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
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
Ratio proportion , scale drawings are the main topics and must be kept in mind to be a good mathematician.
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