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State Board · Class 6 · Mathematics

Lesson 13: Percentage

5 concepts · 40 practice questions with answers · Free to read

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Meaning of percent

From daily life

A shop board says "25% OFF". In exam results, marks are given as 90%. Everyone understands percent quickly, because it is always counted out of 100.

Simple definition

A ratio whose second term is 100 is a percent (टक्का). The word comes from the Latin "per centum", meaning "per hundred", and the symbol is %.

Rule 1: Meaning of percent — 47% means 47 out of every 100, that is 47100. 100% is the whole and 50% is half.

63 of 100 squares shaded: 63 percent.63%63 out of every 10063/100 = 63%40% discountDress ₹100 → pay ₹60Percent = per hundred

In the figure : In the figure 63 of 100 squares: 63 percent.

Live figure

Meaning of percent

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  • Easy : Easy: 50 squares out of 100 shaded is 50%, which is half.
  • Medium : Medium: Meera got 36 out of 40 = 90100 = 90%.
  • Exam-type : Exam: Compare: Meera 36/40 = 90% and Raju 36/48 = 75100 = 75%. Meera is ahead by 15%.

Rule 2: Percent makes comparison easy and is used in discounts — Because all are out of 100, we can compare easily. A 25% discount on a dress of ₹ 200 is ₹ 50 off, so you pay ₹ 150. Do not mix up % (per hundred) with ‰ (per thousand).

  • Easy : Easy: 10% of ₹ 100 is ₹ 10.
  • Medium : Medium: A 20% discount on ₹ 100 gives ₹ 20 off, so you pay ₹ 80.
  • Exam-type : Exam: A 25% discount on ₹ 200 is ₹ 50 off; you pay ₹ 150.
Remember

Percent = per hundred. 100% = whole. Percent makes comparison easy.

Common mistake

Comparing 36/40 and 36/48 by the numerators alone. Convert both to percent.

Shortcut

Memory clue: "टक्का = शंभरातला भाग".

Spot the difference

PercentOut of 100
50%50
25%25
90%90

Practice questions

Easy
  1. 1Write 7 out of 100 as a percent.
  2. 2What does 100% mean?
  3. 3In a hundred-square, 50 squares are shaded. What percent?
Medium
  1. 4What does 15% mean?
  2. 5A student gets 18 out of 20. Find the percent.
  3. 624 out of 40 as a percent.
Challenging
  1. 7A ₹ 300 shirt has a 20% discount. What do you pay?
  2. 8Why does percent make comparison easy?
Show answers (try them yourself first)
  1. 17%.
  2. 2The whole.
  3. 350%.
  4. 415 out of every 100.
  5. 590100 = 90%.
  6. 660100 = 60%.
  7. 7Discount ₹ 60, pay ₹ 240.
  8. 8Every quantity is expressed out of the same total, 100.

Fractions and decimals to percent

From daily life

In a quiz you got 34 of the questions right. A friend says "that's 75%". Turning a fraction or a decimal into a percent is the same as asking, "how many out of 100?"

Simple definition

To change a fraction to a percent, make the denominator 100. A decimal times 100 gives the percent.

Rule 1: Fractions and decimals to percent — 710 = 70100 = 70%, 34 = 75100 = 75%, 920 = 45100 = 45%. Decimals: 0.6 = 60100 = 60%, 0.07 = 7% and 2.5 = 250%. A percent can be more than 100.

Converting fractions and decimals to percent.3/5=60/100=60%× 20 (top and bottom)NumberOver 100Percent0.2525/10025%1.3130/100130%5/862.5/10062.5%3/837.5/10037.5%

In the figure : In the figure fractions and decimals to percent.

  • Easy : Easy: 12 = 50100 = 50%.
  • Medium : Medium: 1320 = 65100 = 65%.
  • Exam-type : Exam: 1.35 = 135100 = 135%.

Rule 2: When 100 is not a multiple of the denominator — Multiply the fraction by 100. 38 = 3008% = 37.5% and 78 = 7008% = 87.5%.

  • Easy : Easy: 18 = 1008% = 12.5%.
  • Medium : Medium: 58 = 5008% = 62.5%.
  • Exam-type : Exam: 38 = 3008% = 37.5%.
Remember

Make the denominator 100. Decimal × 100. Percent can exceed 100.

