Maharashtra Board Class 6 Maths part 2 Chapter 12 Percentage PDF Download

Percentage

Raju : Dada, I can see this sign % after 58 in the picture above. And it's there also after 43 in the other picture. What does it show?

Dada : That is the sign for percentage. The word cent means hundred. We read 58% as '58 percent'.

Raju : Then, what does percentage mean?

Dada : In the first picture, there is 58% water in the dam. It means that if the dam holds 100 units of water when full, then right now it is holding 58 of the same units of water. If the mobile phone has 100 units of charge when it is fully charged, then at this moment 43 units of charge are still left. A percentage is a comparison made with a total which is taken to be 100 parts.

Raju : If there is 50% water in the dam, can we say that the dam is half full?

Dada : Yes, 50% is 50 parts of water out of 100, and half of 100 is 50.

58% is 58 units out of 100 units. We can write this as the fraction \(\frac{58}{100}\). It means that \(\frac{58}{100}\) parts out of the full capacity of the dam are filled with water.

Percentage In The Form Of A Fraction

50% means 50 parts of a total of 100. So, 50 out of 100 or \(\frac{50}{100} = \frac{1}{2}\) part.

In other words, 50% is half of the whole.

25% means 25 parts out of 100. And \(\frac{25}{100} = \frac{1}{4}\) part of the whole (or total).

35% means 35 parts out of 100. And \(\frac{35}{100} = \frac{7}{20}\) part of the whole.

Teacher's Note

Percentage is used in many places in India. When you buy things at a shop, there is a discount percentage. It shows how much less you pay. For example, if a shirt costs 100 rupees and has 20% discount, you pay only 80 rupees.

Exam Trick

Remember: Percentage always means "out of 100". So 50% = 50 out of 100 = half. Just like if 100 students are in a class and 50 pass, then 50% passed.

Points to Remember

Percentage is a way to compare things using the number 100.
The sign % means percent.
50% means 50 parts out of 100 parts.
50% is the same as the fraction \(\frac{1}{2}\).
To write a percentage, you can use fractions with 100 in the bottom.

A Fraction In The Form Of A Percentage

\(\frac{3}{4} = \frac{3 \times 25}{4 \times 25} = \frac{75}{100}\)

\(\frac{3}{4}\) part of the total is \(\frac{75}{100}\) or 75%.

\(\frac{2}{5} = \frac{2 \times 20}{5 \times 20} = \frac{40}{100}\)

\(\frac{2}{5}\) part of the total is \(\frac{40}{100}\) or 40%.

Equivalent fractions can be used to make the denominator 100.

Teacher's Note

When you study fractions, you can change them to percentages. This is very useful. For example, if you get 3 out of 4 marks correct on a test, that is 75%.

Exam Trick

To change a fraction to percentage, make the bottom number 100. Multiply both top and bottom by the same number. For example, \(\frac{1}{4}\) becomes \(\frac{25}{100}\) which is 25%.

Points to Remember

You can change any fraction to a percentage.
To do this, make the bottom number 100.
Multiply both the top and bottom by the same number.
\(\frac{1}{4}\) = 25% and \(\frac{1}{2}\) = 50%.
\(\frac{3}{4}\) = 75% and \(\frac{2}{5}\) = 40%.

Example : Last year Giripremi group planted 75 trees. Of these, 48 trees flourished. The Karmavir group planted 50 trees, of which, 35 flourished. Which group was more successful in conserving the trees they had planted?

The number of trees each group started with is different. Hence, we have to compare the surviving trees in each group to the number of trees planted by them. For this comparison, it would be useful to find out for each group, the percentage of their trees that survived. To do that, let us find the ratio of the number of surviving trees to the total trees planted.

Suppose the surviving trees of the Giripremi group are A%.

Suppose the surviving trees of the Karmavir group are B%.

The Giripremi's ratio of the surviving trees to planted trees is \(\frac{A}{100}\) and also \(\frac{48}{75}\). Therefore, \(\frac{A}{100} = \frac{48}{75}\). In the same way, we can also find the ratio of surviving trees to planted trees for the Karmavir group.

Let us write the same ratio in two forms, obtain equations and solve them.

\(\frac{A}{100} = \frac{48}{75}\) and \(\frac{B}{100} = \frac{35}{50}\)

\(\frac{A}{100} \times 100 = \frac{48}{75} \times 100\) and \(\frac{B}{100} \times 100 = \frac{35}{50} \times 100\)

A = 64 and B = 70

Therefore, the Karmavir group was more successful in conserving the trees they had planted.

Teacher's Note

Comparing percentages helps us make better choices. In villages in India, people plant trees to protect the land. If one group takes better care and more trees survive, we can see this by comparing percentages.

Exam Trick

To compare two different groups, find the percentage for each group. Then compare the percentages. The bigger percentage means better result.

Points to Remember

Percentages help compare things that start different.
Use the formula: (number you want / total number) × 100 = percentage.
The Giripremi group saved 64% of their trees.
The Karmavir group saved 70% of their trees.
70% is more than 64%, so Karmavir group did better.

Example : In Khatav taluka, it was decided to make 200 ponds in Warudgaon and 300 ponds in Jakhangaon. Of these, 120 ponds in Warudgaon were completed at the end of May, while in Jakhangaon work was complete on 165 ponds. In which village was a greater proportion of the work completed?

To find the answer, we shall find the percentage of work completed in each village and then make a comparison.

Let the number of ponds completed in Warudgaon be A% and in Jakhangaon, B%. We shall find the ratio of the number of ponds completed to the number of ponds planned in each case. We then write those ratios in two forms, obtain equations and solve them.

\(\frac{A}{100} = \frac{120}{200}\) and \(\frac{B}{100} = \frac{165}{300}\)

\(\frac{A}{100} \times 100 = \frac{120}{200} \times 100\) and \(\frac{B}{100} \times 100 = \frac{165}{300} \times 100\)

A = 60 and B = 55

Therefore, a greater proportion of the work was completed in Warudgaon.

Example : For summative evaluation in a certain school, 720 of the 1200 children were awarded A grade in Maths. What is the percentage of students getting A grade?

Suppose the students getting A grade are A%.

Let us write in two forms, the ratio of the number of students getting A grade to the total number of students, obtain an equation and solve it.

\(\frac{A}{100} = \frac{720}{1200}\)

\(\frac{A}{100} \times 100 = \frac{720}{1200} \times 100\)

A = 60

Therefore, 60% students got A grade.

Example : A certain Organization adopted 18% of the 400 schools in a district. How many schools did it adopt?

Let us write in two forms, the ratio of the number of schools adopted to the total number of schools in the district, obtain an equation and solve it.

Here, 18% means 18 schools adopted out of a total of 100.

Total number of schools is 400.

Suppose the number of schools adopted is A.

\(\frac{A}{400} = \frac{18}{100}\)

\(\frac{A}{400} \times 400 = \frac{18}{100} \times 400\)

A = 72

Therefore, the number of schools adopted is 72.

Teacher's Note

In real life, we use percentages to find actual numbers. If a school has 400 students and 18% are absent, we can find how many students are absent using this method.

Exam Trick

When you know the percentage and total number, use this formula: (percentage / 100) × total number = answer. For example, 18% of 400 = (18 / 100) × 400 = 72.

Points to Remember

Percentages help us find actual numbers from totals.
Use the formula: (percentage / 100) × total = answer.
60% of 1200 students = (60 / 100) × 1200 = 720 students.
18% of 400 schools = (18 / 100) × 400 = 72 schools.
Always check your answer makes sense with the total.

This is a preview of the first 3 pages. To get the complete book, click below.