)

Let us take an example of calculating unit pricing:
Q. which is the better but, 5 bars of soap in Rs. 229 or 4 bars for Rs.189?

Solution: here the unit is 1 bar of soap that can be evaluated as
229/5 = 45.8
For the second option
189/4= 47.2

It is clear that the first option is better to buy.

This is all about Ratios and proportions, now it’s time to elaborate next topic that is Percent. Queries of percent evaluation are surely related with ratios and proportions because like ratios, percent form also include fraction representation.

Percent, eventually in mathematics means each hundred like several of percents means ratio of that percent with hundred. A symbol % is used to represent percentage of any number that means 1/100. So if we say 100 % then


100 % =100/100 = 1

While going through the Algebra of grade VI, students will eventually learn that decimals, fractions and percentage can be converted into each other quite easily. Let us see some of the points related to this conversion:
1.    For writing a decimal as a percent number, just multiply the given decimal number by 100 and align a percent sign with it.
2.    For writing a percent as a decimal: divide the percent by 100 and remove the percentage symbol as well.
3.    To write a fraction as a percent: it is executed in two steps, firstly convert the fraction into decimal form and then use the above method to convert the resulted decimal into fraction.
4.    Last one is to write a percent as a fraction: remove the percent sign and add hundred into its denominator, now convert it into its lower fraction form.

There are 3 forms of percent evaluation problems: finding percent of a number, finding the number when percent is known and the third one is to calculate the percent of one number to another. All these three types of problems can be solved by using proportion.
Let us take an example and see how proportion principle is used to sort out various percent related problems:

 What number is 70% of 250?

One way to sort out these kinds of problems is to first convert the percent into fraction and then eventually use the proportion structure to evaluate the unknown variable.
70 % = 70/100 (fraction form of percent)
Now to set up a proportion, students must find the ratio equal to the above one. So the proportion is
70/100 = n /250
Convert the fraction into its lower form
7/10 = n /250
Now imply the general rule of solving proportion that is

Product of means = product of extremes
10 X n = 7 X 250
n = 7 X 250 / 10
 n= 7 X 25
 n = 175

So, 70 % of 250 is 175 that means 175 to 250 is the same ratio as 70 to 100.

This is all about Ratios, proportions and percent problems of grade 6 algebra problems. In this article most of the terms related to these topics  are explained but still to learn more in better manner students can really use online math tutoring websites, where proficient math tutors are available to sort out your mathematical queries and explain various fundamentals of it. The key thing is that every time when students access the online math education website for having the assistance then tutors are instantly available to help him through remote connection. Now to develop a friendly communication so that students can ask their problems more frequently with tutors. Options like live online chat, video conference, and worksheets solving sessions are available.
Students can schedule their regular math learning session with online tutors so that they can be regular with their math lessons to enhance their mathematical skills. This all facility is available for 24 x 7 hours that really generates flexibility in your study schedule. Everything is categorized according to the math grades so nothing gets messed up when you visit the online math websites.

In upcoming posts we will discuss about Factors in Grade VI. Visit our website for information on statistics help