Common mistake

Writing 0.07 as 70%. It is 7%.

Shortcut

Memory clue: "दशांशाला शंभरने गुणा".

Spot the difference

FormPercent
3475%
0.660%
3837.5%
2.5250%

Practice questions

Easy
  1. 1Write 14 as a percent.
  2. 2Write 45 as a percent.
  3. 3Write 1720 as a percent.
Medium
  1. 4Write 0.35 as a percent.
  2. 5Write 0.9 as a percent.
  3. 6Write 1.5 as a percent.
Challenging
  1. 7Write 78 as a percent.
  2. 8Can a percent be more than 100? Give an example.
Show answers (try them yourself first)
  1. 125%.
  2. 280100 = 80%.
  3. 385100 = 85%.
  4. 435%.
  5. 590%.
  6. 6150%.
  7. 77008% = 87.5%.
  8. 8Yes, 2.5 = 250%.

Percent to fractions

From daily life

A battery shows "75%" charged. In a fraction, that is 34 of the battery. Turning a percent back into a fraction helps when we need exact parts.

Simple definition

To change a percent into a fraction, write it over 100 and reduce to the simplest form.

Rule 1: Percent to fraction — 40% = 40100 = 25, 10% = 110, 60% = 35 and 80% = 45.

Converting percent to fractions.PercentOver 100Simplest50%50/1001/225%25/1001/475%75/1003/420%20/1001/5175%175/1007/4Write over 100, then reduce

In the figure : In the figure percent to fractions.

  • Easy : Easy: 50% = 50100 = 12.
  • Medium : Medium: 36% = 36100 = 925.
  • Exam-type : Exam: 150% = 150100 = 32 = 112.

Rule 2: Decimal percent — Remove the decimal point first. 12.5% = 1251000 = 18 and 2.5% = 251000 = 140.

  • Easy : Easy: 0.5% = 51000 = 1200.
  • Medium : Medium: 6.25% = 62510000 = 116.
  • Exam-type : Exam: A tank is 60% full, which is 35 of the tank.
Remember

Percent over 100, then reduce. Decimal percent: remove the point first.

Common mistake

Not reducing: leaving 40% as 40100. Write 25.

Shortcut

Memory clue: "शंभरावर लिहा, मग लहान करा".

Spot the difference

PercentFraction
25%14
40%25
12.5%18

Practice questions

Easy
  1. 1Write 25% as a fraction.
  2. 2Write 75% as a fraction.
  3. 3Write 20% as a fraction.
Medium
  1. 4Write 45% as a fraction.
  2. 5Write 125% as a fraction.
  3. 6Write 2.5% as a fraction.
Challenging
  1. 7Write 6.25% as a fraction.
  2. 8A tank is 60% full. What fraction is full?
Show answers (try them yourself first)
  1. 114.
  2. 234.
  3. 315.
  4. 445100 = 920.
  5. 5125100 = 54.
  6. 6251000 = 140.
  7. 762510000 = 116.
  8. 835.

Percentage of a number

From daily life

A shopkeeper says "20% of today's 80 customers bought sweets". How many is that? "Percent of a number" simply means multiply the number by the percent as a fraction.

Simple definition

p% of a number = number × p100. To find what percent one number is of another, write the fraction and make its denominator 100.

Rule 1: Percentage of a number — 20% of 80 = 80 × 20100 = 16. 150% of 60 = 60 × 150100 = 90. 10% of 250 = 25.

30 percent of 90 is 27.9999999999Total 90 = 10 equal parts of 930%30% of 90 = 90 × 30/100 = 273 parts × 9 = 27

In the figure : In the figure 30 percent of 90.

  • Easy : Easy: 50% of 40 = 20.
  • Medium : Medium: 25% of 160 = 160 ÷ 4 = 40.
  • Exam-type : Exam: 500 students, 60% are girls: girls = 500 × 60100 = 300; boys = 200.

Rule 2: What percent is one number of another — 18 out of 60: 1860 = 30100 = 30%. 9 out of 25: 925 = 36100 = 36%. Check: 36% of 25 = 25 × 36100 = 9 ✓.

  • Easy : Easy: 10 out of 50 = 20100 = 20%.
  • Medium : Medium: 30 out of 40 = 75100 = 75%.
  • Exam-type : Exam: 18 out of 60 is 30%; check 30% of 60 = 18 ✓.
Live figure

Percentage of a number

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Remember

p% of N = N × p/100. Percent of one number in another: fraction, then × 100.

