Grade VII Percentage and Proportions

Hello my lovely students, once again your friend, your tutor is here to help you all in overcoming the mathematics problems. In this article, the main point of focus is on two math topics that is taught to students of class VII. Generally students of the age group of 13-14 study in this class. In this class students learn many important topics. Actually not only in this class but in all classes whatever you study is useful at some stage of life. You must have heard a common proverb “Knowledge is like a garden: if it is not cultivated, it cannot be harvested”. So kids start practicing each topic of mathematics and try to solve all the problems. If you work hard then definitely you will get the output, not only output but a positive output.

 

Now, let’s do some study of percentage of grade VII. What do you understand by the term percentage and from where this word is originated, any idea my dear friends? Yes you are right it is a Latin word that means for every hundred. If we bifurcate the term percentage as: per and cent then it simply gives its meaning i.e. per hundred. Learning percentage is also as simple as its definition. If you have to calculate the percentage then it must be like this

 

Amount	x100 = Percentage
Total

 

 

This formula can also be given as:

 

x	x100
y

 

It is used to express the value of x as percent of y.

 

Let us see, how to implement the values in the formula and how to calculate the percentage. Suppose we have an example given as: A person is having 500 stocks in a company, and the company is having a total share stock of 5000. How much of the company do that person owns.

 

For, the solution of this question, we will first determine what is the total amount and what’s percentage is to be calculated. In the above question total stock is company’s share that is 5000, and the person’s share is amount which is 500 stocks.

Now, put both the value in the formula:

 

Amount	x100 = Percentage
Total

 

 

500	x100
5000

 

In this we can simply cancel the zero’s so first cancel the 500 zero with the zero of 5000,

On doing this we get,

5	x100
50

 

Now, single one zero of 100 with the zero of 50, this will give us,

5	x10
5

Now, simply cut 5 from 5 on doing this only 10 remains,

This shows that the person is having 10% stock in the company. This is a simple example of percentage.

 

In percentage we also deal with increment and decrement. Finding the percentage of change is using the ratio of the amount of change to the original amount. The increased amount reflects the increased percentage and the decreased amount shows the decrement and sometimes it may be a negative value. So whenever you find percentage try to find that whether it is decreasing or increasing.

The Formula for increment and decrement is given as:

Increase % = 

Increase	x100
Original

In the same way decrease percentage is given as:

Decrease % = 

Decrease	x100
Original

 

To understand the concept of increment and decrement let’s see an example.

The amount of a pen is decreased from Rs 16 to Rs 14. Find the percentage decrease in the price of pen?

How you will solve this problem in this we can’t use the formula which is used to express the value of x as percent of y. In this we will go with the formula of decrease % as in question it is defined decreased price. 

First write what things are given to us:

Original price of pen = Rs 16.

Reduced price of pen is = Rs 14,

Now, decrement in price is= original price – reduced price,

                                          = Rs 16 – Rs 14,

                                           = Rs 2.

Now, Decreased % = 

Decrease	x100
Original

.

 

We have all the values to be put in the formula:

                             

2	x100
16

=

1	x100
8

=

 

25

2

 

= 12.5 %.

Thus, the decrement in the price of pen is 0.5 %.

Hopefully you must have understood the question and with this the concept of decrement. In the same way we calculate the increased percentage. For this also have an example so that I can clear all your doubts and with this you can easily understand the base of the problem and how to solve. If you get the central idea of the problem then it will be very easy for you to solve all types of problems. But before having example I would like to tell you one thing that same formulas are used in case of population increment and decrement. So, here is an example to see the increased population percentage:

The population of a town is 2500 last year. This year it reached to 4000. Determine the total increase or decrease in the percentage of population of town.

Solution: first kids, find whether there is increase or decrease in percentage. In this question we can simply understand as the population was 2500 last year and now 4000 so there is increment in the population so percentage will also increase.

Given,

Population of last year = 2500.

Present population is = 4000,

Difference in population = 4000 – 2500,

Increased population is = 1500.

Put values in the formula:

Increase % =

Increase	x100
Original

=

1500	x100
2500

=

15	x100
25

=

3	x100
5

=  3 X 20 %,

= 60%.

Thus the increased % of population is 60%.

In this way we can deal with all types of percentage questions without any problem.  You can also switch to online service providers that help you in solving all the problems related to all math topics. Thousands of websites are playing there games to help you and to solve your math problems easily and more effectively so that, kids can learn all the topics easily and score good grades.

 

Now, we will matriculate proportional relationships. What do you mean by Proportion?  Proportion is a name given to a statement that two ratios are equal. I think you all must know of ratios as you all read this in the pervious classes still I want to provide a basic idea of this.  Ratios are defined as a quantity used to compare two numbers. In ratios we separate the two numbers with a colon (:) and in proportion we use double colon (::). For illustration, if you have to write the ratio of 4 and 12,

Then we will write it as:

4:12 or it can also be represented as a fraction like 4/12 and in mathematical language we will call it the ratio of four is twelve.

Proportion defines the ratio of two numbers to it expresses their proportional relationships.

Like,

A/B = C/D in other terms it can also be represented in a way in which we use colon, like

A:B = C:D,

Or,

A/B::C/D

If the two ratios are equal then the cross products of the ratios must be equal, if not then ratios are not equal.

For proportions,  

 

A:B = C: D,

A X D = B X C.

 

Now, have an example of proportions to understand it more properly,

48/21=81/x ,

In this proportional relationship we have to calculate the value of the x variable,

You all must be familiar with the cross multiplication; in cross multiplication we take the right side denominator value to other side and on numerator and vice-versa,

 

So, take the x to left side and multiply it with 41 and 21 on right side and multiply it with 81.

See how,

X  * 48 = 81 * 21,

48x = 1701,

X = 1701/48,

X = 35.4375,

And we can write it as 35. 4. Remember the rounding off values, which you have learned in pervious class, in which we write the values after decimal in round figure.

 

Now, let’s see one more example, in which we see both the percentage and ratio. As I told you that all the math topics are interrelated so, there is an example to see how both topics that we studied today are related with each other.

Question: A mixture of milk and water, are mixed in the ratio as4:1. Find the percentage of milk in the mixture?

Solution:  in the above question, Milk: water = 4:1 so,

 

% of milk is =4/4+1,

 

 = 4/5

 =  

4	x100
5

= 80 %.

In this way you see how we are solving problems in percentage.

Students, this is all about both the topics from my side. If you still have any query related to this topic then you can take help of online math service providers. These online math service providers help you in learning different math topics and in solving the problems related to math. In this online help, you will find several kinds of solvers which directly solve your entire math problem and help you in overcoming them. Now, onwards if any problem occur switch to online help rather then wasting many hours on single problem. So, take online help and say bye to math problems.