Common mistake

Dividing by the percent instead of multiplying by p100.

Shortcut

Memory clue: "चे" म्हणजे गुणा ("of" means multiply).

Spot the difference

QuestionMethod
p% of NN × p ÷ 100
x out of y, percentx ÷ y × 100

Practice questions

Easy
  1. 1Find 10% of 200.
  2. 2Find 50% of 90.
  3. 3Find 25% of 80.
Medium
  1. 4Find 40% of 150.
  2. 5Find 125% of 80.
  3. 612 out of 48 is what percent?
Challenging
  1. 730 out of 40 is what percent?
  2. 8A school has 500 students and 60% are girls. How many boys?
Show answers (try them yourself first)
  1. 120.
  2. 245.
  3. 320.
  4. 460.
  5. 5100.
  6. 61248 = 25100 = 25%.
  7. 775%.
  8. 8Girls 300, boys 500 − 300 = 200.

Word problems

From daily life

Shops offer a "₹ 100 off" or a "10% off". Which is better? To decide, we turn every offer into the same kind of number, a percent.

Simple definition

In a discount, discount amount = price × discount%, and the amount you pay = price − discount.

Rule 1: Discount and subsidy — A bag of ₹ 800 with a 25% discount: discount = 800 × 25100 = ₹ 200, so you pay 800 − 200 = ₹ 600. A subsidy of 20% on ₹ 45,000 is 45,000 × 20100 = ₹ 9,000.

Comparing a fixed discount with a percent discount.Shoes ₹ 500Rohan₹ 375−125Rajat₹ 350−150Rohan: ₹125 off Rajat: 30% = ₹150 offRajat pays less (₹350)

In the figure : In the figure a fixed discount versus a percent discount.

  • Easy : Easy: 10% of ₹ 500 is ₹ 50.
  • Medium : Medium: 15% off on ₹ 400: discount ₹ 60, pay ₹ 340.
  • Exam-type : Exam: A flat ₹ 100 off on ₹ 800 is 100800 = 12.5%, better than 10% off (₹ 80).

Rule 2: Comparing with percent — Attendance of four classes: 6A 36/40 = 90%, 6B 42/50 = 84%, 6C 45/60 = 75%, 6D 40/50 = 80%. The highest percent is 90%, so class 6A wins.

  • Easy : Easy: 45 out of 50 = 90%.
  • Medium : Medium: 42 out of 60 = 70100 = 70%.
  • Exam-type : Exam: 6A 90% > 6B 84% > 6D 80% > 6C 75%, so 6A is first.
Remember

Discount = price × %. Pay = price − discount. Compare using percent.

Common mistake

Giving the discount amount as the amount to pay. Subtract it from the price.

Shortcut

Memory clue: "सवलत वजा, मग देणे".

Spot the difference

QuantityFormula
Discountprice × % ÷ 100
Payprice − discount
Percent scoredmarks ÷ total × 100

Practice questions

Easy
  1. 1A ₹ 200 item has a 10% discount. Find the discount and the price to pay.
  2. 2A ₹ 90 toy is 50% off. What do you pay?
  3. 3Find 20% of ₹ 1500.
Medium
  1. 4A ₹ 600 shirt has 30% off. Find the price to pay.
  2. 5Raju scored 42 out of 60. Find his percent.
  3. 6Sneha got 27 out of 30 and Tara 35 out of 50. Who did better?
Challenging
  1. 7A 40% subsidy on a ₹ 25,000 pump. Find the subsidy and what the farmer pays.
  2. 8Shop A gives a flat ₹ 100 off on ₹ 800 and Shop B gives 10% off. Which is better?
Show answers (try them yourself first)
  1. 1Discount ₹ 20, pay ₹ 180.
  2. 2₹ 45.
  3. 3₹ 300.
  4. 4Discount ₹ 180, pay ₹ 420.
  5. 570%.
  6. 6Sneha 90%, Tara 70%; Sneha.
  7. 7Subsidy ₹ 10,000; farmer pays ₹ 15,000.
  8. 8Shop B gives ₹ 80, so Shop A (₹ 100) is better; it is 12.5%.